STARGAZING:
PAST AND PRESENT
[Illustration]
[Illustration:
R. S. NEWALL’S TELESCOPE.
]
STARGAZING:
PAST AND PRESENT.
BY
J. NORMAN LOCKYER, F.R.S.,
CORRESPONDENT OF THE INSTITUTE OF FRANCE.
EXPANDED FROM SHORTHAND NOTES OF A COURSE OF ROYAL INSTITUTION LECTURES,
WITH THE ASSISTANCE OF G. M. SEABROKE, F.R.A.S.
London:
MACMILLAN AND CO.
1878.
[_The Right of Translation and Reproduction is Reserved._]
LONDON:
R. CLAY, SONS, AND TAYLOR,
BREAD STREET HILL, E.C.
PREFACE.
In the year 1870 I gave a course of eight Lectures on Instrumental
Astronomy at the Royal Institution. The Lectures were taken down by a
shorthand writer, my intention being to publish them immediately. In
this, however, I was prevented by other calls upon my time.
In 1875 my friend Mr. Seabroke generously offered to take the burden of
preparing the notes for the press off my shoulders; I avail myself of
this opportunity of expressing my very great obligations to him for his
valuable services in this particular as well as for important help in
the final revision of the proofs.
On looking over the so completed MSS., however, I saw that the eight
hours at my disposal had not permitted me to touch upon many points of
interest which could hardly be omitted from the book. Besides this, the
progress made in the various instrumental methods in the interval, and
the results obtained by them, had been very remarkable. I felt,
therefore, that the object I had in view, namely, to further the cause
of physical astronomy, by creating and fostering, so far as in me lay, a
general interest in it, and by showing how all departments of physical
inquiry were gradually being utilized by the astronomer, would only be
half attained unless the account were more complete. I have, therefore,
endeavoured to fill up the gaps, and have referred briefly to the new
instruments and methods.
The autotype of the twenty-five inch refractor is the gift of my friend
Mr. Newall, and I take this opportunity of expressing my obligation to
him, as also to Messrs. Cooke, Grubb and Browning for several of the
woodcuts with which the chapters on the Equatorial are illustrated; and
to Mr. H. Dent-Gardner for some of those illustrating Clock and
Chronometer Escapements, and for revising my account of them.
Nor can I omit to thank Mr. Cooper for the pains he has taken with the
woodcuts, especially those copied from Tycho Brahe’s description of his
Observatory, and Messrs. Clay for the careful manner in which they have
printed the book.
J. NORMAN LOCKYER.
_November 16th, 1877._
CONTENTS.
BOOK I.
THE PRE-TELESCOPIC AGE.
CHAP. PAGE
I.— THE DAWN OF STARGAZING 1
II.— THE FIRST INSTRUMENTS 16
III.— HIPPARCHUS AND PTOLEMY 25
IV.— TYCHO BRAHE 37
BOOK II.
THE TELESCOPE.
V.— THE REFRACTION OF LIGHT 55
VI.— THE REFRACTOR 73
VII.— THE REFLECTION OF LIGHT 90
VIII.— THE REFLECTOR 100
IX.— EYEPIECES 109
X.— PRODUCTION OF LENSES AND SPECULA 117
XI.— THE “OPTICK TUBE” 139
XII.— THE MODERN TELESCOPE 152
BOOK III.
TIME AND SPACE MEASURERS.
XIII.— THE CLOCK AND CHRONOMETER 175
XIV.— CIRCLE READING 211
XV.— THE MICROMETER 218
BOOK IV.
MODERN MERIDIONAL OBSERVATIONS.
XVI.— THE TRANSIT CIRCLE 233
XVII.— THE TRANSIT CLOCK AND CHRONOGRAPH 253
XVIII.— “GREENWICH TIME,” AND THE USE MADE OF IT 271
XIX.— OTHER INSTRUMENTS USED IN ASTRONOMY OF PRECISION 284
BOOK V.
THE EQUATORIAL.
XX.— VARIOUS METHODS OF MOUNTING LARGE TELESCOPES 293
XXI.— THE ADJUSTMENTS OF THE EQUATORIAL 328
XXII.— THE EQUATORIAL OBSERVATORY 337
XXIII.— THE SIDEROSTAT 343
XXIV.— THE ORDINARY WORK OF THE EQUATORIAL 349
BOOK VI.
ASTRONOMICAL PHYSICS.
XXV.— THE GENERAL FIELD OF PHYSICAL INQUIRY 371
XXVI.— DETERMINATION OF THE LIGHT AND HEAT OF THE STARS 377
XXVII.— THE CHEMISTRY OF THE STARS: CONSTRUCTION OF THE 386
SPECTROSCOPE
XXVIII.— THE CHEMISTRY OF THE STARS (CONTINUED): PRINCIPLES OF 401
SPECTRUM ANALYSIS
XXIX.— THE CHEMISTRY OF THE STARS (CONTINUED): THE 422
TELESPECTROSCOPE
XXX.— THE TELEPOLARISCOPE 441
XXXI.— CELESTIAL PHOTOGRAPHY.—THE WAYS AND MEANS 454
XXXII.— CELESTIAL PHOTOGRAPHY (CONTINUED): SOME RESULTS 463
XXXIII.— CELESTIAL PHOTOGRAPHY (CONTINUED): RECENT RESULTS 469
LIST OF ILLUSTRATIONS.
FIG. PAGE
1. The heavens according to Ptolemy 3
2. The zodiac of Denderah 7
3. Illustration of Euclid’s statements 10
4. The plane of the ecliptic 13
5. The plane of the ecliptic, showing the inclination of the 14
earth’s axis
6. The first meridian circle 20
7. The first instrument graduated into 360° (west side) 21
8. Astrolabe (armillæ æquatoriæ of Tycho Brahe) similar to the 26
one contrived by Hipparchus
9. Ecliptic astrolabe (the armillæ zodiacales of Tycho Brahe), 28
similar to the one used by Hipparchus
10. Diagram illustrating the precession of the equinoxes 31
11. Revolution of the pole of the equator round the pole of the 32
ecliptic caused by the precession of the equinoxes
12. The vernal equinox among the constellations, B.C. 2170 34
13. Showing how the vernal equinox has now passed from Taurus and 34
Aries
14. Instrument for measuring altitudes 35
15. Portrait of Tycho Brahe (from original painting in the 39
possession of Dr. Crompton, of Manchester)
16. Tycho Brahe’s observatory on the island of Huen 43
17. Tycho Brahe’s system 46
18. The quadrans maximus reproduced from Tycho’s plate 48
19. Tycho’s sextant 50
20. View and section of a prism 56
21. Deviation of light in passing at various incidences through 57
prisms of various angles
22. Convergence of light by two prisms base to base 59
23. Formation of a lens from sections of prisms 60
24. Front view and section of a double convex lens 61
25. Double concave, plane concave, and concavo-convex lenses 61
26. Double convex, plane convex, and concavo-convex lenses 62
27. Convergence of rays by convex lens to principal focus 62
28. Conjugate foci of convex lens 63
29. Conjugate images 64
30. Diagram explaining Fig. 29 64
31. Dispersion of rays by a double concave lens 65
32. Horizontal section of the eyeball 66
33. Action of eye in formation of images 68
34. Action of a long-sighted eye 69
35. Diagram showing path of rays when viewing an object at an 70
easy distance
36. Action of short-sighted eye 71
37. Galilean telescope 73
38. Telescope 75
39. Diagram explaining the magnifying power of object-glass 76
40. Scheiner’s telescope 78
41. Dispersion of light by prism 80
42. Diagram showing the amount of colour produced by a lens 81
43. Decomposition and recomposition of light by two prisms 83
44. Diagram explaining the formation of an achromatic lens 84
45. Combination of flint- and crown-glass lenses in an achromatic 86
lens
46. Diagram illustrating the irrationality of the spectrum 87
47. Diagram illustrating the action of a reflecting surface 91
48. Experimental proof that the angle of incidence = angle of 92
reflection
49. Convergence of light by concave mirror 94
50. Conjugate foci of convex mirror 94
51. Formation of image of candle by reflection 95
52. Diagram explaining Fig. 51 96
53. Reflection of rays by convex mirror 98
54. Reflecting telescope (Gregorian) 101
55. Newton’s telescope 102
56. Reflecting telescope (Cassegrain) 103
57. Front view telescope (Herschel) 103
58. Diagram illustrating spherical aberration 105
59. Diagram showing the proper form of reflector to be an ellipse 106
60. Huyghens’ eyepiece 110
61. Diagram explaining the achromaticity of the Huyghenian 111
eyepiece
62. Ramsden’s eyepiece 112
63. Erecting or day eyepiece 113
64. Images of planet produced by short and long focus lenses, &c. 123
65. Showing in an exaggerated form how the edge of the speculum 128
is worn down by polishing
65*. Section of Lord Rosse’s polishing machine 131
66. Mr. Lassell’s polishing machine 132
67. Simple telescope tube, showing arrangement of object-glass 140
and eyepiece
68. Appearance of diffraction rings round a star when the 141
object-glass is properly adjusted
69. Appearance of same object when object-glass is out of 141
adjustment
70. Optical part of a Newtonian reflector of ten inches aperture 143
71. Optical part of a Melbourne reflector 143
72. Mr. Browning’s method of supporting small specula 144
73. Support of the mirror when vertical 146
74. Division of the speculum into equal areas 147
75. Primary, secondary, and tertiary systems of levers shown 148
separately
76. Complete system consolidated into three screws 148
77. Support of diagonal plane mirror (Front view) 150
78. Support of diagonal plane mirror (Side view) 150
79. A portion of the constellation Gemini seen with the naked eye 154
80. The same region, as seen through a large telescope 155
81. Orion and the neighbouring constellations 156
82. Nebula of Orion 157
83. Saturn and his moons 160
84. Details of the ring of Saturn 161
85. Ancient clock escapement 177
86. The crown wheel 178
87. The clock train 180
88. Winding arrangements 181
89. The cycloidal pendulum 185
90. Graham’s, Harrison’s, and Greenwich pendulums 188
91. Greenwich clock: arrangement for compensation for barometric 194
pressure
92. The anchor escapement 197
93. Graham’s dead beat 199
94. Gravity escapement (Mudge) 200
95. Gravity escapement (Bloxam) 202
96. Greenwich clock escapement 204
97. Compensating balance 207
98. Detached lever escapement 208
99. Chronometer escapement 209
100. The fusee 209
101. Diggs’ diagonal scale 213
102. The vernier 214
103. System of wires in a transit eyepiece 220
104. Wire micrometer 221
105. Images of Jupiter 224
106. Object-glass cut into two parts 225
107. The parts separated, and giving two images of any object 225
108. Double images seen through Iceland spar 227
109. Diagram showing the ordinary and extraordinary rays in a 227
crystal of Iceland spar
110. Crystals of Iceland spar 228
111. Double image micrometer 229
112. Tycho Brahe’s mural quadrant 235
113. Transit instrument (Transit of Venus Expedition) 236
114. Transit instrument in a fixed observatory 237
115. Diagram explaining third adjustment 239
116. The mural circle 241
117. Transit circle, showing the addition of circles to the 242
transit instrument
118. Perspective view of Greenwich transit circle 243
119. Plan of the Greenwich transit circle 245
120. Cambridge (U.S.) meridian circle 248
121. Diagram illustrating how the pole is found 249
122. Diagram illustrating the different lengths of solar and 255
sidereal day
123. System of wires in transit eyepiece 257
124. The Greenwich chronograph. (General view) 261
125. Details of the travelling carriage which carries the magnets 262
and prickers. (Side view and view from above)
126. Showing how on the passage of a current round the soft iron 263
the pricker is made to make a mark on the spiral line on
the cylinder
127. Side view of the carriage carrying the magnets and the 263
pointer that draws the spiral
128. Wheel of the sidereal clock, and arrangement for making 266
contact at each second
129. Arrangement for correcting mean solar time clock at Greenwich 268
130. The chronopher 276
131. Reflex zenith tube 286
132. Theodolite 288
133. Portable alt-azimuth 289
134. The 40-feet at Slough 294
135. Lord Rosse’s 6-feet 295
136. Refractor mounted on alt-azimuth tripod for ordinary 296
star-gazing
137. Simple equatorial mounting 298
138. Cooke’s form for refractors 300
139. Mr. Grubb’s form applied to a Cassegrain reflector 301
140. Grubb’s form for Newtonians 303
141. Browning’s mounting for Newtonians 304
142. The Washington great equatorial 309
143. General view of the Melbourne reflector 312
144. The mounting of the Melbourne telescope 313
145. Great silver-on-glass reflector at the Paris observatory 316
146. Clock governor 319
147. Bond’s spring governor 320
148. Foucault’s governor 323
149. Illuminating lamp for equatorial 325
150. Cooke’s illuminating lamp 326
151. Dome 338
152. Drum 338
153. New Cincinnati observatory—(Font elevation) 338
154. Cambridge (U.S.) equatorial 339
155. Section of main building—United States naval observatory 341
156. Foucault’s siderostat 344
157. The siderostat at Lord Lindsay’s observatory 348
158. Position circle 353
159. How the length of a shadow thrown by a lunar hill is measured 354
160. The determination of the angle of position of the axis of 358
Saturn’s ring
161. Measurement of the angle of position of the axis of a figure 359
of a comet
162. Double star measurement 360
163. Ring micrometer 368
164. Thermopile and galvanometer 374
165. Rumford’s photometer 378
166. Bouguer’s photometer 379
167. Kepler’s diagram 387
168. Newton’s experiment, showing the different refrangibilities 388
of colours
169. First observation of the lines in the solar spectrum 391
170. Solar spectrum 392
171. Student’s spectroscope 393
172. Section of spectroscope 394
173. Spectroscope with four prisms 396
174. Automatic spectroscope (Grubb’s form) 397
175. Automatic spectroscope (Browning’s form) 397
176. Last prism of train for returning the rays 398
177. Spectroscope with returning beam 399
178. Direct-vision prism 399
179. Electric lamp 404
180. Electric lamp arranged for throwing a spectrum on a screen 405
181. Comparison of the line spectra of iron, calcium, and 406
aluminium, with common impurities
182. Coloured flame of salts in the flame of a Bunsen’s burner 408
183. Spectroscope arranged for showing absorption 409
184. Geissler’s tube 413
185. Spectrum of sun-spot 415
186. Diagram explaining long and short lines 416
187. Comparison of the absorption spectrum of the sun with the 418
radiation spectra of iron and calcium, with common
impurities
188. Comparison prism 423
189. Comparison prism 423
190. Foucault’s heliostat 424
191. Object-glass prism 426
192. The eyepiece end of the Newall refractor 427
193. Solar telespectroscope (Browning’s form) 428
194. Solar telespectroscope (Grubb’s form) 428
195. Side view of spectroscope 429
196. Plan of spectroscope 429
197. Cambridge star spectroscope elevation 430
198. Cambridge spectroscope plan 430
199. Direct-vision star spectroscope (Secchi) 431
200. Types of stellar spectra 433
201. Part of solar spectrum near F 436
202. Distortions of F line on sun 438
203. Displacement of F line on edge of sun 439
204. Diagram showing the path of the ordinary and extraordinary 445
ray in crystals of Iceland spar
205. Appearance of the spots of light on the screen shown in the 446
preceding figure, allowing the ordinary ray to pass and
rotating the second crystal
206. Appearance of spots of light on screen on rotating the second 447
crystal, when the extraordinary ray is allowed to pass
through the first screen
207. Instrument for showing polarization by reflection 448
208. Section of plate-holder 456
209. Enlarging camera 458
210. Instantaneous shutter 460
211. Photoheliograph as erected in a temporary observatory for 461
photographing the transit of Venus in 1874
212. Copy of photograph taken during the eclipse of 1869 474
213. Part of Beer and Mädler’s map of the moon 476
214. The same region copied from a photograph by De La Rue 477
215. Comparison between Kirchhoff’s map and Rutherfurd’s 480
photograph
216. Arrangement for photographically determining the coincidence 481
of solar and metallic lines
217. Telespectroscope with camera for obtaining photographs of the 482
solar prominences
BOOK I.
_THE PRE-TELESCOPIC AGE._
STARGAZING: PAST AND PRESENT
CHAPTER I.
THE DAWN OF STARGAZING.
Some sciences are of yesterday; others stretch far back into the youth
of time. Among these there is one of the beginnings of which we have
lost all trace, so coeval was it with the commencement of man’s history;
and that science is the one of which we have to trace the instrumental
developments.
Although our chief task is to enlarge upon the modern, it will not be
well, indeed it is impossible, to neglect the old, because, if for no
other reason, the welding of old and new has been so perfect, the
conquest of the unknown so gradual.
The best course therefore will be to distribute the different fields of
thought and work into something like marked divisions, and to commence
by dividing the whole time during which man has been observing the
heavens into two periods, which we will call the Pre-telescopic and the
Telescopic Ages. The work of the Pre-telescopic age of course includes
all the early observations made by the unaided eye, while that of the
Telescopic age includes those of vastly different kinds, which that
instrument had rendered possible; so that it divides itself naturally
into some three or four sub-ages of extreme importance.
It is unnecessary to say one word here on the importance of the
invention of the telescope; it is well for the present purpose, however,
to emphasize the further distinctions we obtain when we consider the
various additions made from time to time to the telescope.
The Telescope, in fact, was comparatively little used until astronomy
annexed that important branch of physics to its aid which gave us a
Clock—a means of dividing time in the most accurate manner.
In quite recent times the addition of the Camera to the Telescope marks
an important advance; indeed the importance of photography is not yet
recognised in the way it should be.
Then, again, there is the addition of the Spectroscope, which, though it
is only now beginning to yield us rich fruit, really dates from the
beginning of the present century. This is an ally to the telescope of
such power that he would be a bold man who would venture to set bounds
to the conquests their combined forces will make.
Now not only is it essential for the proper understanding of the
instruments used nowadays in every observatory, by every stargazer, to
go back to the origin of the science of observation, but in no other way
can one fully see in what way the new instrumental methods have added
themselves to the old ones.
Further, it is of importance to go back to the actual old field of work
in which the geometric conceptions which grew up in the minds of the men
of ancient time—conceptions which we are now utilizing and
extending—were gradually elaborated. To do this, there is no better way
than to dwell very briefly on the work actually done by the old
astronomers.
* * * * *
This programme, then, being agreed to, the first point is to trace the
progress of astronomical instruments down to the time of Copernicus and
Galileo. During all this period the most generally received doctrine
was, that the earth was the centre of the visible heavens; and although
there were many variations of this, still the arrangement of Ptolemy,
Fig. 1, is a good type of the ideas of the ancients.
[Illustration:
FIG. 1.—The Heavens according to Ptolemy.
]
We begin with man’s first feeble efforts, the work which man was enabled
to do by his unaided eye; and we end with the tremendous addition which
he got to his observing powers by the invention of the telescope.
The first instrument used for astronomical observations was none of
man’s making. In the old time the only instrument was the horizon; and,
truth to tell, in a land of extended plains and isolated hills, it was
not a bad one. Hence it was, doubtless, that observations in the first
instance were limited to certain occurrences such as the risings and
settings of the stars and the relative apparent distances of the
heavenly bodies from each other.
So far as we are able to learn from ancient authors, the observations
next added were those of the conjunctions of the planets and of
eclipses. The Egyptians are stated to have recorded 373 solar, and 832
lunar eclipses; and this statement is probably correct, as the
proportions are exact, and there should be the above number of each in
from 1,200 to 1,300 years.
The Chinese also record an observation, made between the years 2514 and
2436 B.C., of five planets being in conjunction.
The Chaldeans appear to have observed the motions of the moon, and an
observation in 2227 B.C. is recorded; but these old dates are probably
fictitious.
It is impossible to regard without surprise the general attention given
to astronomical investigation in those early days compared with what we
find now. Yet if we attempt to build up for ourselves any idea as to the
problems of which the ancients attempted the solution, it is difficult
if not impossible to do it; we cannot realize the blank which the
heavens presented to them, so many great men have lived between their
time and our own, by whose labours we, even if unconsciously, have
profited. The first idea seems to have been to observe which stars were
rising or setting at seed or harvest time, to divide the heavens into
Moon Stations, and then to mark astronomically their monthly and yearly
festivals.
If one looks into the old records we find that all the labours of man
which had to be performed in the country or elsewhere were determined,
by the rising or setting of the stars. All the exertions of the
navigator and the agriculturist were thus regulated. Of the planets in
those early times we hear little, except from the Chinese annals which
record conjunctions.
This was before man began to use the sun as a standpoint, and hence it
is that there are so many references in the ancient writers to the
rising and setting of the most striking star cluster—the Pleiades, and
the most striking constellation—Orion. It is known that the year, in
later times at all events, began in Egypt when the brightest star in the
heavens, Sirius, the dog-star, rose with the sun, this day being called
the 1st of the month Thoth,[1] which was the commencement of the Sothiac
period of 1461 years.
It would appear that observations of culminations, that is, of the
highest points reached by the stars, were not made till long after
horizon observations were in full vigour; and here it is a question
whether pyramids and the like were not the first astronomical
instruments constructed by man, because for great nicety in such
observations—a nicety, let us say, sufficient to determine
astronomically by means of culminations the time for holding a
festival—a fixed instrument of some kind was essential. The rich mine
recently opened up by Mr. Haliburton and Mr. Ernest de Bunsen concerning
the survival in all nations—in our own one takes the name the Feast of
All Souls’—of ancient festivals governed by the midnight culmination of
the Pleiades will doubtless ere long call general attention to this
earliest form of accurate astronomical observation, and the
determination by Professor Piazzi Smyth of the fact that in 2170 B.C.,
when the Pleiades culminated at midnight at the vernal equinox, the
passages in the north and south faces of the pyramid of Gizeh were
directed, the southern one to this culmination, and the northern one to
the then pole star, α Draconis, at its transit, about 4° from the pole.
Hence one may regard the pyramid as the next astronomical instrument to
the horizon. While then it is possible that such culmination
observations soon replaced in some measure that class of observations
which heretofore had been made on the horizon, another teaching of
horizon observations became apparent. By and by travellers observed that
as they travelled northwards the stars that were just visible on the
southern horizon, when culminating, gradually disappeared below it.
These observations were at once seized on, and Anaximander accounted for
them by supposing that the earth was a cylinder.[2] The idea of a sphere
did not come till later; when it did come then came the circle as an
astronomical instrument. For let us consider that a person on the earth
stands, say, at the equator; then he will just be able to see along his
north and south horizon the stars pointed to by the axis of the globe:
if now he is transported northwards, his horizon will change with him;
he will no longer be able to see the southern stars, but the northern
ones will gradually rise above his horizon till he gets to the north
pole, when the north pole star, instead of being on his horizon, as was
the case when he was at the equator, will be over his head. So by moving
from the equator to the pole (or a quarter of the distance round the
earth) the stars have moved from the horizon to the point overhead, or
the zenith, that is also a quarter of a circle. So it appears that if an
observer moves to such a distance that the stars appear to move over a
certain division of a circle with reference to the horizon, he must have
moved over an equal division on the earth’s surface. Then, as now, the
circle in the Western world was divided into 360°, so that the observer
in moving 1° by the stars would have moved over 1/360 of the distance
round the earth, on the assumption that the earth is a globe; and if the
distance over which the observer has moved be multiplied by 360, the
result will be the distance round the earth.
[Illustration:
FIG. 2.—The Zodiac of Denderah.
]
Now let us see how Posidonius a long time afterwards (he was born about
135 years B.C.) applied this conception. He observed that at Rhodes the
star Canopus grazed the horizon at culmination, while at Alexandria it
rose above it 7½°. Now 7½° is 1/48 of the whole circle; so he found that
from the latitude of Rhodes to that of Alexandria was 1/48 of the
circumference of the earth. He then estimated the distance, getting
5,000 stadia as the result; and this multiplied by 48 gave him 240,000
stadia, his measure of the circumference of the earth.
When the sun’s yearly course in the heavens had been determined, it was
found that it was restricted to that band of stars called the Zodiac,
Fig. 2; the sun’s position in the zodiac at any one time of the year
being found by the midnight culmination of the stars opposite the sun;
this and the apparent and heliacal risings and settings were alone the
subjects of observation.
It is obvious, then, that when observations of this nature had gone on
for some time, men would be anxious to map the stars, to make a chart of
the field of heaven; and such a work was produced by Autolycus three and
a half centuries before Christ. We also owe to Autolycus and Euclid, who
flourished about the same time (300 B.C.), the first geometrical
conceptions connected with the apparent motions of the stars.
In the theorems of Autolycus there is a particular reference to the
twelve parts of the zodiac, as denoted by constellations. The following
are the most important propositions which he lays down:—
1. “The zodiacal sign occupied by the sun neither rises nor sets,
but is either concealed by the earth or lost in the sun’s rays. The
opposite sign neither rises nor sets, _i.e._, visibly, _i.e._, after
sundown, but it is visible during the whole night.
2. “Of the twelve signs of the zodiac, that which precedes the sign
occupied by the sun rises visibly in the morning; that which
succeeds the same sign sets visibly in the evening.
3. “Eleven signs of the zodiac are seen every night. Six signs are
visible, and the five others, not occupied by the sun, afterwards
rise.
4. “Every star has an interval of five months between its morning
and its evening rising, during which time it is visible. It has an
interval of at least thirty days—between its evening setting, and
its morning rising—during which time it is invisible.” (That is, the
space passed over by the sun in its annual path is such that a star
which you see on one side of the sun, when the sun rises at one
time, would be seen a month afterwards on the other side of the
sun.)
Autolycus makes no mention of the planets. Their irregular movements
rendered them unsuited to the practical object which he had in view. He
is, however, stated by Simplicius, as quoted by Sir G. C. Lewis to have
proposed some hypothesis for explaining their anomalous motions, and to
have failed in his attempt.
Euclid carries the results arrived at in this early pre-telescopic age
much further; in a little-known treatise, the _Phenomena_,[3] he thus
sums up the knowledge then acquired:—
“The fixed stars rise at the same point, and set at the same point;
the same stars always rise together, and set together, and in their
course from the east to the west they always preserve the same
distance from one another. Now, as these appearances are only
consistent with a circular movement, when the eye of the observer is
equally distant from the circumference of the circle in every
direction (as has been demonstrated in the treatise on Optics), it
follows that the stars move in a circle and are attached to a single
body, and that the vision is equally distant from the circumference.
[Illustration:
FIG. 3.—Illustration of Euclid’s statements. _P_ the star between
the Bears. _D D´_ the region of the always visible. _C B A_ the
regions of the stars which rise and set.
]
“A star is visible between the Bears, not changing its place, but
always revolving upon itself. Since this star appears to be equally
distant from every part of the circumference of each circle
described by the other stars, it must be assumed that all the
circles are parallel, so that all the fixed stars move along
parallel circles, having this star as their common pole.
“Some of these neither rise nor set, on account of their moving in
elevated circles, which are called the ‘always visible.’ They are
the stars which extend from the visible pole to the Arctic circle.
Those which are nearest the pole describe the smallest circle, and
those upon the Arctic circle the largest. The latter appears to
graze the horizon.
“The stars to the south of this circle all rise and set, on account
of their circles being partly above and partly below the earth. The
segments above the earth are large and the segments below the earth
are small in proportion as they approach the Arctic circle, because
the motion of the stars nearest the circle above the earth is made
in the longest time, and of those below the earth in the shortest.
In proportion as the stars recede from this circle, their motion
above the earth is made in less time, and that below the earth in
greater. Those that are nearest the south are the least time above
the earth, and the longest below it. The stars which are upon the
middle circle make their times above and below the earth equal;
whence this circle is called the Equinoctial. Those which are upon
circles equally distant from the equinoctial make the alternate
segments in equal times. For example, those above the earth to the
north correspond with those below the earth to the south; and those
above the earth to the south correspond with those below the earth
to the north. The joint times of all the circles above and below the
earth are equal. The circle of the milky way and the zodiacal circle
being oblique to the parallel circles, and cutting each other,
always have a semicircle above the earth.
“Hence it follows that the heaven is spherical. For if it were
cylindrical or conical, the stars upon the oblique circles, which
cut the equator, would not in the revolution of the heaven always
appear to be divided into semicircles; but the visible segment would
sometimes be greater and sometimes less than a semicircle. For if a
cone or a cylinder were cut by a plane not parallel to the base, the
section is that of an acute-angled cone, which resembles a shield
(an ellipse). It is, therefore, evident that if a figure of this
description is cut in the middle both in length and breath, its
segments will be unequal. But the appearances of the heaven agree
with none of these results. Therefore the heaven must be supposed to
be spherical, and to revolve equally round an axis of which one pole
above the earth is visible and the other below the earth is
invisible.
“The Horizon is the plane reaching from our station to the heaven,
and bounding the hemisphere visible above the earth. It is a circle;
for if a sphere be cut by a plane the section is a circle.
“The Meridian is a circle passing through the poles of the sphere,
and at right angles to the horizon.
“The Tropics are circles which touch the zodiacal circle, and have
the same poles as the sphere. The zodiacal and the equinoctial are
both great circles, for they bisect one another. For the beginning
of Aries and the beginning of the Claws (or Scorpio) are upon the
same diameter; and when they are both upon the equinoctial, they
rise and set in conjunction, having between their beginnings six of
the twelve signs and two semicircles of the equinoctial; inasmuch as
each beginning, being upon the equinoctial, performs its movement
above and below the earth in equal times. If a sphere revolves
equally round its axis, all the points on its surface pass through
similar axes of the parallel circles in equal times. Therefore these
signs pass through equal axes of the equinoctial, one above and the
other below the earth; consequently the axes are equal, and each is
a semicircle; for the circuit from east to east and from west to
west is an entire circle. Consequently the zodiacal and equinoctial
circles bisect one another; each will be a great circle. Therefore
the zodiacal and equinoctial are great circles. The horizon is
likewise a great circle; for it bisects the zodiacal and
equinoctial, both great circles. For it always has six of the twelve
signs above the earth, as well as a semicircle of the equator. The
stars above the horizon which rise and set together reappear in
equal times, some moving from east to west, and some from west to
east.”
We have given this long extract in justice to the men of old, containing
as it does many of those geometrical principles which all our modern
instruments must and actually do fulfil.
It is true that the present idea of the earth’s place in the system is
different. Euclid imagined the earth to be at the centre of the
universe. It is now known that the earth is one of various planets which
revolve round the sun, and further, that the journey of the earth round
the sun is so even and beautifully regulated that its motion is confined
to a single plane. Year after year the earth goes on revolving round the
sun, never departing, except to a very small extent, from this plane,
which is one of the fundamental planes of the astronomer and called the
Plane of the Ecliptic.
[Illustration:
FIG. 4.—The Plane of the Ecliptic.
]
Suppose this plane to be a tangible thing, like the surface of an
infinite ocean, the sun will occupy a certain position in this infinite
ocean, and the earth will travel round it every year.
If the axis of the earth were upright, one would represent the position
of things by holding a globe with its axis upright, so that the equator
of the earth is in every part of its revolution on a level with this
ecliptic sea. But it is known that the earth, instead of floating, as it
were, upright, as in Fig. 4, has its axis inclined to the plane of the
ecliptic, as in Fig. 5.
It is also known that by turning a globe round, distant objects would
appear to move round an observer on the globe in an opposite direction
to his own motion, and these distant objects would describe circles
round a line joining the places pointed to by the poles of the earth,
_i.e._, round the earth’s axis.
[Illustration:
FIG. 5.—The Plane of the Ecliptic, showing the Inclination of the
Earth’s Axis.
]
It is now easy to explain the observations referred to by Euclid by
supposing the surface of the water in the tub to represent the plane of
the ecliptic, that is, the plane of the path which the sun apparently
takes in going round the earth; and examining the relative positions of
the sun and earth represented by two floating balls, the latter having a
wire through it inclined to the upright position; it will be seen at
once by turning the ball on the wire as an axis to represent the diurnal
motion of our earth, how Euclid finds the Bear which never sets, being
the place in the heavens pointed to by the earth’s pole; and how all the
stars in different portions of the heavens appear to move in complete
circles round the pole-star when they do not set, and in parts of
circles when they pass below the horizon. By moving the ball
representing the earth round the sun and so examining their relative
positions, during the course of a year it will be seen how the sun
appears to travel through all the signs of the zodiac in succession in
his yearly course, remaining a longer or shorter time above the horizon
at different times of the year.
For it will be seen that if the spectator on the globe, when in the
position that its inclined axis, as shown in Fig. 5, points towards the
sun, were looking at the sun from a place where one can imagine England
to be at midday, the sun would appear to be very high up above the
horizon; and if he looked at it from the earth in the opposite part of
its orbit it would be very low and near the horizon. When the earth,
therefore, occupied the intermediate positions, the sun would be half
way between the extreme upper position and the extreme lower position as
the earth moves round the sun, and in this way the solstices, equinoxes,
and the seasonal changes on the surface of our planet, are easily
explained.
-----
Footnote 1:
Corresponding to 20th July, 139 B.C.
Footnote 2:
Anaximander flourished about 547 B.C.
Footnote 3:
Quoted by Sir G. C. Lewis in his _Astronomy of the Ancients_, p. 187.
CHAPTER II.
THE FIRST INSTRUMENTS.
The ancients called the places occupied by the sun when highest and
lowest the Solstices, and the intermediate positions the Equinoxes. The
first instrument made was for the determination of the sun’s altitude in
order to fix the solstices. This instrument was called the Gnomon. It
consisted of an upright rod, sharp at the end and raised perpendicularly
on a horizontal plane, and its shadow could be measured in the plane of
the meridian by a north and south line on the ground. Whenever the
shadow was longest the sun was naturally lowest down at the winter
solstice, and _vice versâ_ for the summer solstice.
Here then we leave observations on the horizon and come to those made on
the meridian.
The Gnomon is said to have been known to the Chinese in the time of the
Emperor Yao’s reign (2300 B.C.), but it was not used by the Greeks[4]
till the time of Thales, about 585 B.C., who fixed the dates of the
solstices and equinoxes, and the length of the tropical year—that is,
the time taken by the sun to travel from the vernal equinoctial point
round to the same point again.
The next problem was to discover the inclination of the ecliptic, or,
what is the same thing, the amount that the earth’s equator is inclined
to the ecliptic plane (represented by the surface of the water in our
tub).
Now in order to ascertain this, the angular distance between the
positions occupied by the sun when at the solstices must be measured;
or, since one solstice is just as much below the equinoctial line as the
other is above it, we might take half the angle between the solstices as
being the obliquity required.
The first method of measuring the angle was to measure the length of the
sun’s shadow at each solstice, and so, by comparison of the length of
the shadow with the height of the gnomon, calculate the difference in
altitude, the half of which was the angle sought. And this was probably
the method of the Chinese, who obtained a result of 23° 38´ 11˝ in the
time of Yao; and also of Anaximander in his early days, who obtained a
result of 24°. But before trigonometrical tables, the first of which
seem to have been constructed by Hipparchus and Ptolemy, were known, in
order to find this angle it was constructed geometrically, and then what
_aliquot part_ of the circumference it was, or _how much of the
circumference_ it contained was determined; for the division of the
circle into 360° is subsequent to the first beginning of astronomy—and
hence it was that Eratosthenes said that the distance from the tropics
was 11/83 of the circumference, and not that it was 47° 46´ 26˝.
The gnomon is, without exception, of all instruments the one with which
the ancients were able to make the best observations of the sun’s
altitude. But they did not give sufficient attention to it to enable it
to be used with accuracy. The shadow projected by a point when the sun
is shining is not well defined, so that they could not be quite certain
of its extremity, and it would seem that the ancient observations of the
height of the sun made in this manner ought to be corrected by about
half the apparent diameter of the sun; for it is probable that the
ancients took the strong shadow for the true shadow; and so they had
only the height of the upper part of the sun and not that of the centre.
There is no proof that they did not make this correction, at least in
the later observations.
In order to obviate this inconvenience, they subsequently terminated the
gnomon by a bowl or disc, the centre of which answered to the summit; so
that, taking the centre of the shadow of this bowl, they had the height
of the centre of the sun. Such was the form of the one that Manlius the
mathematician erected at Rome under the auspices of Augustus.
But in comparatively modern times astronomers have remedied this defect
in a still more happy manner, by using a vertical or horizontal plate
pierced with a circular hole which allows the rays of the sun to enter
into a dark place, and in fact to form a true image of the sun on a
floor or other convenient receptacle, as we find is the case in many
continental churches.
Of course at this early period the reference of any particular
phenomenon to true time was out of the question. The ancients at the
period we are considering used twelve hours to represent a day,
irrespective of the time of the year—the day always being reckoned as
the time between sunrise and sunset. So that in summer the hours were
long and in winter they were short. The idea of equal hours did not
occur to them till later; but no observations are closer than an hour,
and the smallest division of space of which they took notice was
something like equal to a quarter or half of the moon’s diameter.
When we come down, however, to three centuries before Christ, we find
that a different state of things is coming about. The magnificent museum
at Alexandria was beginning to be built, and astronomical observations
were among the most important things to be done in that vast
establishment. The first astronomical workers there seem to have been
Timocharis and Aristillus, who began about 295 B.C., and worked for
twenty-six years. We are told that they made a catalogue of stars,
giving their positions with reference to the sun’s path or ecliptic.
It was soon after this that the gnomon gave way to the invention of the
Scarphie. It is really a little gnomon on the summit of which is a
spherical segment. An arc of a circle passing out of the foot of the
style was divided into parts, and we thus had the angle which the solar
ray formed with the vertical. Nevertheless the scarphie was subject to
the same inconveniences, and it required the same corrections, as the
gnomon; in short, it was less accurate than it. That did not, however,
hinder Eratosthenes from making use of it to measure the size of the
earth and the inclination of the ecliptic to the equator. The method
Eratosthenes followed in ascertaining the size of the earth was to
measure the arc between Syene and Alexandria by observing the altitude
of the sun at each place. He found it to be 1/50 of the circumference
and 5,000 stadia, so that if 1/50 of the circumference of the earth is
5,000 stadia, the whole circumference must be 50 times 5,000, or 250,000
stadia.[5]
[Illustration:
FIG. 6.—The First Meridian Circle.
]
And now still another instrument is introduced, and we begin to find the
horizon altogether disregarded in favour of observations made on the
meridian.
The instrument in question was probably the invention of Eratosthenes.
It consisted of two circles of nearly the same size crossing each other
at right angles, (Fig. 6); one circle represented the equator and the
other the meridian, and it was employed as follows:—
The circle A was fixed perfectly upright in the meridian, so that the
greatest altitude of the sun each day could be observed; the circle B
was then placed exactly in the plane of the earth’s equator by adjusting
the line joining C and D to the part of the heavens between the Bears,
about which the stars appear to revolve. This done, the occurrence of
the equinox was waited for, at which time the shadow of the part of the
circle E must fall upon the part marked F, so as exactly to cover it.
[Illustration:
FIG. 7.—The First Instrument Graduated into 360° (West Side).
]
We now come to the time when the circle began to be divided into 360
divisions or degrees—about the time of Hipparchus (160 B.C.). There are
two instruments described by Ptolemy for measuring the altitude of the
sun in degrees instead of in fractions of a circle. They, like the
gnomon, were used for determining the altitude of the sun. The first,
Fig. 7, consisted of two circles of copper, one, C D, larger than the
other, having the smaller one, B, so fitted inside it as to turn round
while the larger remained fixed. The larger was divided into 360°, and
the smaller one carried two pointers. This instrument was placed
perfectly upright and in the plane of the meridian, and with a fixed
point, C, always at the top by means of a plumb-line hanging from C over
a mark, D. On this small circle are two square knobs projecting on the
side, E and F. When the sun was on the meridian the small circle was
turned so as to bring the shadow of the knob E over the knob F, and then
the degree to which the pointer pointed was read off on the larger
circle. And of course, as the position of the knobs had to be changed as
the sun moved in altitude, the angle through which the sun moved was
measured, and the circle being fixed, the sun’s altitude could always be
obtained.
The other instrument consisted of a block of wood or stone, one side of
which was placed in the plane of the meridian; and on the top corner of
this side was fixed a stud; and round it as a centre a quarter of a
circle was described, divided into 90°. Below this stud was another, and
by means of a plumb-line one stud could always be brought over the
other; so that the instrument could always be placed in a true position.
At midday then, when the sun was shining, the shadow of the upper stud
would fall across the scale of degrees, and at once give the altitude of
the sun.
Ptolemy, who used this instrument, found that the arc included between
the tropics was 47⅔°.
The result of all these accurate determinations of the solstices and
equinoxes was the fixing of the length of the year.
We have so far dealt with the methods of observation which depend upon
the use of the horizon and of the meridian; we will now turn our
attention to extra-meridional observations, or those made in any part of
the sky.
Before we discuss them, let us consider the principles on which we
depend for fixing the position of a place on a globe. On a terrestrial
globe there are lines drawn from pole to pole, called meridians of
longitude; and if a place is on any one meridian it is said to be in so
many degrees of longitude, east or west of a certain fixed meridian, as
there are degrees intercepted between this meridian and the one on which
the place is situated. There are also circles at right angles to the
above and parallel to the equator; these are circles of latitude, and a
place is said to have so many degrees N. or S. latitude as the circle
which passes through it intercepts on a meridian between itself and the
equator, so that the latitude of a place is its angular distance from
the equator, and the longitude is its angular distance E. or W. of a
fixed meridian—that of Greenwich being the one used for English
calculation; and each large country takes the meridian of its central
observatory for its starting-point. The distance round the equator is
sometimes expressed in hours instead of degrees; for as the earth turns
round in twenty-four hours, so the equator can be divided into hours,
minutes, and seconds. So that if a star be just over the meridian of
Greenwich, which is 0° 0´ 0˝, or 0^h 0^m 0^s longitude at a certain
time, in an hour after it will be over a meridian 15° or one hour west
of Greenwich, and so on, till at the end of twenty-four hours it would
be over Greenwich again.
Now let us turn to the celestial globe.
What we call latitude and longitude on a terrestrial globe is called
declination and right ascension on the celestial globe, because in the
heavens there is a latitude and longitude which does not correspond to
our latitude and longitude on the earth. If we imagine the lines of
latitude and longitude on the earth to be projected, say as shadows
thrown on the heavens by a light in the centre of the earth, the lines
of right ascension (generally written R.A.) and declination (written
Dec. or D.) will be perfectly depicted.
But there is another method of co-ordinating the stars, in which we have
the words latitude and longitude used also, as we have said, for the
heavens; meaning the distance of a star from the ecliptic instead of the
equator, and its distance east or west measured by meridians at right
angles to the ecliptic.
This premised, we are in a position to see the enormous advance rendered
possible by the methods of observation introduced by Hipparchus and
Ptolemy.
-----
Footnote 4:
This instrument is also reported to have been used by the Chaldeans in
850 B.C.; the invention of it being attributed to Anaximander. This
philosopher, says Diogenes Laertes, observed the revolution of the
sun, that is to say, the solstices, with a gnomon; and probably he
measured the obliquity of the ecliptic to the equator, which his
master had already discovered.
Footnote 5:
28,279 miles.
CHAPTER III.
HIPPARCHUS AND PTOLEMY.
Among the astronomers of antiquity there are two figures who stand out
in full relief—Hipparchus and Ptolemy. The former, “the father of
astronomy,” is especially the father of instrumental astronomy. As he
was the first to place observation on a sure basis, and left behind him
the germs of many of our modern instruments and methods, it is desirable
to refer somewhat at length to his work and that of his successor,
Ptolemy.
Hipparchus introduced extra-meridional observations. He followed Meton,
Anaximander, and others in observing on the meridian instead of on the
horizon, and then it struck him that it was not necessary to keep to the
meridian, and he conceived an instrument, called an Astrolabe, fixed on
an axis so that the axis would point to the pole-star, like the one
represented in Fig. 8. This engraving is of one of Tycho Brahe’s
instruments, which is similar to but more elaborate than that of
Hipparchus no drawing of which is extant. C, D, is the axis of the
instrument pointed to the pole of the heavens; E, B, C, the circle
placed North and South representing the meridian; R, Q, N, the circle
placed at right angles to the polar axis, representing the equator, but
in the instrument of Hipparchus it was fixed to the circle E, B, C, and
not movable in its own plane as this one is. M, L, K, is a circle at
right angles to the equator, and moving round the poles, being a sort of
movable meridian. Thus, then, if the altitude of a star from the equator
(or its declination) was required to be observed, the circle was turned
round on the axis, and the sights, Q, M, moved on the circle till they,
together with the sight A, pointed to the star; the number of degrees
between one of the sights and the equator, was then read off, giving the
declination required. The number of degrees, or hours and minutes, of
Right Ascension, from K to E could be then read off along the circle R,
Q, N, giving the distance of the object from the meridian. As the stars
have an apparent motion, the difference in right ascension between two
stars only could be obtained by observing them directly after each
other, and allowing for the motion during the interval between the two
observations.
[Illustration:
FIG. 8.—Astrolabe (Armillæ Æquatoriæ of Tycho Brahe) similar to the
one contrived by Hipparchus.
]
In this manner, then, Hipparchus could point to any part of the heavens
and observe, on either side of the meridian, the sun, moon, planets or
any of the stars, and obtain their distance from the equatorial plane;
but another fixed plane was required; and Hipparchus, no longer content
with being limited to measuring distances from the equator, thought it
might be possible to get another starting-point for distances along the
equator. It was the determination of this plane, or starting-point from
which to reckon right ascension, that was one of the difficulties
Hipparchus had to encounter. This point he decided should be the place
in the heavens where the sun crosses the equator at the spring equinox.
But the stars could not be seen when the sun was shining; how, then, was
he to fix that point so that he could measure from it at night?
[Illustration:
FIG. 9.—Ecliptic Astrolabe (the Armillæ Zodiacales of Tycho Brahe),
similar to the one used by Hipparchus.
]
He found it at first a tremendous problem, and at last hit upon this
happy way of solving it. He reasoned in this way: “As an eclipse of the
moon is caused by the earth’s shadow being thrown by the sun on the
moon, if this happen near the equinox, the sun and moon must then be
very near the equator, and very near the ecliptic—in fact, near the
intersection of the two fundamental planes which are supposed to cross
each other. If I can observe the distance, measured along the equator,
between the moon and a star, I shall have obtained the star’s actual
place, because, of course, if the moon is exactly opposite the sun, the
sun will be 180 degrees of right ascension from the moon, and the right
ascension of the sun being known it will give me the position of the
star.” This method of observation was an extremely good one for the
time, but it could only have been used during an eclipse of the moon,
and when the sun was so near the equator that its distance from the
equinoctial point along the ecliptic, as calculated by the time elapsed
since the equinox, differed little from the same distance measured along
the equator, or its right ascension, so that the right ascension of the
sun was very nearly correct. Hipparchus hit upon a very happy alteration
of the same instrument to enable him to measure latitude and longitude
instead of declination and right ascension—in fact, to measure along the
ecliptic instead of the equator. Instead of having the axis of the inner
rings parallel to the axis of the earth, as in Fig. 9, he so arranged
matters that the axis of this system was separated from the earth’s axis
to the extent of the obliquity of the ecliptic, the circle R, Q, N,
therefore instead of being in the plane of the equator, was in that of
the ecliptic. Then it was plain to Hipparchus that he would, instead of
being limited to observe during eclipses of the moon, be able to reckon
from the sun at all times; because the sun moves always along the
ecliptic and the latitude of the sun is nothing.
We will now describe the details of the instrument. There is first a
large circle, E, B, C, Fig. 9 (which is taken from a drawing of this
kind of instrument as constructed subsequently by Tycho Brahe), fixed in
the plane of the meridian, having its poles, D, C, pointing to the poles
of the heavens; inside this there is another circle, F, I, H, turning on
the pivots D, C, and carrying fixed to it the circle, O, P, arranged in
a plane at right angles to the points I, K, which are placed at a
distance from C and D equal to the obliquity of the ecliptic; so that I
and K represent the poles of the ecliptic, and the circle, O, P, the
ecliptic itself. There is then another circle, R, M, turning on the
pivots I and K, representing a meridian of latitude, and along which it
is measured.
Then, as the sun is on that part of the ecliptic nearest the north pole,
in summer, its position is represented by the point F on the ecliptic,
and by N at the winter solstice; so, knowing the time of the year, the
sight Q can be placed the same number of degrees from F as the sun is
from the solstice, or in a similar position on the circle O P as the sun
occupies on the ecliptic.
The circle can then be turned round the axis C, D, till the sight Q, and
the sight opposite to it, Q´, are in line with the sun. The circle, O,
R, will then be in the plane of the ecliptic, or of the path of the
earth round the sun. The circle, R, M, is then turned on its axis, I, K,
and the sights, R, R, moved until they point to the moon. The distance
Q, L, measured along O, P, will then be the difference in longitude of
the moon and sun, and its latitude, L, R, measured along the circle R,
M.
But why should he use the moon? His object was to determine the
longitude of the stars, but his only method was to refer to the motion
of the sun, which could be laid down in tables, so that its longitude or
distance from the vernal equinox was always known. But we do not see the
stars and the sun at the same time; therefore in the day time, while the
moon was above the horizon, he determined the difference of longitude
between the sun and the moon, the longitude of the sun or its distance
from the vernal equinox being known by the time of the year; and after
the sun had set he determined the difference of longitude between the
moon and any particular star; and so he got a fair representation of the
longitude of the stars, and succeeded in tabulating the position of
1,022 of them.
It is to the use of this instrument that we owe the discovery of the
precession of the equinoxes.
[Illustration:
FIG. 10.—Diagram Illustrating the Precession of the Equinoxes.
]
After Hipparchus had fixed the position of a number of stars, he found
that on comparing the place amongst them of the sun at the equinoxes in
his day with its place in the time of Aristillus that the positions
differed—that the sun got to the equinox, or point where it crossed the
equator, a short time before it got to the place amongst the stars where
it crossed in the time of Aristillus; in fact, he found that the
equinoctial points retrograded along the equator, and Ptolemy (B.C. 135)
appears to have established the fact that the whole heavens had a slow
motion of one degree in a century which accounted for the motion of the
equinoxes.
[Illustration:
FIG. 11.—Revolution of the Pole of the Equator round the Pole of the
Ecliptic caused by the Precession of the Equinoxes.
]
Let us see what we have learned from the observation of this motion, for
motion there is, and the ancients must be looked on with reverence for
their skill in determining it with their comparatively rude instruments.
In Fig. 10, A represents the earth at the vernal equinox, and at this
time the sun appears near a certain star, S, which was fixed by
Aristillus; but in the time of Hipparchus the equinox happened when the
sun was near a star, S´, and before it got to S. Now we know that the
sun has no motion round the earth, and that the equinox simply depends
on the position of the earth’s equator in reference to the ecliptic; so
that in order to produce the equinox when the earth is at E and before
it get to A, its usual place, all we have to do is to turn the pole of
the earth through a small arc of the dotted circle, and so alter its
position to that shown at F, when its equator and poles will have the
same position as regards the sun as they have at A, so the equinox will
happen when the earth is at E, and before it reaches A. This may be
practically represented by taking an orange and putting a
knitting-needle through it, and drawing a line representing the equator
round it, and half immersing it in a tub of water, the surface of which
represents the ecliptic. We are then able to examine these motions by
moving the orange round the tub to represent the earth’s annual motion,
and at the same time making the orange slowly whobble like a
spinning-top just before it falls, by moving the top of the
knitting-needle through a small arc of a circle in the same direction as
the hands of a clock at every revolution of the orange round the centre
of the tub.
The points where the equator is cut by the surface of the water (or
ecliptic) will then change, as the orange whobbles, and the line joining
them, will rotate, and as the equinox happens when this line passes
through the sun, it will be seen that this will take place earlier at
each revolution of the orange round the tub.
The equinox will therefore appear to happen earlier each year, so that
the tropical year, or the time from equinox to equinox, is a little
shorter than the sidereal year, or the time that the earth takes to
travel from a certain place in its orbit to the same again; for if the
earth start from an equinoctial point, the equinox will happen before it
gets to the same place where the equinoctial point was at starting.
This is called the precession of the equinoxes.
[Illustration:
FIG. 12.—The Vernal Equinox among the Constellations, B.C. 2170.
]
[Illustration:
FIG. 13.—Showing how the Vernal Equinox has now passed from Taurus and
Aries.
]
This discovery must be regarded as the greatest triumph obtained by the
early stargazers, and there is much evidence to show that when the
zodiac was first marked out among the central zone of stars, the Bull
and not the Ram was the first of the train. Even the Ram, owing to
precession, is no longer the leader, for the _sign_ Aries is now in the
constellation Pisces. The two accompanying drawings by Professor Piazzi
Smyth of the position of the vernal equinox among the stars in the years
2170 B.C. and 1883 A.D. will show how precession has brought about
celestial changes which have not been unaccompanied by changes of
religious ideas and observances in origin connected with the stars.
[Illustration:
FIG. 14.—Instrument for Measuring Altitudes.
]
We now come to Ptolemy. There was another instrument used by Ptolemy,
and described by him, which we may mention here; it was called the
Parallactic Rules, so named perhaps because that ancient astronomer used
it first for the observation of the parallax of the moon. It consists of
three rods, D E, D F, E F, Fig. 14, two of which formed equal sides of
an isosceles triangle; and the third, which had divisions on it, made
the one at the base, or was the chord of the angle at the summit. One of
the equal sides, D F, was furnished with pointers, over which a person
observed the star, whilst the other, D E, was placed vertically, so that
they read off the divisions on E F, and then, by means of a table of
chords, the angle was found; this angle was the distance of the star
from the zenith. Ptolemy, wishing to observe with great accuracy the
position of the moon, made himself an instrument of this kind of a
considerable size; for the equal rulers were four cubits long, so that
its divisions might be more obvious. He rectified its position by means
of a plumb-line. Purbach, Regiomontanus, and Walther, astronomers of the
fifteenth century, employed this manner of observing, which, considering
the youth of astronomy, was by no means to be despised. This instrument,
constructed with great care, would have sufficiently been useful as far
as concerns certain measurements and would have furnished results
sufficiently exact; but the part of ancient astronomy that failed was
the way of measuring time with any precision.
There were astronomers who proposed clepsydras for this purpose; but
Ptolemy rejected them as very likely to introduce errors; and indeed
this method is subject to much inconvenience and to irregularities
difficult to prevent. However, as the measurement of time is the soul of
astronomy, Ptolemy had recourse to another expedient which was very
ingenious. It consisted in observing the height of the sun if it were
day, or of a fixed star if it were night, at the instant of a phenomenon
of which he wished to know the time of occurrence, for the place of the
sun or star being known to some minutes of declination and right
ascension as also was the latitude of the place, he was able to
calculate the hour; thus when they observed, for example, an eclipse of
the moon, it was only necessary to take care to get the height of some
remarkable star at each phase of the eclipse, say at the commencement
and at the end, in order to be able to conclude the true time at which
it took place. This was the method adopted by astronomers until the
introduction of the pendulum.
CHAPTER IV.
TYCHO BRAHE.
Leaving behind us the results of the researches of Ptolemy, who
succeeded Hipparchus and whose methods have been described, and passing
over the astronomy of the Arabs and Persians as being little in advance
of Hipparchus and Ptolemy, we come down to the sixteenth century of our
era.
Here we find ourselves in presence of the improvements in instruments
effected by a man whose name is conspicuous—Tycho Brahe—a Danish
nobleman who, in the year 1576, established a magnificent observatory at
Huen, which may be looked upon as the next building of importance after
that great edifice at Alexandria which has already been referred to.
What Hipparchus was to the astronomy of the Ancients such was Tycho to
the astronomy of the Middle Ages. As such his life merits a brief notice
before we proceed to his work. He was born at Knudsthorp, near
Helsingborg, in Sweden, in 1546, and went to the University of
Copenhagen to prepare to study law; while there he was so struck with
the prediction of an eclipse of the sun by the astrological almanacks
that he gave all his spare time to the study of astronomy. In 1565 his
uncle died and Tycho Brahe fell into possession of one of his uncle’s
estates; and as astronomy, or astrology as it was then called, was
thought degrading to a man in his position by his friends, who took
offence at his pursuits and made themselves very objectionable, he left
for a short stay at Wittenberg, then he went to Rostock and afterwards
to Augsburg, where he constructed his large quadrant. He returned to his
old country in 1571; while there, Frederick II., King of Denmark,
requested him to deliver a course of lectures on astronomy and astrology
and became his most liberal patron. The King granted to Tycho Brahe for
life the island of Huen, lying between Denmark and Sweden, and built
there a magnificent observatory and apartments for Tycho, his assistants
and servants. The main building was sixty feet square, with observing
towers on the north and south, and a library and museum. Tycho called
this Uraniberg—the city of the heavens; and he afterwards built a
smaller observatory near called by him Sternberg—city of the stars, the
former being insufficiently large to contain all his instruments.
The following is a list of these instruments as given in Sir David
Brewster’s excellent memoir of Brahe, in _Martyrs of Science_:—
_In the South and greater Observatory._
1. A semicircle of solid iron, covered with brass, four cubits
radius.
2. A sextant of the same materials and size.
3. A quadrant of one and a half cubits radius, and an azimuth circle
of three cubits.
4. Ptolemy’s parallactic rules, covered with brass, four cubits in
the side.
5. Another sextant.
6. Another quadrant, like No. 3.
[Illustration:
FIG. 15.—Portrait of Tycho Brahe (from original painting in the
possession of Dr. Crompton, of Manchester).
]
7. Zodiacal armillaries of melted brass, and turned out of the
solid, of three cubits in diameter.
Near this observatory there was a large clock with one wheel two
cubits in diameter, and two smaller ones which, like it, indicated
hours, minutes, and seconds.
_In the South and lesser Observatory._
8. An armillary sphere of brass, with a steel meridian, whose
diameter was about four cubits.
_In the North Observatory._
9. Brass parallactic rules, which revolved in azimuth above a brass
horizon, twelve feet in diameter.
10. A half sextant, of four cubits radius.
11. A steel sextant.
12. Another half sextant with steel limb, four cubits radius.
13. The parallactic rules of Copernicus.
14. Equatorial armillaries.
15. A quadrant of a solid plate of brass, five cubits in radius,
showing every ten seconds.
16. In the museum was the large globe made at Augsburg.
_In the Sternberg Observatory._
17. In the central part, a large semicircle, with a brass limb, and
three clocks, showing hours, minutes, and seconds.
18. Equatorial armillaries of seven cubits, with semi-armillaries of
nine cubits.
19. A sextant of four cubits radius.
20. A geometrical square of iron, with an intercepted quadrant of
five cubits, and divided into fifteen seconds.
21. A quadrant of four cubits radius, showing ten seconds, with an
azimuth circle.
22. Zodiacal armillaries of brass, with steel meridians, three
cubits in diameter.
23. A sextant of brass, kept together by screws, and capable of
being taken to pieces for travelling with. Its radius was four
cubits.
24. A movable armillary sphere, three cubits in diameter.
25. A quadrant of solid brass, one cubit radius, and divided into
minutes by Nonian circles.
26. An astronomical radius of solid brass, three cubits long.
27. An astronomical ring of brass, a cubit in diameter.
28. A small brass astrolabe.
Tycho Brahe carried on his work at Uraniberg for twenty-one years, and
appears to have been visited by many of the princes of the period and by
students anxious to learn from so great a man. In Frederick’s treatment
of Tycho Brahe we have an early and munificent and, in its results, most
successful instance of the endowment of research. On the death of
Frederick II., in 1588, Christian IV. came to the throne. The successor
cared little for astronomy, and his courtiers, who were jealous of
Tycho’s position, so acted upon him that the pension, estate and canonry
with which Tycho had been endowed were taken away. Unable to put up with
these insults and loss of his money, he left for Wandesburg in 1597,
where he was entertained by Count Henry Rantzau. It was now that he
wrote and published the _Astronomiæ instauratæ Mechanica_, a copy of
which, together with his catalogue of 1000 stars, was sent to the
Emperor Rudolph II., who invited him to go to Prague. This he accepted,
and he and his family went to the castle of Benach in 1599, and a
pension of 3000 crowns was given to him. Ten years afterwards he removed
with his instruments into Prague to a house purchased and presented to
him by the Emperor; here he died in the same year.
The wonderful assistance which Tycho Brahe was able to bring to
astronomy shows that then, as now, any considerable advance in physical
investigation was more or less a matter of money, and whether that money
be found by individuals or corporations, now or then, we cannot expect
any considerable advance without such a necessary adjunct.
[Illustration:
FIG. 16.—Tycho Brahe’s Observatory on the Island of Huen.
]
The principal instruments used at first by Tycho Brahe resembled the
Greek ones, except that they were much larger. Hipparchus was enabled to
establish the position of a heavenly body within something less than one
degree of space—some say within ten minutes; but there was an immense
improvement made in this direction in the instruments used by Tycho.
One of the instruments which he used was in every way similar to the
equatorial astrolabe designed, by Hipparchus, and was called by Tycho,
the ‘armillæ equatoriæ’ (Fig. 8). With that instrument in connection
with others Tycho was enabled to make an immense advance upon the work
done by Hipparchus.
Tycho, like Hipparchus, having no clock, in the modern sense, was not
able to determine the difference of time between the transit of the sun
or a particular star over the meridian, so that he was compelled to
refer everything to the sun at the instant of observation, and he did
that by means of the moon. Hipparchus, as we have seen, determined the
difference of longitude, or right ascension, between the sun and the
moon and between the moon and the stars, in the manner already
described, and so used the moon as a means of determining differences
between the longitude or right ascension of the sun and the stars.
Now Tycho, using an instrument similar to that of Hipparchus, saw that
he would make an improvement if instead of using the Moon he used Venus;
for the measure of the surface of the moon was considerable, and could
not be easily reckoned, and its apparent position in the heavens was
dependent on the position of a person on the earth,—because it is so
near the earth that it has a sensible parallax, that is, a person at the
equator of the earth might see the moon in the direction of a certain
star; but, on going to the pole, the moon would appear below the line of
the star. If one were looking at a kite in the air to the south and then
walked towards the south, the kite would gradually get over head, and on
proceeding further it would get north. To persons at different stations
the kite would appear in different positions, and the nearer the kite
was to the observer the less distance he would have to go to make it
change its place. So also with the moon; it is so near to us that a
change of place on the earth makes a considerable difference in the
direction in which it is seen. Instead, therefore, of using the Moon,
Tycho used Venus, and so mapped 1,500 stars after determining their
absolute right ascensions, in this manner without the use of clocks.
Fig. 8 shows the instrument called the “armillæ equatoriæ,” which he
constructed, and which was based upon the principle of that which
Hipparchus had used. Here the axis of motion, C, D, of these circles is
so arranged that it is absolutely parallel to the axis of the earth; but
instead of the circle R, Q, N, representing the equator, being fixed, it
revolved in its own plane while held by the circle G, H, I, making its
use probably more easy, but leaving the principles unaltered.
Tycho Brahe also used another similar instrument of much larger size for
the same purposes as the one we have just considered. It consisted of a
large circle, which was seven cubits in diameter, corresponding to the
circle K, L, M, Fig. 8; and carrying the sights in the same manner, it
was placed in a circular pit in the ground, with its diameter pointing
towards the pole. This was used for measuring declinations. The circle
R, Q, N, Fig. 9, was represented by a fixed circle carried on pillars
surrounding the pit, and along which the right ascension of the star was
measured. This instrument, therefore, was more simple than the smaller
one, and probably much more accurate.
Tycho was not one of those who was aware of the true system of the
universe; he thought the earth fixed, as Ptolemy and others did; but
whether we suppose the earth to be movable in the middle of the vault of
stars or stationary, in either case that position is absolutely
immaterial in ascertaining the right ascension of stars. If one takes
the terrestrial globe, and looks upon the meridians, it is at once clear
that the distance from meridian to meridian remains unaltered, whether
the globe is still or turning round: so the stars maintain their
relative positions to each other, whether we consider the earth in
motion or the sphere in which the stars are placed to revolve round it.
[Illustration:
FIG. 17.—Tycho Brahe’s System.
]
The introduction of clocks gave Tycho the invention of the next
instrument, which was the transit circle. At this time the pendulum had
not been invented; but it struck him and others that there was no
necessity for having two or more circles rotating about an axis parallel
to the earth’s axis, as in the astrolabes or armillæ, but only to have
one circle in the plane of the meridian of the place. So that, by the
diurnal movement of the earth round its own axis, all the stars in the
heavens would gradually and seriatim be brought to be visible along the
arc of the circle, so he arranged matters in the following way.
The stars were observed through a hole in a wall and through an eyehole,
sliding on a fixed arc. The number of degrees marked at the eyehole on
the arc at once gave the altitude of the heavenly bodies as seen through
that hole. If a star was very high, it would be necessary for an
observer to place his eye low down to be able to see it. If it were near
the horizon, he would have to travel up to the top of this circle to
determine its altitude, and having done that, and knowing the latitude
of the place of observation, the observer will be able to determine the
position of the star with reference to the celestial equator. The actual
moment at which the star was seen was noted by the clock, and the time
that the sun had passed the hole being also previously noted, the length
of time between the transits was known; and as the stars appear to
transit or pass the meridian every twenty-four hours, it was at once
known what part of the heavens was intercepted between the sun and the
star in degrees, or, as is usually the case, the right ascension of the
star was left expressed in hours and minutes instead of degrees; thus he
had a means of determining the two co-ordinates of any celestial body.
The places of the comet of 1677, which Tycho discovered, and of many
stars, were determined with absolute certainty; but astronomers began to
be ambitious. It was necessary in using this instrument to wait till a
celestial body got to the meridian. If it was missed, then they had to
wait till the next day; and further, they had no opportunity whatever of
observing bodies which set in the evening.
[Illustration:
FIG. 18.—The Quadrans Maximus reproduced from Tycho’s plate.
]
Seeing, therefore, that clocks were improving, it was suggested by one
of Tycho’s compeers, the Landgrave of Hesse-Cassel, that by an
instrument arranged something like Fig. 18, it would be possible to
determine the exact position of any body in the heavens when examined
out of the meridian, and so they got again to extra-meridional
observations.
The instrument used by Tycho Brahe for the purpose, called the _Quadrans
Maximus_, is represented in Fig. 18. In this there is the quadrant B, D,
one pointer being placed, as shown at the bottom, near H, and the other
at the top, C. These pointers or sights were directed at the star by
moving the arm C, H, on the pivot A, and turning the whole arm and
divided arc round on the axis N, R. The altitude of the star is then
read off on the quadrant B, D, and the azimuth, or number of degrees
east or west of the north and south line, is then read off on the circle
Q, R, S. The screws Y, Y, served to elevate the horizontal circle, and
level it exactly with the horizon, and the plummets W and V, hanging
from G, were to show when the circle was level or not; for the part A,
G, being at right angles to the circle should be upright when the circle
is level, so that if A, G, is upright in all positions when moved round
the circle in azimuth, the circle is horizontal.
Here, then, is an instrument very different in principle from what we
had before. In this case the heavens are viewed from the most general
standpoint we can obtain—the horizon; but observations such as these
refer to the position of the place of observation absolutely, without
any reference to the position of the body with respect to the equator or
the ecliptic; but knowing the latitude of the place of observation _and
the time_, it was possible for a mathematical astronomer to reduce the
co-ordinates to right ascension and declination, and so actually to look
at the position of these bodies with reference to the celestial sphere.
Tycho also had various other instruments of the same kind, differing
only in the position of the quadrant D, B, and of the circle on which
the azimuth was measured. These instruments are the same in principle as
our modern alt-azimuth, which will be described hereafter, one form
having a telescope and the other being without it.
[Illustration:
FIG. 19.—Tycho’s Sextant.
]
Fig. 19 is yet another very important instrument invented by Tycho
Brahe; it is the prototype of our modern much used sextant. It was used
by Tycho Brahe for determining the distance from one body to another in
a direct line; a star or the moon, say, was observed by the pointers C,
A, while another was observed by the pointers N, A, by another observer.
The number of degrees then between N and C gave the angular distance of
the two bodies observed. This instrument was mounted at E, so that it
could be turned into any position. Not only then had this instrument its
representative in our present sextant, but it was used in the same way,
not requiring to be fixed in any one position. We also find represented
in Tycho Brahe’s book another form of the same instrument, the sight A
being next the observer, instead of away from him, so that he could
observe the two stars through the sights N and C without moving the eye.
In this form only one observer was required instead of two as in the
last.
There was also another instrument, Fig. 6, used by this great
astronomer, very similar to Ptolemy’s parallactic rules, used for
measuring zenith distances, or the distances of stars from the part
exactly overhead. The star or moon was observed by the sights H, I, and
the angle from the upright standard D, K, given by divisions on the rod
E, F, D, E being placed exactly upright by a plummet, and being also
able to turn on hinges at B and C, any part of the sky could be reached.
There is one more of his instruments that needs notice—he had so many of
all kinds that space will not allow reference to more than a very few.
This one was for measuring the altitudes of the stars as they passed the
meridian; it is a more convenient form of the mural quadrant, and
instead of a hole in the wall, there are sights on a movable arm,
working over a divided quadrant fixed in the plane of the meridian, just
like the quadrant outside the horizontal circle, so the observer had no
reason to move up or down according as the star was high or low.
Here then ends the pre-telescopic age. Tycho was one of the very last of
the distinguished astronomers who used instruments without the
telescope. We began with the horizon, and we have now ended with the
meridian. We also end with a power of determining the position of a
heavenly body to ten seconds of space, the instrument of the Greeks
reading to 10´ and those of Tycho to 10˝.
We began with the immovable earth fixed in the midst of the vault of the
sky, and on this assumption Tycho Brahe made all his observations, which
ended in enabling Kepler to give us the true system of the world, which
was the requisite basis for the crowning triumph of Newton.
BOOK II.
_THE TELESCOPE._
CHAPTER V.
THE REFRACTION OF LIGHT.
It is difficult to give the credit of the invention of the telescope to
any one particular person, for, as in the case of most instruments, its
history has been a history of improvements; and whether we should give
the laurel to Jansen, Baptista Porta, Galileo or to others whose names
are unknown, is an invidious task to decide; we will therefore not enter
in any way into the question, interesting though it be, as to who was
the inventor of the “optick tube,” as the telescope was called by its
first users.
The telescope is not a thing in the ordinary sense—it is a combination
of things, the things being certain kinds of lenses, concave and convex,
known and used as spectacles long before they were combined to form the
telescope.
The first telescopes depended on the refraction of light; others, to
which attention will be called in a future chapter, depended on
reflection.
[Illustration:
FIG. 20.—View and Section of a Prism.
]
In order to understand the action of a lens, it is necessary to
understand the action of a prism. By the aid of Fig. 20 the action of
the lenses of which telescopes are constructed will be understood. A
prism is a piece of glass, or other transparent substance, the sides of
which are so inclined to each other that its section is a triangle, and
its action on light passing through it is to change the direction of the
course of the beam. If we examine Fig. 21 we shall understand the action
clearly. It is a known law, that when a beam of light falls obliquely on
the surface of a medium more dense than that through which it has been
passing, its direction is changed to a new one, nearer the line drawn at
right angles to that surface, railed the normal. For instance, the ray
S, I, falling on the prism at I, is bent into the course I, E, which is
in a direction nearer to that of N, I, produced inside the prism. On
emerging, the reverse takes place, and the ray is bent away from the
normal E, N´, and takes the course E, R. In the second diagram, Fig. 21,
the ray S, I, called the incident ray, coincides with the normal to the
surface, so it is not refracted until it reaches the second surface,
when it has its path changed to E, R, instead of taking its direct
course shown by the dotted line. This bending of the ray is very plainly
shown with an electric lamp and screen. If a trough with parallel sides
be placed so as to intercept part of the light coming from the electric
lamp, so that part shall pass through it and part above, we have the
image of the hole in the diaphragm of the lantern on the screen
unchanged. Now, if the trough be filled with water, no difference
whatever is made in the position of the light on the screen, because the
water, which is denser than the air, is contained in a trough with
parallel sides; but by opening the sides like opening a book, or by
interposing another trough with inclined sides, shaped like a =V=, that
parallelism is destroyed, and then the light passing through it will be
deflected upwards from its original course, and will fall higher on the
screen; by opening the sides more and more, one is able to alter the
direction of the light passing through the prism, which has been
constructed by destroying the parallelism of the two sides.
[Illustration:
FIG. 21.—Deviation of Light in Passing at Various Incidences through
Prisms of Various Angles.
]
The refraction of light then depends upon the density of the substance
through which it passes, on the angle of incidence of the ray, on the
angle of the prism, and also on the colour of the light, about which we
shall have something to say presently.
Let us now pass from the prism to the lens; for having once grasped the
idea of refraction there will be no difficulty in seeing what a lens
really is.
With the prism just considered, placed so that a vertical section is
represented by a =V=, a ray is thrown upwards; if another similar prism
be placed with its base in contact with the base of the other, and its
apex upwards, so that its section will be represented by a =V= reversed,
=Ʌ=, it is clear this will turn the rays downwards, so that the rays, on
emerging from both prisms will tend to meet each other, as shown, in
Fig. 22, where one ray is turned down to the same extent that the other
is turned up; so that by the combination of two prisms the two rays are
brought to a point, which is called a _focus_. Now, if instead of
putting the prisms base to base, they are put apex to apex, a contrary
action takes place, and by this means one is able to cause two rays of
light to diverge instead of converging, so that the prisms, placed apex
to apex, cause the rays to diverge, and when placed base to base they
cause the light to converge.
[Illustration:
FIG. 22.—Convergence of Light by Two Prisms Base to Base.
]
If instead of having two prisms merely, there be taken a system having
different angles at their apices, and from each prism there be cut a
section, beginning by cutting off the apex of the most powerful prism, a
slice from below the apex of the next, and a slice below the
corresponding part of the next, and so on; and then if these slices be
laid on each other so as to form a compound prism, and another similar
prism be placed with its base to this one, we get what is represented in
Fig. 23. These different slices of prisms become more and more
prismatic, that is, they form parts of prisms of greater angle, as they
approach the ends. We can imagine a section of such a system as thin as
we please. Suppose we had such a section and put it in a lathe, rotating
it on the axis A B, we should describe a solid figure, and if we suppose
all the angles rounded off, so that it is made thinner and thinner as we
recede from the centre, the prism system is turned into a lens having
the form represented in Fig. 24. In a similar manner, lenses thinner in
the middle than at the edges, called concave lenses, can he constructed,
some forms of which are represented in section in Fig. 25. It is also
obvious that convex lenses of all curves and combinations of curves can
be made, some of which appear in Fig. 26.
[Illustration:
FIG. 23.—Formation of a Lens from Sections of Prisms.
]
[Illustration:
FIG. 24.—Front View and Section of a Double Convex Lens.
]
[Illustration:
FIG. 25.—Double Concave, Plane Concave, and Concavo-Convex Lenses.
]
The action of such lenses upon the light proceeding from any source may
now be considered. If there is a parallel beam proceeding from a lamp,
or from the sun, and it falls on the form of lens, called a convex lens,
which bulges out in the middle, we learn from Fig. 27, that the upper
part acts like the upper prism just considered and turns the light down,
and the lower acts in the reverse manner and turns the light up, and the
sides act in a similar manner; and as the inclination of the surfaces of
the lens increases as we approach the edge, the rays falling on the
parts near the edge are turned out of their course more than those
falling near the centre, so that we have the rays converged to a point
F, called the focus of the lens; and as the rays from an electric lamp
are generally rendered parallel by means of the lenses in the lantern,
called the condensers, the rays from such a lamp falling on a convex
lens will come to a focus at just the same distance from the lens,
called its principal focal length as they would do if they came from the
sun or stars.
[Illustration:
FIG. 26.—Double Convex, Plane Convex, and Concavo-Convex Lenses.
]
[Illustration:
FIG. 27.—Convergence of Rays by Convex Lens to Principal Focus.
]
So far we have brought rays to a focus, and on holding a piece of paper
at the focus of the convex lens, as just mentioned, there appears on it
a spot of light; and every one knows that if this experiment be
performed with the sun, one brings all the rays falling on the lens
almost to a point, and the longer waves of light will set fire to the
paper; and on this principle burning-glasses are constructed. If,
however, the rays are not parallel when falling on the lens, but
diverging, they are not brought to a focus so near the lens, and the
nearer the luminous source or object is, the further off will the light
be brought to a focus on the other side. If matters are reversed, and
the luminous source be placed in the focus, the rays of light, when they
leave the lens, will converge to the position of the original source; so
that there are two points, one on either side of the lens, which are the
foci of each other S, S´, Fig. 28, called conjugate foci; as one
approaches the lens the other recedes, and _vice versâ_, and it is
obvious that when the one approaches the lens so as to coincide with the
principal focus, the other recedes to an infinite distance, and the
emergent rays are parallel.
[Illustration:
FIG. 28.—Conjugate Foci or Convex Lens.
]
[Illustration:
FIG. 29.—Conjugate Images.
]
[Illustration:
FIG. 30.—Diagram explaining Fig. 29.
]
Now let us consider how images are formed. If we take a candle, Fig. 29,
and hold the lens a little distance away from it, then, on placing a
screen of paper just on the other side of the lens, there will be a
small flame depicted on it, an exact representation of the real flame:
and it is formed in this way: Consider the rays proceeding from the top
of the flame, which are represented separately in Fig. 30, where A
represents the top. One of these rays, A _a_, passing through the centre
of the lens _o_, will he unaffected because the surfaces through which
it passes are parallel to each other; and we know from the property of
the lens that all the other rays from A will, on passing through it, be
brought to a focus somewhere on A _a_, depending on the curvature of the
lens, and in the case of our lens it is at _a_.
[Illustration:
FIG. 31.—Dispersion of Rays by a Double Concave Lens.
]
In like manner also all the rays from B are brought to a focus at _b_,
and so on with all other parts of A, B, which in this case represents
the flame, each will have its corresponding focus; there being cones of
rays from every point of the object and to every point of the image,
having for their bases the convex lens, and we get an image or exact
representation of our candle flame. It will further be noticed that the
image _a b_ is smaller than A B, in proportion as the distance _a b_ is
less than A B; so that if we increase the focal length of the lens till
_a b_ is twice the distance away from the lens, it will become double
its present size.
If now the flame be brought nearer the lens, its image _a b_ becomes
indistinct; and we must move the screen further away in order to render
the image again clear; hence the place of the focus depends on the
distance of the object, and the candle and its image must correspond to
two conjugate foci.
[Illustration:
FIG. 32.—Horizontal Section of the Eyeball. _Scl_, the sclerotic coat;
_Cn_, the cornea; _R_, the attachments of the tendons of the recti
muscles; _Ch_, the choroid; _Cp_, the ciliary processes; _Cm_, the
ciliary muscle; _Ir_, the iris; _Aq_, the aqueous humour; _Cry_, the
crystalline lens; _Vi_, the vitreous humour; _Rt_, the retina; _Op_,
the optic nerve; _Ml_, the yellow spot.
]
If now rays be passed from the lantern or sun through a concave lens,
Fig. 31, they are not brought to a focus, but are dispersed and travel
onwards, as if they came from a point, F, which is called its virtual
focus; and if rays are first converged by a convex lens, and then,
before they reach the focus are allowed to fall on a concave one, we
can, by placing the lenses a certain distance apart, render the
converging rays again parallel; or we can make them slightly divergent,
as if they came, not from an infinite distance, but from a point a foot
or two off. The application of this arrangement will appear hereafter.
What has now been said on the action of the convex lens will enable us
to consider the optical action of the eye, without which we do little in
astronomy. As to the way that the brain receives impressions from the
eye we need say nothing, for that belongs to the domain of physiology,
except indeed this, that an image is formed on the retina by a chemical
decomposition, brought about by the dissociating action of certain rays
of light in exactly the same way as on a photographic plate. Optically
considered, the eye consists of nothing more than a convex lens, _Cry_,
Fig. 32, and a surface, _Rt_, extending over the back of the eyeball,
called the retina, on which the objects are focussed, but the rays of
light falling on the cornea _Cn_, are refracted somewhat, so that it is
not quite true to say that the crystalline lens does all the work, but
for our present purpose it is sufficiently correct, and we shall
consider their combined action as that of a single lens.
The outer coat of the eyeball, shown in section in Fig. 32, is called
the sclerotic, with the exception of that more convex part in front of
the eye, called the cornea; behind this comes the aqueous humour and
then the iris, that membrane of which the colour varies in different
people and races. In the centre of this is a circular aperture called
the pupil, which contracts or expands according to the brightness of the
objects looked at, so that the amount of light passing into the eye is
kept as far as possible constant. Close behind the iris comes the
crystalline lens, the thickness of which can be altered slightly by the
ciliary muscle. In the space between the lens and the back of the eye is
a transparent jelly-like substance called the vitreous humour. Finally
comes the retina, a most delicate surface chiefly composed of nerve
fibres. It is on this surface, that the image is formed by the curved
surfaces of the anterior membranes, and through the back of the eyeball
is inserted the mass of filaments of the optic nerve making
communication with the brain; these filaments on reaching the inside of
the eye spread out to receive the impressions of light.
Here then, we have a complete photographic camera; the crystalline lens
and cornea, separated by the aqueous humour, representing the
compound-glass camera lens, and the retina standing in the place of the
sensitive plate.
[Illustration:
FIG. 33.—Action of Eye in Formation of Images.
]
The path of the light forming an image on the retina is shown in Fig.
33, where A B is the object, and _a b_ its image, formed in exactly the
same way as the image of the candle-flame which we have just considered;
in fact, the eye is exactly represented by a photographic camera, the
iris acting in the same manner as the stops in the lens, limiting its
available area, and by contracting, decreasing the amount of light from
bright objects, and at the same time increasing the sharpness of
definition, for in the case of the eye, the luminous rays obey the known
laws of propagation of light in media of variable form and density, and
we have only simple refraction to deal with. The next matter to be
considered is that the nearer the object A B is to the eye, the larger
is the angle A, _o_, B, and also _a_, _o_, _b_, and therefore the image
on the retina is larger; but there is a limit to the nearness to which
the object can be brought, for, as we found with the candle, the
distance between the lens and the image must be increased as the object
approaches, or the curvature of the lens itself must be altered, for if
not the ray forming the rays from each point of the object will be too
divergent for the lens to be able to bring them to a focus. Now in the
eye there is an adjustment of this sort, but it is limited so that
objects begin to get indistinct when brought nearer the eye than perhaps
six inches, because the rays become too divergent for the lens to bring
them to a focus on the retina, and they tend to come to a focus behind
the retina, as in Fig. 34; but we may assist the eye lens by using a
glass convex lens in front of it, between it and the object. It is for
this reason that spectacle glasses are used to enable long-sighted
persons to see clearly.
[Illustration:
FIG. 34.—Action of a Long-sighted Eye.
]
We may also use a much stronger lens, and so get the object very near
the lens and eye, as in Fig. 35, where _a b_ is the object so near the
eye that, if it were not for the lens L, its image would not come to a
focus on the retina at all. The effect of the lens is to make the rays
proceeding in a cone from _a_ and _b_ less divergent, so that after
passing through it, they proceed to the eye-lens as if they were coming
from the points A and B, a foot or so away from the eye, and so the
object _a b_ appears to be a much larger object at a greater distance
from the eye.
[Illustration:
FIG. 35.—1. Diagram showing path of rays when viewing an object at an
easy distance. 2. Object brought close to eye when the lens L is
required to assist the eye-lens to observe the image when it is
magnified.
]
A convex lens then has the power of magnifying objects when brought near
the eye, and its action is clearly seen in Fig. 35, where the upper
figure shows the arrow at as short a distance from the eye as it can be
seen distinctly with an ordinary eye, and the lower figure shows the
same arrow brought close to the eye, and rendered distinctly visible by
the lens when a magnified image is thrown on the retina, as if there was
a real larger arrow somewhere between the dotted lines at the ordinary
distance of distinct vision. It is also obvious that the nearer the
object can be brought to the eye-lens the more magnified it is, just as
an object appears larger the nearer it is brought to the unaided eye.
We have been hitherto dealing with the effect of a _convex_ lens on the
rays passing to the eye. We will now deal with a _concave_ one.
We found that the power of adjustment of the normal eye was sufficient
to bring parallel rays, or those proceeding from a very distant object,
and also slightly diverging rays, to a focus on the retina. Parallel or
slightly divergent rays are most easily dealt with, and slightly
convergent rays can also be focussed on the retina; but if the eye-lens
is too convex, as is the case with short-sighted people, Fig. 36, a
concave lens of slight curvature is used to correct the eye-lens and
bring the image to a focus on the retina instead of in front of it.
[Illustration:
FIG. 36.—Action of Short-sighted Eye.
]
If the rays are very convergent, as those proceeding from a convex lens
and coming to a focus, the lens of a normal eye will bring them to a
focus far in front of the retina, as if the person were very
short-sighted. But by interposing a sufficiently powerful concave lens
the rays are made less convergent or parallel, and the eye-lens brings
them to a focus on the retina, as if they came from a near object, so
the use of convex and concave lenses placed close to the eye is to
render divergent or convergent rays nearly parallel, so that the
eye-lens can easily focus them, and therefore one of the conditions of
the telescope is that the rays which come into our eye shall be parallel
or nearly so.
CHAPTER VI.
THE REFRACTOR.
In the telescope as first constructed by Galileo there are two lenses,
so arranged that the first, a convex one, A B Fig. 37, converges the
rays, while the second, C D, a concave one, diverges them, and renders
them parallel, ready for the eye; the rays then, after passing through C
D, go to the eye as if they were proceeding along the dotted lines from
an object M M, closer to the eye instead of from a distant object, and
so, by means of the telescope, the object appears large and close.
[Illustration:
FIG. 37.—Galilean Telescope. A B, convex lens converging rays; C D,
concave lens sending them parallel again and fit for reception by
the eye.
]
It is this that constitutes the telescope. But nowadays we have other
forms, as we are not content with the convex combined with the concave
lens, and modern astronomy requires the eyepiece to be of more elaborate
construction than those adopted by Galileo and the first users of
telescopes, although this form is still used for opera-glasses and in
cases where small power only is required. Having the power of converging
the light and forming an image by the first convex lens or object glass,
as we saw with the candle flame (Fig. 29), and an opportunity of
enlarging this image by means of a magnifying or convex eyepiece, we can
bring an image of the moon, or any other object, close to the eye, and
examine it by means of a convex lens, or a combination of such lenses.
So we get the most simple form of refracting telescopes represented in
Fig. 38, in which the rays from all points of the object—let us take for
instance an arrow—are brought to a focus by the object-glass A, forming
there an exact representation of the real arrow. In the figure two cones
of rays only are delineated, namely, those forming the point and feather
of the arrow, but every other point in the arrow is built up by an
infinite number of cones in the same way, each cone having the
object-glass for its base. By means of the lens C we are able to examine
the image of the arrow B, since the rays from it are thus rendered
parallel, or nearly so, and to the eye they appear to come from a much
larger arrow at a short distance away. We can draw their apparent
direction, and the apparent arrow (as is done in Fig. 37 by the dotted
lines), and so the object appears as magnified, or, what comes to the
same thing, as if it were nearer.
The difference between this form and that contrived by Galileo is this:
in the latter the rays are received by the eyepiece while converging,
_and rendered parallel by a concave lens_, while in the former case the
rays are received by the eyepiece on the other side of the focus, where
they have crossed each other and are diverging, _and are rendered
parallel by a convex lens_.
We may now sum up the use of the eye-lens. The image is brought to a
focus on the retina, because the object is some distance off, and the
rays from every point, (as from A and B, Fig. 35), on reaching the eye,
are nearly parallel; but it is not necessary that they should be
absolutely parallel, as the eye is capable of a small adjustment, but if
one wishes to see an object much nearer (as in the lower figure), it is
impossible to do it unless some optical aid is obtained, for the rays
are too divergent, and cannot be brought to a focus on the retina. What
does that optical aid effect? It enables us to place the object in the
focus of another lens which shall make the rays parallel, and fit for
the lens of the eye to focus on the retina, and since the object can by
this means be brought close to the lens and eye, it forms a larger image
on the retina. Dependent on this is the power of the telescope.
[Illustration:
FIG. 38.—Telescope. A, object-glass, giving an image at B; C, lens for
magnifying image B.
]
We shall refer later on to the mechanical construction of the telescope.
Here it may be merely stated that the smaller ones consist of a brass
tube, the object-glass held in a brass ring screwed in at one end of the
tube and a smaller tube carrying the eyepiece sliding in and out of the
large tube and sometimes moved by a rack and pinion motion, at the
other. The larger ones as mounted for special uses will also be fully
described farther on.
[Illustration:
FIG. 39.—Diagram Explaining the Magnifying Power of Object-glass.
]
The power of the telescope depends on the object-glass as well as on the
eyepiece; if we wish to magnify the moon, for instance, we must have a
large image of the moon to look at, and a powerful lens to see that
image. By studying Fig. 39 the fundamental condition of producing a
large image by a lens will be seen. Suppose we wish to look at an object
in the heavens, the diameter of which is one degree; if the lens throws
an image of that body on to the circumference of a circle of 360 inches,
then, as there are 360 degrees in a circle, that image will cover one
inch; let the circle be 360 yards, and the image of a body of one degree
will cover one yard; and to take an extreme case and suppose the
circumference of the circle to be 360 miles, then the image will be one
mile in diameter.
This is one of the principal conditions of the action of the
object-glass in enabling us to obtain images which can be magnified by a
lens, and by such magnification made to appear nearer to us than they
are.
Galileo used telescopes which magnified four or five times, and it was
only with great trouble and expense that he produced one which magnified
twenty-three times.
Now, after what has been said of focal length, one will not be surprised
to hear of those long telescopes produced in the very early days, a few
of which are still extant; these show as well as anything the enormous
difficulty which the early employers of telescopes had to deal with in
the material they employed. One can scarcely tell one end of the
telescope from the other; all the work was done in some cases by an
object-glass not more than half an inch in effective diameter.
It might be supposed that those who studied the changes of places and
the positions of the heavenly bodies would have been the first to gain
by the invention of the telescope, and that telescopes would have been
added to the instruments already described, replacing the pointers. For
such a use as this a telescope of half an inch aperture would have been
a great assistance. But things did not happen so, because the invention
of the telescope gave such an impetus to physical astronomy that the
whole heavens appeared novel to mankind. Groups of stars appeared which
had never been seen before; Jupiter and Saturn were found to be attended
by satellites; the sun, the immaculate sun, was determined after all to
have spots, and the moon was at once set upon and observed with
diligence and care; so that there was a very good reason why people
should not limit the powers of the telescope to employing it to
determine positions only. The number of telescopes was small, and they
could not be better employed than in taking a survey of all the
marvellous things which they revealed. It was at this time that the
modern equatorial was foreshadowed. Galileo, and his contemporaries
Scheiner and others, were observing sun-spots, and the telescope, Fig.
40, which Scheiner arranged, a very rough instrument, with its axis
parallel to the earth’s axis, and allowed to turn so that Scheiner might
follow the sun for many hours a day, was one of the first. This
instrument is here reproduced, because it was one of the most important
telescopes of the time, and gathered in to the harvest many of the
earliest obtained facts.
[Illustration:
FIG. 40.—Scheiner’s Telescope.
]
Since by means of little instruments like these, so much of beauty and
of marvel could be discovered in the skies, it is no wonder that every
one who had anything to do with telescopes strained his nerves to make
them of greater power, by which more marvels could be revealed.
It was not long before those little instruments of Scheiner expanded
into the long telescopes to which reference has been made. But there was
a difficulty introduced by the length of the instrument. The length of
the focus necessary for magnification spread the light over a large
area, and therefore it was necessary to get an equivalent of light by
increasing the aperture of the object-glasses in order that the object
might be sufficiently bright to bear considerable magnification by the
eyepiece,—and now arose a tremendous difficulty.
One part of refraction, namely, deviation, enables us to obtain, but the
other half, dispersion, prevents our obtaining, except under certain
conditions, an image we can make use of. By dispersion is meant the
property of splitting up ordinary light into its component colours, of
which we shall say more in dealing with spectrum analysis. If we wish to
get more light by increasing the aperture of the telescope, the
deviation of the light passing through the edge of the object-glass is
increased, and with it the dispersion, the result of this increase of
deviation. If the light of the sun be allowed to fall through a hole
into a darkened chamber, and then through a prism, Fig. 41, it is
refracted, and instead of having an exact reproduction of the bright
circle we have a coloured band or spectrum. The white light when
refracted is not only driven out of its original course—deviated—but it
is also broken up—dispersed—into many colours. We have a considerable
amount of colour; and this the early observers found when they increased
the size of their telescopes, for it must be remembered that a lens is
only a very complex prism.
[Illustration:
FIG. 41.—Dispersion of Light by Prism.
]
First, they increased the size by enlarging the object-glasses, and not
the focal length; but when they had done that they had that extremely
objectionable colour which prevented them seeing anything well. The
colour and indistinctness came from an overlapping of a number of
images, as each colour had its own focus, owing to varying
refrangibilities. They found, therefore, that the only _effective_ way
of increasing the power of the telescope was by increasing its focal
length so as to reduce the _dispersing_ action as much as possible, and
so enlarging the size of the actual image to be viewed, without at the
same time increasing the angular deviation of the rays transmitted
through the edges of the lens. The size of the image corresponding to a
given angular diameter of the object is in the direct proportion of the
focal length, while the flexure of the rays which converge to form any
point of it is in the same proportion inversely.
[Illustration:
FIG. 42.—Diagram Showing the Amount of Colour Produced by a Lens.
]
To take an example. In the case of an object-glass of crown-glass, the
space over which the rays are dispersed is one-fiftieth of the distance
through which they are deviated, and it will be seen by reference to
Fig. 42, that if the red rays are at R, and the blue at B, the distance
A B is fifty times R B, and as these distances depend on the diameter of
the lens only, we can increase the focal length, and so increase the
size of the image without altering the dispersion R B, and so throw the
work of magnifying on the object-glass instead of on the eyepiece, which
would magnify R B equally with the image itself. So that in that time,
and in the time of Huyghens, telescopes of 100, 200, and 300 feet focal
length were not only suggested but made, and one enthusiastic stargazer
finished an object-glass, the focal length of which was 600 feet.
Telescopes of 100 and 150 feet focal length were more commonly used. The
eyepiece was at the end of a string, and the object-glass was placed
free to move on a tall pole, so that an observer on the ground, by
pulling the string, might get the two glasses in a line with the object
which he wished to observe.
So it went on till the time of Sir Isaac Newton, who considered the
problem very carefully—but not in an absolutely complete way. He came to
the conclusion, as he states in his _Optics_, that the improvement of
the refracting telescope was “desperate;” and he gave his attention to
reflecting telescopes, which are next to be noticed.
Let us examine the basis of Sir Isaac Newton’s statement, that the
improvement of the refracting telescope was desperate. He came to the
conclusion that in refraction through different substances there is
always an unchanged relation between the amount of dispersion and the
amount of deviation, so that if we attempt to correct the action of one
prism by another acting in an opposite direction in order to get white
light, we shall destroy all deviation. But Sir Isaac Newton happened to
be wrong, since there are substances which, for equivalent deviations,
disperse the light more or less. So by means of a lens of a certain
substance of low dispersive power we can form an image slightly
coloured, and we can add another lens of a substance having a high
dispersive power and less curvature and just reverse the dispersion of
the first lens without reversing all its deviating power.
The following experiments will show clearly the application of this
principle. We first take two similar prisms arranged as in Fig. 43. The
last through which the light passes corrects the deviation and
dispersion of the first. We then take two prisms, one of crown glass and
the other of flint glass, and since the dispersion of the flint is
greater than that of the crown, we imagine with justice that the
flint-glass prism may be of a less angle than the other and still have
the same dispersive power, and at the same time, seeing that the angles
of the prisms are different, we may expect to find that we shall get a
larger amount of deviation from the crown-glass prism than from the
other.
[Illustration:
FIG. 43.—Decomposition and Recomposition of Light by Two Prisms.
]
If then a ray of light be passed through the crown-glass prism, we get
the dispersion and deviation due to the prism A Fig. 44, giving a
spectrum at D. And now we take away the crown glass and place in its
stead a prism of flint glass inverted; the ray in this instance is
deviated less, but there is an equal amount of colouring at D´. If now
we use both prisms, acting in opposite directions, we shall be able to
get rid of the colours, but not entirely compensate the deviation. We
now place the original crown-glass prism in front of the lantern and
then interpose the flint-glass prism, so that the light shall pass
through both. The addition of this prism of flint, of greater dispersive
power, combines, or as it were shuts off, the colour, leaving the
deviation uncompensated, so that we get an uncoloured image of the hole
in front of the lantern at D˝. This is the foundation of the modern
achromatic telescope.
[Illustration:
FIG. 44.—Diagram Explaining the Formation of an Achromatic Lens. A,
crown-glass prism; B, flint-glass prism of less angle, but giving
the same amount of colour; C, the two prisms combined, giving a
colourless yet deviated band of light at D˝.
]
Another method of showing the same thing is to bring a V-shaped
water-trough into the path of the rays from the lantern; then, while no
water is in it, the beam of light passing through it is absolutely
uncoloured and undeviated. In this case we have no water inclosed by
these surfaces, and it is not acting as a prism at all. If, however, a
prism of flint glass, a substance of high dispersive power, is
introduced into it, with its refracting edge upwards, it destroys the
condition we had before, and we have a coloured band on the screen,
because the glass that the prism is made of has the faculty of strong
dispersion in addition to its deviation. We can get rid of that
dispersion by throwing dispersion in a contrary direction by filling up
the trough with water, and so making, as it were, a water prism on
either side of the glass one, water being a substance of low dispersive
power. We have a colourless beam thrown on the screen, which is deviated
from the original level, because the water prisms are together of a
greater angle than the glass one.
The experiments of Hall and Dolland have resulted in our being able to
combine lenses in the same way that we have here combined prisms,
bearing in mind what has been said in reference to the action of lenses
being like that of so many prisms; and we may consider two lenses, one
of crown and the other of flint glass, Fig 45. The crown glass being of
a certain curvature will give a certain dispersion; the flint glass, in
consequence of its great dispersive power, will require less curvature
to correct the crown glass. What will happen will be this: assuming the
second lens to be away, the rays will emerge from the first (convex)
lens and form a coloured image at A. But if the second flint-glass
concave lens be interposed it will, by means of its action in a contrary
direction, undo all the dispersion due to this first lens and a certain
amount of deviation, so that we shall get the combination giving an
almost colourless image at B.
[Illustration:
FIG. 45.—Combination of Flint- and Crown-glass Lenses in an Achromatic
Lens.
]
It will not be absolutely colourless, for the reasons which will be now
explained. If light be passed through different substances placed in
hollow prisms, or through prisms of flint and crown glass, and the
spectra thus produced be observed, we find there are important
differences. When we expand the spectra considerably, we see that the
action of these different substances is not absolutely uniform, some
colours extending over the spectrum further than others. In the case of
one kind of glass the red end of the spectrum is crushed up, while in
the other we have the red end expanded.
This is called the _irrationality of the spectrum_ produced by prisms of
different substances. The crown and the flint-glass lenses—and for
telescopes we must use such glass—give irrational spectra, so that the
achromatic telescope is not absolutely achromatic, in consequence of
this peculiarity; for if R, G, B, Fig. 46, are the centres of the red,
green, and violet in the spectrum given by a prism composed of the glass
of which one lens is made, and R´, G´, B´, are those of the other, if
the lenses are placed so as to counteract each other, and are of such
curves that the reds and violets are combined, the greens will remain
slightly outstanding. Suppose, as in the drawing, the second prism
disperses the violet as much as the first one does, then, when these are
reversed they will exactly compensate red and violet. But the second one
acts more strongly on the green than the first, which will be
over-compensated; and if we weaken the second prism so that the green
and red are correct, then the violet will be slightly outstanding, which
in practice is not much noticed, except with a very bright object when
there is always outstanding colour.
[Illustration:
FIG. 46.—Diagram Illustrating the Irrationality of the Spectrum.
]
This is, however, not a matter of any very great importance for ordinary
work, since the visual rays all lie in the neighbourhood of the yellow,
so that opticians take care to correct their lenses for the rays in this
part of the spectrum, and at the same time, as a matter of necessity,
over-correct for the violet rays, that is, reverse the dispersion of the
exterior lens, so that the violet rays have a longer instead of a
shorter focus than the red, and, therefore, in looking at a bright
object, such as a first magnitude star, it appears surrounded by a
violet halo; with fainter objects the blue light is not of sufficient
intensity to be visible. It is, therefore, always preferable to correct
for the most visible rays and leave the outstanding violet to take care
of itself; but nevertheless various proposals have been made to get rid
of it. Object-glasses containing fluids of different kinds have been
tried, but they have never become of any practical value, and it does
not seem probable that they ever will.
In order to get rid of the outstanding violet colour when the remainder
of the spectrum was corrected, Dr. Blair constructed object-glasses the
space between the lenses of which were filled with certain liquids,
generally a solution of a salt of mercury or antimony, with the addition
of hydrochloric acid; for in the spectrum given by the metallic solution
the green is proportionally nearer the red than is the case with the
spectrum produced by hydrochloric acid, so that by the adjustment of the
different solutions he exactly destroyed the outstanding colour of the
ordinary combination. In this way Sir John Herschel tells us he was able
to construct lenses of three inches aperture and only nine inches focal
length, free from chromatic and spherical aberration.
It was proposed by Mr. Barlow to correct a convex crown-glass lens for
chromatic aberration by a hollow concave lens containing bisulphide of
carbon, a highly dispersive fluid, having double the power of flint
glass. This lens was placed in the cone of rays between the object-glass
and the eyepiece. Its surfaces were concavo-convex, calculated to
destroy spherical aberration, and its distance from the object-glass was
varied until exact achromatism was obtained. A telescope of this
principle of eight inches aperture was made by Mr. Barlow, which proved
highly satisfactory. In the early part of the last century it was
proposed by Wolfius to interpose between the object-glass and eyepiece a
concave lens in order to give greater magnification of the image, with a
slight increase of focal length; if an ordinary lens be used the
achromatism of the images given by the object-glass will be destroyed.
Messrs. Dolland and Barlow, however, proposed to make the concave lens
achromatic, so that the image is as much without colour when the lens is
used as without it. Mr. Dawes found such a lens to work extremely well.
These lenses, usually called “Barlow lenses,” are generally made about
one inch in diameter, and by varying their distance from the eyepiece
the image is altered in size at pleasure.
In the reflecting telescope, with which we will now proceed to deal,
there is an absence of colour; but the reflector is not without its
drawbacks, for there are imperfections in it as great as those we have
been considering in the case of the refractor.
CHAPTER VII.
THE REFLECTION OF LIGHT.
We have now dealt with the refraction of light in general, including
deviation and dispersion, in order to see how it can assist us in the
formation of the telescope; and we have shown how the chromatic effect
of a single lens can be got rid of by employing a compound system
composed of different materials, and so we have got a general idea of
the refracting telescope. We have now to deal with another property of
light, called reflection; and our object is to see how reflection can
help us in telescopes.
In the case of reflection we get the original direction of the ray
changed as in the case of refraction, but the deviation is due to a
different cause. Take a bright light, a candle will do, and a mirror
fixed so that the light falls on its surface and is thrown back to the
eye, Fig. 47, we see the image of the candle apparently behind the
mirror; the rays of light falling on the mirror are reflected from it at
exactly the same angle at which they reach it. This brings us in the
presence of the first and most important law of reflection; and it is
this, at whatever angle the light falls on a mirror, at that angle will
it be reflected. As it is usually expressed, the angle of incidence,
which is the angle made by the incident ray with an imaginary line drawn
at right angles to the mirror, called the normal, is equal to the angle
of reflection, that is, the angle contained by the reflected ray, and
the normal to the surface. In order, therefore, to find in what
direction a ray of light will travel after striking a flat polished
surface, we must draw a line at right angles to the surface at the point
where the ray impinges on it, then the reflected ray will make an angle
with the normal equal to that which the incident ray makes, or the
angles of incidence and reflection will be equal.
[Illustration:
FIG. 47.—Diagram Illustrating the Action of a Reflecting Surface.
]
Very simple experiments, which every one can make will show us the laws
which govern the phenomena of reflection. Let us employ a bath of
mercury for a reflecting surface, and for a luminous object a star, the
rays of which, coming from a distance which is practically infinite, to
the surface of the earth, may be considered exactly parallel. The
direction of the beams of light coming from the star, and falling on the
mirror formed by the mercury, is easily determined by means of a
theodolite, Fig. 48. If we look directly at the star, the line I´ S´ of
the telescope indicates the direction of the incident luminous rays, and
the angle S´ I´ N´, equal to the angle S, I, N, is the angle of
incidence, that is to say, that formed by the luminous ray with the
normal to the surface at the point of incidence.
[Illustration:
FIG. 48.—Experimental Proof that the Angle of Incidence = Angle of
Reflection.
]
In order to find the direction of the reflected luminous rays, we must
turn the telescope on its axis, until the rays reflected by the surface
of the mercury bath enter it and produce an image of the star. When the
image is brought to the centre of the telescope, it is found that the
angle R´ I´ N´ is equal to the angle of reflection N, I, R. Thus, in
reading the measure on the graduated circle of the theodolite the angle
of reflection can be compared with the angle of incidence.
Now, whatever may be the star observed, and whatever its height above
the horizon, it is always found that there is perfect equality between
these angles. Moreover, the position of the circle of the theodolite
which enables the star and its image to be seen evidently proves that
the ray which arrives directly from the luminous point and that which is
reflected at the surface of the mercury are both in the same vertical
plane.
Now this demonstrates one of the most important laws of reflection. The
laws of refraction do not deal directly with the angles themselves, but
with the _sines_ of the angles; in reflection the _angles_ are equal; in
refraction the _sines_ have a constant relation to each other.
So far we have dealt with plane surfaces, but in the case of telescopes
we do not use plane surfaces, but curved ones, so we will proceed at
once to discuss these.
[Illustration:
FIG. 49.—Convergence of Light by Concave Mirror.
]
[Illustration:
FIG. 50.—Conjugate Foci of Convex Mirror.
]
In Fig. 49, A represents a curved surface, such as that of a concave
mirror, the centre of curvature being C. Now we can consider that this
curved surface is made up of an infinite number of small plane surfaces,
and since all lines drawn from the centre, C, to the mirror, will be at
right angles to the surface at the points where they meet it, we find,
from our experiment with the plane mirror, that rays falling on the
mirror at these points will be reflected so that the angles on either
side of each of these lines shall be equal; so, for instance, in Fig.
49, we wish to find to what point the upper ray will be reflected, and
we draw a line from the centre, C, to the point where it falls on the
mirror, and then draw another line from that point making the angle of
reflection equal to that made by the incident ray, and we can consider
the small surface concerned in reflection flat, so that the ray will in
this case be reflected to F. If now we take any other ray, and perform
the same operation we shall find that it is also reflected _nearly_ to
F, and so on with all other parallel rays falling on the mirror; and
this point, F, is therefore said to be the focus of the mirror. If now
the rays, instead of falling parallel on the mirror, as if they came
from the sun or a very distant object, are divergent, as if they came
from a point S, Fig. 50, near the mirror, the rays approach nearer to
the lines drawn from the centre to the mirror, one of which is
represented by the dotted line; or, in other words, the angles of
incidence become reduced, and so the angles of reflection will also be
reduced, and the focus of the rays from S will approach the centre of
the mirror, and be at _s_; just so it will be seen that if an
illuminated point be at _s_, its focus will be at S, and these two
points are therefore called conjugate foci.
[Illustration:
FIG. 51.—Formation of Image of Candle by Reflection.
]
[Illustration:
FIG. 52.—Diagram explaining Fig. 51.
]
If a candle is held at a short distance in front of a concave mirror, as
represented in Fig. 51, its image appears on the paper between the
candle and the mirror, so that the rays from every point of the flame
are brought to a focus, and produce an image just as the image is
produced by a convex lens. If we study Fig. 52 the formation of this
image will be clearly understood. First we must note that the rays A, C,
_a_, and B, C, _b_, which pass through the centre of curvature of the
mirror C, will fall perpendicularly on the surface, and be reflected
back on themselves, so that the focus of the part a of the arrow will be
somewhere on A _a_, and that of B on B _b_, and by drawing another ray
we shall find it reflected to _a_, which will be the focus of the point
A, and so also by drawing another line from B, we shall find it is
reflected to _b_, which is the focus of the part B; and we might repeat
this process for every part of the arrow, and for every ray from those
parts. We now see that since the rays A _a_ and B _b_ cross each other
at C, the distance from _a_ to _b_ bears the same proportion to the
distance from A to B as their respective distances from the point C; or,
in other words, the image is smaller than the object in the same
proportion as the distance from the image to C is smaller than the
distance from the object to C. Now, in dealing with the stars, which are
at a practically infinite distance, the rays are parallel, and will be
brought to a focus half-way between the mirror and its centre of
curvature. In this case, therefore, the distance from the image to the
mirror is equal to that from the image to the centre, so that we can
express the size of the image by saying that it is smaller than the
object, in proportion as its distance from the mirror is smaller than
the distance of the object from C; and as it makes little difference
whether we measure the distance of the stars from C or from the mirror,
and as C is not always known, we can take the relation of the distances
of the object and image from the mirror as representing the
proportionate sizes of the two.
We will now consider the case of rays falling on a mirror curved the
other way, that is, a convex mirror. Let us consider the ray impinging
at D, Fig. 53, which would go on to C, the centre of the mirror. Now, as
C D is drawn from the centre, it is at right angles to the mirror at D,
and the ray L D, being in the same straight line on the opposite side,
will also be at right angles, and will be reflected back on itself. Now
take the ray I A, draw C E through A, then E A will be perpendicular to
the surface at A, and I A E will be the angle of incidence, and E A G
the angle of reflection, so that this ray A G will be reflected away
from L D, and so will all the other rays falling on the mirror as K B:
and if we continue the lines G A and H B backwards, they will meet at M,
and therefore the rays diverge from the mirror as if they came from a
point at M, and this point is called the virtual focus.
[Illustration:
FIG. 53.—Reflection of Rays by Convex Mirror.
]
So much for parallel rays. Next let us consider another case which
happens in the telescope, namely, where converging rays fall on a convex
mirror, as in Fig. 53, where we consider the light proceeding to the
mirror from a converging lens along the lines H B and G A, these will be
made parallel, at B K and A F, after reflection, and it is manifest that
by making the mirror sufficiently convex, these rays, tending to come to
a focus at M, could be rendered divergent; and if the curvature is
decreased by making the centre of curvature at a certain distance beyond
C, it will be seen at once by the diagram that these rays will after
reflection, converge towards L and will come to a focus in front of the
mirror at a point further in front than C is behind it, so that they
have been rendered less convergent only by the mirror in this supposed
case.
It will be seen from what has been stated here and in Chapter V., that
we get nearly the same results from reflection as we did from refraction
when we were considering the functions of glasses instead of mirrors;
that a concave mirror acts exactly as a convex lens, and _vice versâ_,
so that they can be substituted the one for the other. If we take a
mirror, and allow the light to fall on it from a lamp, no one will have
any difficulty in seeing that the mirror grasps the beam, and forms an
image which is seen distinctly in front of the mirror, just as one gets
an image from a convex lens behind it.
CHAPTER VIII.
THE REFLECTOR.
The point we have next to determine is how we can utilise the properties
of reflection for the purposes of astronomical observation. Many
admirable plans have been suggested. The first that was put on paper was
made by Gregory, who pointed out that if we had a concave mirror, we
should get from this mirror an image of the object viewed at the focus
in front of it, as in Fig. 51. Of course we cannot at once utilise this
focal image by using an eyepiece in the same way as we do in a
refractor, because the observer’s head would stop the light, and the
mirror would be useless, and all the suggestions which have been made,
have reference to obtaining the image in such a position that we are
able to view it conveniently.
Gregory, the Scottish astronomer above referred to, in 1663 suggested a
method, and it has turned out to be a good one, of utilizing reflection
by placing a small mirror D C, Fig. 54, on the other side of the focus A
of the large one, at such a distance that the image at A is again
focussed at B by reflection from the small mirror; and at B we get of
course an enlarged image of A. The rays of light proceeding to B would,
however, be intercepted by the large mirror, unless an aperture were
made in the large mirror of the size of the small one through which the
rays could pass and be rendered parallel by means of an eyepiece placed
just behind the large mirror. So that towards the object is the small
mirror C, and there is an eyepiece E, which enables the image of the
object to be viewed after two reflections, first from the large mirror
and then from the small one. Mr. Short (who made the best telescopes of
this construction, and did much for the optical science of the last
century) altered the position of the small mirror with reference to the
focus of the large one, by sliding it along the tube by a screw
arrangement, F, and so was enabled to focus both near and distant
objects without altering the eyepiece.
[Illustration:
FIG. 54.—Reflecting Telescope (Gregorian).
]
But before this was put into practice, Sir Isaac Newton (in 1666) made
telescopes on a totally different plan.
The eyepiece of the Newtonian telescope is at the side of the tube, and
not at the end, as in Gregory’s. We have next to inquire how this
arrangement is carried out, and, like most things, it is perfectly
simple when one knows how it is done. There is a large mirror at the
bottom of the tube as in the Gregorian, but not perforated, and the
focus of the mirror would be somewhere just in front of the end of the
tube. Now in this case we do not allow the beam to get to the focus at
all in the tube or in front of it; but before it comes to the focus it
is received on a small diagonal plane surface m, and thus it is at once
thrown outwards at right angles through the side of the tube, and comes
to a focus in front of an eyepiece, placed at the side, ready to be
viewed the same as an image from a refractor (Fig. 55).
[Illustration:
FIG. 55.—Newton’s Telescope.
]
The next arrangement is one which Mr. Grubb has recently rescued from
obscurity, and it is called the Cassegrainian form. It will be seen on
referring to that, Fig. 56, if the small mirror, C, were removed, the
rays from the mirror A B would come to a focus at F.
In the Gregorian construction a concave reflector was used outside that
focus (at C, Fig. 54), but Cassegrain suggested that if, instead of
using a concave reflector outside the focus, a reflector with a convex
surface were placed inside it, we should arrive at very nearly the same
result, provided we retain the hole in the large mirror. The converging
rays from A B will fall on the convex surface of the mirror C, which is
of such a curvature and at such a distance from F, the focus of the
large mirror, that the rays are rendered less converging, and do not
come to a focus until they reach D, where an image is formed ready to be
viewed by the eyepiece E. It appears from this, that the convex mirror
is in this case acting somewhat in the same manner as the concave lens
does in the Galilean telescope.
[Illustration:
FIG. 56.—Reflecting Telescope (Cassegrain).
]
[Illustration:
FIG. 57.—Front View Telescope (Herschel).
]
Then, lastly, we have the suggestion which Sir William Herschel soon
turned into more than a suggestion. The mirror M in this arrangement is
placed at the bottom of the tube as in the other forms, but, instead of
being placed flat on the bottom it is slightly tipped, so that if the
eyepiece is placed at the edge of the extremity of the tube all parallel
rays falling on the mirror are reflected to the side of the tube at the
top where the eyepiece is, instead of being reflected to a convex or
other mirror in the middle.
This is called the front view telescope, and it enabled Sir William
Herschel to make his discoveries with the forty-feet reflector. With
small telescopes this form could not be adopted, as the observer’s head
would cover some part of the tube and obstruct the light, but with large
telescopes the amount of light stopped by the head is small in
proportion to what would be lost by using a small mirror.
These are in the main the four methods of arranging reflecting
telescopes—the Gregorian, the Cassegrainian, the Newtonian, and the
Herschelian.
In order to make large reflectors perfect—large telescopes of short
focus, because that is one of the requirements of the modern
astronomer—we have to battle against spherical aberration.
We have already seen that the power of substances to refract light
differs for different colours, and we have seen the varied refraction of
different parts of the spectrum, and the necessity of making lenses
achromatic. Now there is one enormous advantage in favour of the
reflector. We do not take our light to bits and put it together again as
with an achromatic lens. But curiously enough, there is a something else
which quite lowers the position of the reflector with regard to the
refractor. Although, in the main all the light falling in parallel lines
on a concave surface is reflected to a focus, this is only true in a
general sense, because, if we consider it, we find an error which
increases very rapidly as the diameter of the mirror increases or as the
focal length diminishes. For instance, D I, Fig. 58, is the segment of a
circle, or the section of a sphere—if we deal with a solid figure. D C,
E G and H I, are three lines representing parallel rays falling on
different parts of it. According to that law which we have considered,
we can find where the ray E G will fall. We draw a line L, G, from the
centre to the point of reflection, and make the angle F G L, equal to
the angle of incidence E G L; then F will be the focus, so far as this
part of the mirror is concerned. Now let us repeat the process for the
ray H I, and we shall find that it will be reflected to K, a point
nearer the mirror than F, and it will be seen that the further the rays
are from the axis D C, the further from the point F is the light
reflected; so that if we consider rays falling from all parts of the
reflecting surface, a not very large but a distinctly visible surface is
covered with light, so that a spherical surface will not bring all the
rays exactly to a point, and with a spherical mirror we shall get a
blurred image. We can compare this imperfection of the reflector, called
spherical aberration, with the chromatic aberration of the object-glass.
[Illustration:
FIG. 58.—Diagram Illustrating Spherical Aberration.
]
[Illustration:
FIG. 59.—Diagram Showing the Proper Form of Reflector to be an
Ellipse.
]
Newton early calculated the ratio of imperfection depending upon these
properties of light, first of dispersion and then of spherical
aberration, and he found that in the refracting telescope the chromatic
aberration was more difficult to correct and get rid of than the
spherical aberration of the reflector, so that in Newton’s time, before
achromatic lenses were constructed, the reflector with its aberration
had the advantage. It must now be explained how this difficulty is got
over. What is required to produce a mirror capable of being used for
astronomical purposes, is to throw back the edges of the mirror to the
dotted line A C I, Fig. 58, which will make the margin of the mirror a
part of a less concave mirror, and so its focus will be thrown further
from itself—to F, instead of to K. Now let us consider what curve this
is, that will throw all the rays to one point. It is an ellipse, as will
be seen by reference to Fig. 59, in which, instead of having a spherical
surface the section of which is a circle, we deal with a surface whose
section is an ellipse.
It will be seen in a moment, that by the construction of an ellipse any
light coming in any direction from the point A, which represents one of
the foci of the curve, must necessarily be reflected back to the other
focus, B, of the curve, for it is a well-known property of this curve
that the angles made with a tangent C D, by lines from the foci are
equal; and the same holds good for the angles made at all other
tangents; and it will be seen at once that this is better than a
circular curve, because by making the distance between the foci almost
infinite we shall have the star or object viewed at one focus and its
image at the other; if we use any portion of the reflecting surface we
shall still get the rays reflected to one point only. It must also be
noticed, that unless we have an ellipse so large that one focus shall
represent the sun or a particular star we want to look at, this curve
will not help us in bringing the light to one point, but if we use the
curve called the parabola, which is practically an ellipse with one
focus at an infinite distance, we do get the means of bringing all the
rays from a distant object to a point. Hence the reflector, especially
when of large diameter, is of no use for astronomical purposes without
the parabolic curve.
That it is extremely difficult to give this figure may be gathered from
Sir John Herschel’s statement, that in the case of a reflecting
telescope, the mirror of which is forty-eight inches in diameter and the
focal distance of which is forty feet, the distance between the
parabolic and the spherical surface, at the edges of the mirror, will be
represented by something less than a twenty-one thousandth part of an
inch, or, more accurately, 1/21333 inch. In Fig. 58 the point A
represents the extreme edge of the curve of the parabolic mirror, and D
that of the circular surface before altered into a parabola.
At the time of Sir William Herschel the practical difficulties in
constructing large achromatic lenses led to the adoption by him of
reflectors beginning with small apertures of six inches to a foot, and
increasing till he obtained one of four feet in diameter and forty-six
feet focal length. This has been surpassed by Lord Rosse, whose
well-known telescope is six feet diameter, and fifty-three feet focal
length. Mr. Lassell, Mr. De La Rue, M. Foucault and Mr. Grubb, have also
more recently succeeded in bringing reflectors to great perfection.
How the work has been done will be fully stated in the sequel.
CHAPTER IX.
EYEPIECES.
We have considered the telescope as a combination of an object-glass and
eyepiece in the one case, and of a speculum and eyepiece in the other;
that is to say, we have discussed the optical principles which are
applied in the construction of refracting and reflecting telescopes, the
telescope being taken as consisting of an object-glass or speculum and
an eyepiece of the most simple form, viz., a simple double convex lens.
We must now go into detail somewhat on the subject of eyepieces, and
explain the different kinds.
It will be recollected that when we spoke of the object-glass, its
aberration, both chromatic and spherical, was mentioned. Now every
ordinary lens has these errors, and eyepieces must be corrected for
them, but this is not done in exactly the same way as with
object-glasses.
In the case of eyepieces the error is corrected by using two lenses of
such focal lengths or at such a distance apart that each counteracts the
defects of the other; not by using two kinds of glass as in the case of
the object-glass, but by so arranging the lenses that the coloured rays
produced by the first lens shall fall at different angles of incidence
on the second and become recombined.
[Illustration:
FIG. 60.—Huyghens’ Eyepiece.
]
Let us take the case of a well-known eyepiece, called the Huyghenian
eyepiece, after its inventor. It consists of two plano-convex lenses, A
and B Fig. 60, with their convexities turned towards the object-glass,
and having their focal lengths in the proportion of three to one. The
strongest lens, A, being next the eye, the lens B is placed inside the
focus of the object-glass, so that it assists in bringing the image, say
of a double star, to a focus at F, half way between the lenses, and
nearer to the object-glass than it would have been without the lens.
This image is then viewed by the eye-lens, A, and a magnified image of
it seen apparently at F´, as has been before explained. Now let us see
how the fieldlens renders this combination achromatic. Let us consider
the path of a ray falling on the lens near B, shown in section in Fig.
61: it is there refracted, but, the blue rays being refracted more than
the red, there will be two rays produced, _r_ and _v_, giving of course
a coloured edge to the image; but when this image is viewed by the
eye-glass, A, it no longer appears coloured, for the ray _v_, falling
nearer the axis of A, is less bent than _r_, and they are rendered
nearly parallel and appear to proceed from the point F´ where the whole
image appears without colour. In order to get the best result with this
form of eyepiece the focal length of the fieldlens should be three times
that of the eye-lens and they should be placed at a distance of half
their joint focal lengths apart.
[Illustration:
FIG. 61.—Diagram Explaining the Achromaticity of the Huyghenian
Eyepiece.
]
The next eyepiece which comes under consideration is that called
Ramsden’s, Fig. 62. It consists of two plano-convex lenses of the same
focus, A and B, placed at a distance of two-thirds of the focal length
of either apart; they are both on the eye side of the focus of the
telescope, and act together, to render the rays parallel and give a
magnified virtual image of F´F.
This eyepiece is not strictly achromatic, but it suffers least of all
lenses from spherical aberration; it also has the advantage of being
placed behind the focus of the object-glass, which makes it superior to
others in instruments of precision, as we shall presently see.
[Illustration:
FIG. 62.—Ramsden’s Eyepiece.
]
It must be remembered that these eyepieces give an inverted image—or
rather the object glass gives an inverted image, and the eyepiece does
not right it again; but there are eyepieces that will erect the image,
and Rheita’s is one of this kind. It is, as will be seen from Fig. 63,
merely a second application of the same means that first inverts the
object, namely, a second small telescope. A is the object-glass, _a b_
the image inverted in the usual way; B is an ordinary convex lens
sending the rays from _a_ and _b_ parallel. Now, instead of placing the
eye at C, as in the ordinary manner, another small lens, acting as an
object-glass, is placed in the path of the rays, bringing them to a
focus at _a´_, _b´_, and forming there an erect image which is viewed by
the eye-lens D. This is the erecting eyepiece or “day eyepiece,” of the
common “terrestrial telescope.” Dollond substituted an Huyghenian
eyepiece for the eye-lens D, and so made what is called his four-glass
eyepiece.
Dr. Kitchener devised and Mr. G. Dollond made an alteration in this
eyepiece in order to vary its power at pleasure. It is done in this way:
The size of the image _a´ b´_ depends upon the relation of the distances
_a_ B and E _a´_, which can be varied by altering the distance of the
combination of the lenses B and E, from the image _a b_, and so making
_a´ b´_ larger and at a focus further from E; the tube carrying _d_
slides in and out, so that it can be focussed on _a´ b´_ at whatever
distance from E it may be. This arrangement is called Dollond’s
Pancratic eyepiece.
[Illustration:
FIG. 63.—Erecting or day eyepiece.
]
On the sliding tube carrying the lens D, or rather the Huyghenian
eyepiece in place of the single lens, are marked divisions, showing the
power of the eyepiece when drawn out to certain lengths, so that if we
want the eyepiece to magnify say 100 times, the tube carrying the
eye-lens is drawn out to the point marked 100, and the whole eyepiece
moved in or out of the telescope tube by the focussing screw, until the
image of the object viewed is focussed in the field of the eyepiece D.
To increase the power, we have only to draw out the eyepiece D, and move
the whole combination nearer to the object-glass so as to throw the
image _a´ b´_ further from the lens E. This eyepiece, though so
convenient for changing powers, is little used, owing perhaps chiefly to
four lenses being required instead of two, hence a loss of light, so a
stock of eyepieces of various powers is generally found in
observatories. When very high powers are required, a single plano-convex
lens is sometimes used, but although there is less loss of light in this
case, the field of view is so contracted in comparison with that given
with other eyepieces that the single lens is seldom used. This form is,
however, adopted in Dawes’ solar eyepiece, to be hereafter mentioned,
and a number of lenses are in this case fixed in holes near the
circumference of a disc of metal which turns on its centre, so that by
rotating the disc the lenses come in succession in front of the focus of
the object-glass, and the power can be changed almost instantaneously.
In order that objects near the zenith may be observed with ease, a
diagonal reflector is sometimes used, so that the eye looks sidewise
into the telescope tube instead of directly upwards. This reflector may
take the form of two short pieces of tube joined together at right
angles, and having a piece of silvered glass or a right-angled prism at
the angle, so that when one tube is screwed into the telescope, the rays
of light falling on the reflector are sent up the other, in which the
ordinary eyepiece is placed.
The eyepieces just described are suitable, without further addition, for
observing all ordinary objects, but when the sun has to be examined a
difficulty presents itself. The heat rays are brought to a focus along
with those of light, and with an object-glass of more than one or two
inches aperture there is great danger of the heat cracking the lenses,
but with such telescopes the interposition—and neglect of this may cost
an eye—of smoked or strongly-coloured glass in front of the eye is
generally sufficient to protect it from the intense glare. With larger
telescopes, however, dark glasses are apt to split suddenly and allow
the full blaze of sunlight to enter the eye and do infinite mischief,
and some other method of reducing the heat and light is required.
Perhaps the most simple method of effecting this object is to allow the
light to fall on a diagonal plane glass reflector at an angle of 45°,
which lets the greater part of the light and heat pass through,
reflecting only a small portion onwards to the eyepiece and thence to
the eye; a coloured glass is, however, required as well, and the glass
reflector must form part of a prism of small angle, otherwise there will
be two images, one produced by each surface.
Another arrangement is to reflect the rays from the surfaces of two
plates of glass inclined to them at the polarizing angle, so that by
turning the second plate, or a Nicols’ prism, in its place round the ray
as an axis, the amount of light allowed to pass to the eye can be varied
at pleasure.
The late Mr. Dawes constructed a very convenient solar eyepiece,
depending on the principle of viewing a very small portion of the sun’s
image at one time, and thereby diminishing the total quantity of heat
passing through the eye-lens. The details of the eyepiece are as
follows: very minute holes of varying diameters are made in a brass disc
near its circumference, and as this is turned each successive hole is
brought into the centre of the field of view and the common focus of the
eye-lens and object-glass. Small areas on the sun of different sizes can
thus be examined at pleasure. A number of eye-lenses of different powers
arranged in a disc of metal can be successively brought to bear, giving
a means of quickly varying the power, while coloured glasses of
different shades can be passed in front of the eye in the same manner.
The surface of the disc of brass containing the holes is covered on one
side—that on which the sun’s image falls—with plaster of Paris, which,
being a bad conductor, prevents the heat from affecting the whole
apparatus.
* * * * *
The true magnifying power of the eyepiece is found by dividing the focal
length of the object-glass by that of the eyepiece; in practice it is
found approximately by comparing the diameter of the object-glass with
that of its image formed by the eyepiece when the telescope is in its
usual adjustment; the former divided by the latter giving the power
required. The diameter of the image can be measured by a small compound
microscope carrying a transparent scale in its focus, when the image of
the object-glass is brought to a focus and enlarged on the scale and
then viewed, together with the divisions, by the microscope; or the
image can be measured with tolerable accuracy by Mr. Berthon’s
dynameter, consisting of a plate of metal traversed longitudinally by a
wedge-shaped opening. This is placed close to the eye-lens in the case
of the Huyghenian eyepiece, or at the point where the image of the
object-glass is focussed with other forms of eyepieces, and the plate
moved until the sides of the wedge-shaped opening are exactly tangential
to the image; the point of the opening at which this occurs is read off
on a scale, which gives the width of opening at this point and therefore
the diameter of the image.
CHAPTER X.
PRODUCTION OF LENSES AND SPECULA.
Before we go on to the use and various mountings of telescopes, the
optical principles of which have been now considered, a few words may be
said about the materials used and the method of obtaining the necessary
and proper curves. Object-glasses, of course, have always been made of
glass, and till a few years ago specula were always made of metal; but
so soon as Liebig discovered a method of coating glass with a thin film
of metallic silver, Steinheil, and after him the illustrious Foucault,
so well known for his delicate experiments on the velocity of light and
his invention of the gyroscope, suggested the construction of glass
mirrors coated by Liebig’s process with an exceedingly thin film of
silver, chemically deposited.
This arrangement much reduced the price of reflectors and rendered their
polishing extremely easy, and at the present time discs of glass up to
four feet in diameter are being thus produced and formed into mirrors,
though in the opinion of competent judges this size is likely to be the
limit for some time. But there is this important difference, that
although glass is now used both for reflectors and refractors, almost
any glass, even common glass, will do, if we wish to use it for a
speculum; but if we wish to grind it into lenses it is impossible to
overrate the difficulty of manufacture and the skill and labour required
in order to prepare it for use, first in the simple material, and then
in the finished form in which it is used by the astronomer. In a former
chapter we considered some _chefs-d’œuvre_ of the early opticians, some
specimens of a quarter or half-an-inch in diameter, with extremely long
focus; and as we went on we found object-glasses gradually increasing in
diameter, but they were limited to the same material, namely, crown
glass.
Dollond, whose name we have already mentioned in connection with that of
Hall, gave us the foundation of the manufacture of the precious flint
glass, the connection of which with crown glass he had insisted upon as
of critical importance. The existence of a piece of flint glass two
inches in diameter was then a thing to be devoutly desired, that is to
say, flint glass of sufficient purity for the purpose; it could not be
made of a size larger than that, and not only was the material wanted,
but the material in its pure state.
In the year 1820 we hear of a piece of flint glass six inches in
diameter, and in 1859 Mr. Simms reported that a piece of flint glass of
seven and three-quarter inches was produced, six inches of which were
good for astronomical purposes. But even at this time they did these
things better in Germany and Switzerland, where M. Guinand made large
discs at the beginning of the present century. He was engaged by
Fraunhofer and Utzschneider at their establishment in Bavaria in 1805,
and by his process achromatics of from six to nine inches in diameter
were constructed. Afterwards Merz, the successor of Fraunhofer,
succeeded in obtaining flint glass of the then unprecedented diameter of
fifteen inches.
Now we have in part turned the tables, and Mr. Chance, of Birmingham,
owing to the introduction of foreign talent, has since constructed discs
of glass of a workable diameter of twenty-five inches for Mr. Newall’s
telescope, and for the American Government he has completed the large
discs used in constructing the refractor of 26 inches’ diameter for the
observatory at Washington (the Americans are never content till they go
an inch beyond their rivals), while M. Feil of Paris, a descendant of
the celebrated Guinand, has also made one of nearly 28 inches’ diameter
for the Austrian Government.
Messrs. Chance and Feil, however, have the monopoly of this manufacture,
and the production of these discs is a secret process. What we know is
that the glass is prepared in pots in large quantities, it is then
allowed to cool, and is broken up in order that it may be determined
which portions of the glass are worth using for optical purposes. These
are gathered together and fused at a red heat into a disc, and it is
this disc which, after being annealed with the utmost care, forms the
basis of the optician’s work.
For the glass used for reflectors, purity is of little moment, as we
only require a surface to take a polish, since we look on to it, and not
through it; but in the case of the glass that has to be shaped into a
lens the purity is of the utmost importance. The practical and
scientific optician, on his commencement to make an object-glass, will
grind the two surfaces of both flint and crown as nearly parallel as
possible, and polish them. In this state he can the better examine them
as to veins, striæ, and other defects, which would be fatal to anything
made out of it. He has next to see that the annealing is perfectly done
by examining the discs with polarized light, to see by the absence of
the “black cross” that there is no unequal tension. It is so difficult
to run the gauntlet through all these difficulties when the aperture is
considerable that refractors of forty inches’ aperture may be perhaps
despaired of for years to come, though the glassmaker is willing to try
his part.
Next, as to metallic specula. As we are dealing with the instruments
that are now used, we will be content with considering the compounds
that have been made successfully, and omit the variations which have
never been brought into practice. To put it roughly, the metal used for
Lord Rosse’s reflector consisted of two parts of copper and one part of
tin; but here we have an idea of the Scylla and the Charybdis which are
always present in these inquiries. If we use too much tin, which tends
to give a surface of brilliancy to the speculum, a few drops of hot
water poured on it will be enough to shiver it to atoms. This
brittleness is objectionable, and what we have to do is to reduce the
quantity of tin. But then comes the Charybdis. If we do this, the colour
is no longer white, but it is yellow, and in addition we have introduced
a surface that quickly tarnishes instead of a surface which remains
bright. The proportions which seem to answer best are copper sixty-four
parts and tin twenty-nine. Lord Rosse, we believe, uses 31·79 per cent,
of tin; or very nearly the above proportions. Mr. Grubb in the Melbourne
mirrors used copper and tin in the proportion of 32 to 14·77.
Having the metal, we have roughly to cast it in the shape of a speculum,
but if an ordinary casting is made in a sand mould the speculum metal is
so spongy that we can do nothing with it. If it is put in a close mould
it will probably be cast very well, but it will shiver to atoms with a
very slight change of temperature. The difficulty was got over by Lord
Rosse, using an open mould called a “bed of hoops;” the bottom of the
mould being composed of strips of iron set edgeways, held together by an
iron ring and turned to the proper convexity; sand is then placed round
the iron to form the edges, the metal is then poured in, and the bubbles
and vapours run down through the small apertures at the bottom of the
mould, so that the speculum is fairly cast. Mr. Lassell proposed a
different method, which was introduced by Mr. Grubb in his arrangements
for the Melbourne telescope. Instead of having the bottom of the bed of
hoops perfectly horizontal it is slightly inclined; the crucible, which
contains the metal of which the speculum is to be cast, is then brought
up to it—the amount of metal being something under two tons in the case
of the Melbourne telescope—and the bed of the mould is kept tipped up as
the metal is poured into it, and so arranged as to keep the melted metal
in contact with one side; and as it gets full it is brought into a
perfectly horizontal position.
Having cast the speculum, the next thing is to put it in an annealing
oven, raised to a temperature of 1,000°, where it is allowed to cool
slowly for weeks till it has acquired nearly the ordinary temperature.
On being removed from the oven the speculum is placed on several
thicknesses of cloth and rough ground on front, back, and edge.
Having got the material roughly into form we now pass on to see what is
done next.
In the case of the reflector, whether of metal or glass, the optician
next attempts to get a perfectly spherical surface of the proper
curvature for the required focus.
In the case of the refractor matters are somewhat more complicated; we
have there four spherical surfaces to deal with, and the optician has
work to do of quite a different kind before he even commences to grind.
Presuming the refractive and dispersive properties of the glass not
known, it will be necessary to have a small bit of glass of the same
kind to experiment with. That the optician may make no mistake in this
important matter, some glass manufacturers make the discs with
projecting pieces to be cut off; these the object-glass maker works into
prisms to determine the exact refraction and dispersion, including the
position in the spectrum of the Fraunhofer lines C and G, for both the
crown and flint glass. With these numbers and the desired focal length
he has all the necessary data for the mathematical operation of
calculating the _powers_ to be given to the two lenses—flint and crown,
and the radii of curvature of the four surfaces in order that the
object-glass may be aplanatic or free from aberration both spherical and
chromatic. The problem is what mathematicians call an indeterminate one,
as an infinite number of different curvatures is possible. Assume,
however, the radius of curvature of one surface, and all the rest are
limited. In assuming the radius of curvature on one of the crown-glass
surfaces, it is well to avoid deep ones. It is better to divide the
refraction of the four surfaces as equally as the nature of the problem
will admit, as any little deviation from a true spherical figure in the
polishing will produce less effect in injuring the performance of the
object-glass from surfaces so arranged than if the curves were deep.
But whatever curves he chooses he goes to work so that the spherical
aberration of the compound lens shall be eliminated as far as possible,
and the chromatism in one lens shall be corrected by the other, or in
other words, that what is called the _secondary spectrum_ shall be as
small as possible; and it is to be feared that this will never be
abolished.[6]
[Illustration:
FIG. 64.—Images of planet produced by short and long focus lenses of
the same aperture giving images of different size, but with the same
amount of colour round the edges.
]
This matter requires a somewhat detailed treatment in order that it may
be seen how the four surfaces to which reference has been made are
determined.
The chromatic dispersion, in the case of the object-glass, may be
roughly stated to be measured by about one fiftieth of the aperture.
Suppose for instance the discs, Fig. 64, to represent the image of any
object, say the planet Jupiter. Then round that planet we should have a
coloured fringe, and the dimensions of that coloured fringe, that is,
the joint thickness of colour at A and D, will be found by dividing the
diameter of the object-glass used by fifty. Now this is absolutely
independent of the focal length of the telescope; therefore one way of
getting rid of it is to increase the focal length of telescopes; and as
the size of the image depends on focal length, and has nothing whatever
to do with aperture, we may imagine that with the same sized
object-glass, instead of having a little Jupiter as on the left of Fig.
64, we may have a very large Jupiter, due to the increased focal length
of the telescope. Then, it may be asked, how about the chromatic
aberration? It will not be disturbed. The aperture of the object-glass
remains unaltered, and there is no more chromatic aberration here than
in the first case; so that the relation between the visible planet
Jupiter and the colour round it is changed by altering the focal length.
But as we have seen, we are able by means of a combination of flint and
crown glass to counteract this dispersion to a very great extent. How
then about spherical aberration?
Up to the present we have assumed that all rays falling on a convex lens
are brought to a point or focus, but this is not strictly true, for the
edges of a lens turn the rays rather too much out of their course, so
that they will not come to a point; just as the rays reflected from a
spherical mirror do not form a single focus. The marginal rays will be
spread over a certain circular surface, just as the colour due to
chromatic aberration covered a surface surrounding the focus. It was
explained that for the same diameter of lens the circle of colour
remained the same, irrespective of focal length, but in the case of
spherical aberration this is not so; it diminishes as the square of the
focal length increases; that is to say, if we double the focal length we
shall not only halve, but half-halve, or quarter the aberration. Newton
calculated the size of the circle of aberration in comparison with that
due to colour, and he found that in the case of a lens of four inches
diameter and ten feet focus, the spherical aberration was eighty-one and
a half times less than that of colour. _It is found that by altering the
relative curvatures of the surfaces of the lens, this aberration can be
corrected without altering the focal length_; for any number of lenses
can be made of different curvatures on each side but of the same
thickness in the middle, so that they have all the same focal length,
but the one, having one surface about three times more convex than the
other, will have least aberration, so that it is the adaptation of the
surfaces of lenses to each other that exercises the art of the optician.
So far we have got rid of this aberration in a single lens; it can also
be done in the case of achromatic lenses. The foci of the two lenses in
an achromatic combination must bear a certain relation to each other,
and the curvatures of the surfaces must also have a certain relation for
spherical aberration. In the achromatic lens there are four surfaces,
_two of which can be altered for one aberration and two for the other_.
For instance, in the case of the lens, Fig. 45, where the interior
surfaces of the lenses are cemented together, although shown separate
for clearness, we find that if the exterior surface of the crown double
convex lens be of a curvature struck by a radius 672 units in length,
and the exterior surface of the flint glass lens to a curvature due to a
radius of 1,420 units, the lens will be corrected for spherical
aberration, and these conditions leave the interior surfaces to be
altered so that the relation between the powers of the lenses is such as
to give achromatism.
The flint is as useful in correcting the spherical aberration as the
chromatic aberration; for although the relative thicknesses of the flint
and crown are fixed in order to get achromatism, still we have by
altering both the curvatures of each lens equally, and keeping the same
foci, the power of altering the extent of spherical aberration; and it
is in the applications of these two conditions that much of the higher
art of our opticians is exercised. We have now therefore practically got
rid of both aberrations in the modern object-glass, and hence it is that
lenses of the large diameter of twenty-five and twenty-six inches are
possible.
The nearest approach to achromatism is known to be made when looking at
a star of the first or second magnitude, the eyepiece being pushed out
of focus towards the object-glass, the expanded disc has its margin of a
claret colour. When the eyepiece is pushed beyond the focus outwards the
margin of the expanded disc is of a light green colour.
If the object-glass is well corrected for spherical aberration, the
expanded discs both within and without the focus will be constituted of
a series of rings equally dense with regard to light throughout, with
the exception of the marginal ring, which will be a little stronger than
the rest.
* * * * *
Having determined the radius of curvature of surface, both he who grinds
the speculum, whether of speculum metal or glass, and he who grinds the
object-glass, starts fair; only one has four times the work to do that
the other has. The grinding is managed in a simple way, and the process
of grinding or polishing an object-glass or speculum, either of glass or
of metal, is the same.
Supposing we wish to make a reflecting telescope of six feet focus, or a
surface of an object-glass of twelve feet radius, all we have to do is
to get a long rod, a little more than twelve feet long, and pin it to a
wall at its upper end so that it can swing, pendulum fashion; then at a
distance of twelve feet below the point of suspension a pin is stuck
through the rod and its point made to scratch a line on a sheet of metal
laid against the wall; then this line will be part of a circle struck
with a radius of twelve feet. If then the plate be cut along this line
we get a convex and a concave surface of the desired radius, and then we
can take a block of iron or brass and turn its surface, convex or
concave, to fit the sheet of metal or template. For a reflector we
should make a convex tool, and for a refractor a concave one.
Generally this grinding tool is divided into squares or furrows all over
it, in order that the emery which is used in rough grinding may flow
freely about with the water. A disc of glass is then laid on the tool,
or the tool on the glass, the two being pressed together by a weight or
spring; emery powder, with water, is strewn between them, and one is
rubbed over the other by a machine similar to those used for polishing,
which we shall explain presently. This operation is continued until the
glass is ground all over, and in this process of rough grinding the
rough emery is used between the tool and the glass, so that whatever
irregularities the glass or tool may have they are got rid of, and it is
easy to obtain a spherical surface, and indeed, it is the only surface
that can be obtained. Then finer and finer emery is used, till it ceases
to be a sufficiently fine substance to use, and a surface of iron or
lead is also too hard a surface. Now the polishing begins, and the
optician and amateur avail themselves of a suggestion due to Sir Isaac
Newton, who always saw much further through things than other people.
[Illustration:
FIG. 65.—Showing in an exaggerated form how the edge of the speculum
is worn down by polishing.
]
Even when he first began to make the first reflector, he used pitch, a
substance not too hard, nor yet too soft, and one that can be regulated
by temperature; therefore for polishing, instead of having a tool made
of metal, pitch laid on glass or wood and supplied with rouge and water
is used. This polisher of pitch is divided into squares by channels to
allow free flow of rouge and water, and is laid on the mirror or
object-glass, or vice versâ, and moved about over it.
When the maximum of polish is attained the work is done, and the
object-glass finished, as here we have to do with a spherical surface.
In the grinding of the two discs for Mr. Newall’s telescope 1,560 hours
were consumed, the thickness of the crown disc having been reduced one
inch in the process.
In the case of specula, however, there is more to be done; and it is in
this polishing of specula that the curve is altered from a circle to a
parabola by using a certain length of stroke, size of polisher,
consistency of pitch, and numbers of other smaller matters, the proper
proportionment of which constitutes the practical skill of the optician,
and it is in accomplishing this that the finest niceties of manipulation
come into play, and the utmost patience is required. 1,170 hours were
occupied in the grinding and polishing of the four-feet Melbourne
speculum. This was equivalent to 2,050,000 strokes of the machine at 33
per minute for rough and 24 for fine grinding. Dr. Robinson, in his
description of the grinding operations, states that at the edge of one
of the four-feet specula the distance of its parabola from the circle
was only 0·000106˝.
In the early times of specula the polishing was invariably done by hand,
a handle being cemented by pitch to the back of the speculum to work it
with. Mudge tells us that at first, when the mirror was rough from the
emery grinding, it was worked round and round on the pitch, which was
supplied with rouge and water and cut by channels into small squares,
carrying the edge but little over the polisher, an occasional cross
stroke being made. The effect of this was to press the pitch towards the
centre where the polish always commenced, and gradually spread to the
circumference. As soon as the polishing was complete the speculum was
worked by short straight strokes across the centre, tending to bring it
back to a sphere; then the circular strokes were recommenced to restore
the paraboloid form: these were continued for a short time only,
otherwise it would pass the proper curve and require reworking with
straight strokes again. By this method some small mirrors of first-class
definition were constructed.
When Sir W. Herschel began his labours he constructed a machine for
working the speculum over the polisher; the polisher was a little larger
than the mirror, the proportion given by him from a number of trials
being 1·06 to 1.
The speculum was held in a circular frame, which was free to turn round
in another ring or frame; this frame was moved backwards and forwards by
a vibrating lever to which it was attached by rods, carrying the
speculum over the polisher. This motion he designates the stroke.
Besides this there was the _side motion_ produced by a rod attached to
the side of the frame opposite to that to which the rods giving it the
stroke were attached and at right angles to the direction of stroke:
this rod was in connection, by means of intermediate levers, with a pin
on a rachet wheel, which was turned a tooth at a time by a rod in
connection with the lever giving the _stroke_ motion, so that the rod
giving the _side motion_ was pushed and pulled back by the pin on the
rachet wheel every time it turned round, which it did every twenty or
thirty strokes. There were also teeth on the ring fastened round the
edge at the back of the speculum, into which claws worked which were
attached by rods to a point on the lever a little distance from the
attachment of the rod giving the stroke, so that the claws had a less
motion than the speculum and its ring, and consequently pulled the ring,
and with it the speculum, round a tooth or more at each stroke. The
polisher was also turned round in the same manner in a contrary
direction to the motion of the speculum. The speculum had therefore
three motions, a revolving one on its centre, a stroke, and a side
motion, making its centre describe a number of parallel lines over the
polisher on each side of its centre. Sir W. Herschel gives as a good
working length of stroke, 0·29, and 0·19 side motion measured from side
to side, the diameter of the speculum being 1. To produce a seven-inch
mirror with this instrument he would work continuously for sixteen
hours, his sister “putting the victuals by bits into his mouth.”
[Illustration:
FIG. 65*.—Section of Lord Rosse’s polishing machine.
]
Lord Rosse adopted a similar arrangement; the polisher, K L, Fig. 65,
was worked over the speculum in straight strokes with side motion, the
requisite straight motion being given by a crank-pin and rod and the
side motion by the continuation of this latter rod on the other side of
the polisher working in a guide on another crank-pin, which threw it
from side to side as the wheel carrying the pin revolved. The trough E F
carrying the speculum also revolved slowly, and the requisite motions
were given by pulleys and straps of various sizes under the table on
which the machine rested; the weight of the polisher was in a great
measure counterpoised by strings from its upper surface to a weighted
lever M above. The polisher was free to turn in its ring, which it did
once in about twenty strokes, and for the six feet speculum the velocity
of working was about eight strokes a minute, the length of stroke being
one-third of the diameter of the speculum, and that of the side motion
one-fifth.
The speculum was polished on the same system of levers that were
afterwards to support it, in order that no change of form might be
produced in moving it to a different mounting. The consistency of the
pitch is a matter of importance, Mr. Lassell’s test of the requisite
hardness being the number of impressions left by a sovereign standing on
edge on it; this should leave three complete impressions of the milled
edge in one minute at the ordinary temperature of the atmosphere.
[Illustration:
FIG. 66.—Mr. Lassell’s polishing machine.
]
Fig. 66 represents the machine contrived by Mr. Lassell for his method
of polishing, and shows what a complicated arrangement is essential in
order to arrive at any good result in these matters.
The speculum is placed on a bed, and above it is a train of wheels
terminating in a crank-pin that gives motion to the polisher, which is
made to take a very devious path by the motion of the wheels above. The
pin giving motion to the polisher G at its centre can be set at a
variable distance from the axis of the lowest pinion F to which it is
attached, by moving it in its slide, so that when the pinion is turned,
the pin and centre of the polisher describe a circle. The pinion in
question is carried on a slide C above it, attached to the main vertical
driving shaft A, so that as the shaft revolves the centre of the pinion
describes a circle of a diameter variable at pleasure by moving it in
the slide C, the result of the two motions being that the centre of the
polisher describes circles about a moving centre, and consequently in
constantly varying positions on the speculum. Motion is given to the
vertical shaft by the cog-wheel and endless screw above, worked by some
prime mover, and as the cogwheels on the shaft E parallel to the main
shaft are carried round the latter by the arm D holding them, they are
caused to revolve by gearing into the fixed wheel B, through the centre
of which the main shaft passes, and they in their turn impart motion to
the pinion carrying the pin giving motion to the polisher. The speculum
is also maintained in slow rotation by the wheel and endless screw below
it. The speculum and its supports are surrounded by water contained in a
circular trough not shown in the engraving, so that the consistency of
the pitch shall be constant.
This arrangement, pure and simple, was found to bring on the polish in
rings over the speculum, and as an improvement, the speculum, or rather
the system of levers supporting it, was carried on a plate which had the
power of sliding backwards and forwards on the wheel turning it round;
the edges of this plate pressed against a fixed roller, and it was made
of such a shape that as it revolved it was forced to take a side motion
as its edges passed by the fixed roller, so that the speculum had a side
motion in addition to the rotatory one.
Mr. De La Rue improved on this by giving the speculum a rotatory motion
irrespective of that of the sliding plate, so that the side motion
should not always be along the same diameter of the speculum. This was
done by allowing the speculum to turn freely on a pivot on the sliding
plate, and giving it a rotatory motion by means of a cord going round
the plate carrying the speculum supports. As a further improvement Mr.
De La Rue controls the motion of the polisher on the central pin, giving
it motion by a crank carrying a system of wheels in place of the lowest
crank, so that the pin gets a rotatory motion in addition to these.
Mr. Grubb’s arrangement for polishing is different. The speculum is made
to rotate, the polisher is made to execute curves variable at pleasure
by altering the throw of the cranks which move rods attached to the
centre of the polisher, giving it a motion similar to that of Mr.
Lassell’s machine. The polisher moves a little off the edge, so that the
edge is worn down more than the centre, thus giving the parabolic form.
M. Foucault, of whom we have already spoken, proceeds in a different
manner in parabolising his glass mirrors. He first obtains a spherical
surface, fairly reflective, by grinding. He then alters the surface to a
paraboloid form by handwork, only testing the surface from time to time
to ascertain the parts requiring reduction by the polishing pad. The
method of testing is as beautiful as it is simple. The approximate
estimate of the curvature of the speculum is made by placing a small and
well-defined object, such as the point of a pin, close to the centre of
curvature and examining its image formed close by its side with a lens.
As a nicer test, he places an object having parallel sides, say a flat
ruler, near the centre of curvature, and views its image with the naked
eye at the distance of distinct vision, then each point of the edge is
seen by rays converging only from a small portion of the surface of the
mirror, the remainder of the diverging cone from each point of the edge
passes on beside the eye, and by moving the eye about, any point of the
edge can be seen formed by rays proceeding from any particular part of
the mirror, viz., that part in line with the eye and point of the edge
examined; if the curvature be not uniform the edge will appear
distorted, and points on it will appear in different positions, as rays
from different parts of the mirror are received by the eye as it is
moved, making the edge appear to move in waves. Finally, he allows light
from a very small hole in a metal plate near the centre of curvature to
fall on the mirror, and places the eye just on the side opposite to the
point where the image is formed, so as to receive the rays as they
diverge after having come to a focus. The whole of the light thus passes
into the eye, and the mirror is seen illuminated in every part. A sharp
edge of metal is then gradually brought into the focus, when the
illumination of the mirror decreases, and just before the light
disappears the irregularities will plainly appear, showing themselves by
patches of light, which prove that those parts still bright are so
inclined as to reflect the rays by the side of the true focus. By moving
the metallic edge so as to advance upon the focus from all sides, a very
good idea of the irregularities may be obtained. If, however, the
surface be truly spherical, the light will disappear regularly over the
whole surface.
M. Foucault commences by making the surface truly spherical, and then by
polishing off in concentric circles, increasing the polishing from the
centre, an elliptic and at last a parabolic curve is attained. The
ellipse is tested from time to time by removing the perforated plate
further and further away from the mirror until the ellipse becomes
practically a parabola. The great advantage of this method is, that the
effect of the polishing can be examined as it proceeds, and the work can
always be applied wherever necessary, and the test is entirely
independent of hot-air currents which are seen to fluctuate over the
mirror as waves of light, leaving the irregularities of form permanently
marked. It further appears that the method may be varied to form a
first-rate test of a finished mirror already mounted; for one has
nothing to do but bring a star into the field of view, and remove the
eyepiece, and bring the eye into such a position as to receive the
diverging rays from the focus of the star. A knife is then gradually
moved across in front of the eye, say from the right; then if the mirror
commences to get darkened on the right side distinctly before the left
the knife is on the mirror side of the focus; if, however, the left side
of the mirror becomes darkened first it is on the eye side of the focus.
After a few trials it can be got to cut across the focus and darken the
mirror at all points at once, and show up all irregularities.
We have now, then, by one system or another, got our mirror, either of
speculum metal or of glass, and if of the latter substance we have to
silver it; processes have been published by Mr. Browning, and M.
Martin,[7] by which, on the plan proposed in the first instance by
Liebig, an extremely thin coating of silver is deposited on the glass.
This film is susceptible of taking a high polish, which, in the case of
small mirrors, can be renewed as often as is wished without repolishing
the mirror; the resilvering of one of large aperture however is a most
formidable affair. To those who wish to silver their own mirrors, let us
say that it should be done in summer, or in a room kept by a stove at an
equable summer heat, and the silvering solution should be kept for a day
or more to settle, and for probably some chemical change to take place
before the reducing solution is added. It will be found easy enough to
silver the small planes for Newtonian reflectors, but large mirrors
require much greater care and trouble.
-----
Footnote 6:
Professor Stokes and Mr. Vernon Harcourt some time ago made
experiments with phosphatic glass, and some of this material was
worked into a lens by Mr. Grubb, who states that “the result was
successful so far as the obtaining of specimens of phosphatic glass
with rational spectra; but phosphatic glass is almost unworkable, and
when the experiment was tried on a siliceous glass it failed. Some
alleviation of this secondary spectrum can be got by using a triple
objective, but with, of course, a corresponding loss of light.”
Footnote 7:
Mr. Browning’s method of silvering glass specula is as follows:—
Prepare three standard solutions:
Solution A { Crystals of nitrate of silver 90 grains } Dissolve.
{ Distilled water 4 ounces }
Solution B { Potassa, pure by alcohol 1 ounce } Dissolve.
{ Distilled water 25 ounces }
Solution C { Milk-sugar (in powder) ½ ounce } Dissolve.
{ Distilled water 5 ounces }
Solutions A and B will keep, in stoppered bottles, for any length of
time; Solution C must be fresh. To prepare sufficient for silvering an
8 in. speculum, pour two ounces of Solution A into a glass vessel
capable of holding thirty-five fluid ounces. Add, drop by drop,
stirring all the time (with a glass rod), as much liquid ammonia as is
just necessary to obtain a clear solution of the grey precipitate
first thrown down. Add four ounces of Solution B. The brown-black
precipitate formed must be _just_ re-dissolved by the addition of more
ammonia, as before. Add distilled water until the bulk reaches fifteen
ounces, and add, drop by drop, some of Solution A, until a grey
precipitate, which does not re-dissolve after stirring for three
minutes, is obtained; then add fifteen ounces more of distilled water.
Set this solution aside to settle; do not filter. When all is ready
for immersing the mirror, add to the silvering solution two ounces of
Solution C, and stir gently and thoroughly. Solution C may be
filtered.
The mirror should be suspended face downwards about ½-inch deep in the
liquid, by strings attached to pieces of wood fastened to the back of
the mirror with pitch, and before being immersed should be cleaned
with nitric acid and washed with distilled water. The silvering is
completed in about an hour, and when finished the surface should be
washed in distilled water and dried, and then polished with soft
leather, finishing with a little rouge.
The following method is used by M. Martin:—
Make solutions:
1. Nitrate of silver 4 per cent.
2. Nitrate of ammonia 6 per cent. } perfectly free
3. Caustic potash 10 per cent. } from carbonates.
4. Dissolve twenty-five grammes of sugar in 250 grammes of water; add
three grammes of tartaric acid; heat it to ebullition during ten
minutes to complete the conversion of sugar; cool down, and add fifty
cubic centimetres of alcohol in summer to prevent fermentation, add
water to make the volume to ½ litre in winter and more in summer.
_Clean well_ the surface of the glass.
Take equal quantities of the four solutions: mix 1 and 2 together, and
3 and 4 also together: mix the two, pouring it at once into the vessel
where the silvering is to be done. The mirror is suspended face
downwards in the liquid, and the deposit begins after about three
minutes, and is finished after twenty minutes. Take out the mirror,
clean well with water, dry it in the air, and rub it then gently with
a very fine leather.
CHAPTER XI.
THE “OPTICK TUBE.”
Having now obtained the lenses and specula we come, in order to complete
our consideration of the purely optical portion of the subject, to the
question of mounting these lenses and specula in tubes and thus
connecting them with the eyepieces so as to become of practical utility.
We will first consider the adjustment of lenses in a tube, the
combination forming a simple telescope that can be supported, in any
manner desirable, by mountings we shall presently consider, according to
the purpose for which it is required. The adjustment of specula will be
considered as we advance further.
The smaller telescopes consist of a brass tube, the object-glass, held
in a brass ring, being screwed in at one end of the tube: a smaller tube
sliding in and out of the other end of the large tube, generally moved
by a rack and pinion motion, carries the eyepiece. In larger telescopes
the mounting is similar, only somewhat more elaborate, the object-glass
being carried in a brass cell, or a steel one if the dimensions are very
large. This screws into the ring at the end of the tube, and this ring
can be slightly tipped on either side by set screws, so that the
object-glass can be brought exactly at right angles to the axis of the
tube.
[Illustration:
FIG. 67.—Simple telescope tube, showing arrangement of object-glass
and eyepiece.
]
It is important, in order that an object-glass shall perform its best,
that the lenses forming it shall be properly centred: this is generally
done by the maker once and for ever. Wollaston pointed out an ingenious
method of centring them; it is as follows:—The eyepiece is removed, and
a lighted candle put in its place: the object-glass is then examined
from the opposite side, when, if all the lenses are correctly placed,
the images of the candle produced by the successive reflections of the
candle from the surfaces of the lenses will be concentric, and in a
straight line from the candle through the centre of the system of
lenses, a fact easily judged of, by moving the eye slightly from side to
side, and if they are not, they are easily corrected by tipping the lens
in fault slightly in the cell. In case the lenses are cemented together,
this method of course is applicable in setting the object-glass at right
angles to the axis of the tube. The adjustment of an object-glass can
also be judged of by examining a star as it is thrown in and out of
focus by the focusing screw; the disc of the star should be perfectly
round in and out of focus, and the rings produced by interference should
also be circular when in focus, and the disc of light, when out of
focus, must be circular. Any elongation of the disc or rings, or a
“flare” appearing, shows a want of a slight alteration of the setting
screw, on the same side of the object-glass as the “flare” or elongation
appears.
In some object-glasses the curves of the two interior surfaces are such
that three pieces of tin foil are placed at equal distances round the
edge to prevent the central portions from coming in contact.
[Illustration:
FIG. 68.—Appearance of diffraction rings round a star when the
object-glass is properly adjusted.
]
[Illustration:
FIG. 69.—Appearance of same object when object-glass is out of
adjustment.
]
The flexure of small object-glasses by their own weight is of little
importance, because every surface is affected alike; but when the
aperture is large special precautions have to be taken. The late Mr.
Cooke when he had completed the 25-inch object-glass for Mr. Newall’s
telescope, introduced a system of counterpoise levers just within the
edge which helped to support the object-glass in all positions. Mr.
Grubb states that with an aperture of 15 inches, supported on three
points, there is decided evidence of flexure, and he proposes, in the
27-inch Vienna refractor, not only to introduce six intermediate
supports, thereby following in the footsteps of Mr. Cooke, but with
larger apertures to introduce boldly a central support, or to
hermetically seal the tube and fill it with compressed air. He has
calculated that in the case of an object-glass 40 inches aperture,
weighing 600 lbs., two-thirds of its weight could be supported by an air
pressure of one-third of a pound to the square inch.
The tube of the telescope when of large size is usually made of iron or
wood, and a tube of the latter substance may be made very light and yet
sufficiently strong, by wrapping layers of veneer round a central core
and fastening the layers firmly with glue. There are generally two or
more tubes sliding inside each other at the eye end of the telescope, to
carry the eyepiece so as to give plenty of power of adjustment of the
length of the tube to suit the different eyepieces, or other instruments
used in their place. The tube then is ready to be adapted to any of the
mountings to be hereafter considered.
* * * * *
We now come to the mounting of specula, and when we recollect the
enormous weights of some of the specimens to which we have referred, it
will be obvious that some additional precautions, which are not at all
necessary in the case of a refractor, must be taken to insure success.
In reflecting telescopes, the speculum is carried at the bottom of a
tube in a sort of tray or cell, which can be adjusted by screws at the
back, so as to set the mirror at right angles to the tube, and the
conditions of support should be such that the mirror should be as free
from strain as if it were floating in mercury. A system of lateral
supports in all positions is also necessary.
The action of the telescope depends greatly on the backing of the
speculum, and numerous methods of carrying specula on soft backing and
systems of levers have been suggested, all aiming at carrying them so
that they are free from all possible strain and flexure occasioned by
their own weight. For smaller mirrors a soft back of flannel or cloth
can be used, and a leather strap placed round the mirror and its back,
so as to form the side of a sort of circular tray, will give it
sufficient support when inclined to the horizontal. Mr. Browning adopts
the plan of making the back of the mirror and its support perfectly
flat, so as not to require levers or soft backing; this arrangement
would probably fail for mirrors larger than one foot in diameter,
although answering admirably for those of less size.
[Illustration:
FIG. 70.—Optical part of a Newtonian reflector of ten inches aperture,
showing eyepiece, adjusting screws for large speculum, finder, door
for uncovering speculum, and counterpoise.
]
[Illustration:
FIG. 71.—Optical part of Melbourne reflector, showing the lattice
arrangement for supporting the convex mirror _Y_, _T_ more solid
part of tube fixed to declination axis, _W_ finder.
]
[Illustration:
FIG. 72. Mr. Browning’s method of supporting small specula. The bottom
of the speculum A is a carefully prepared plane surface, and the
outer rim of the inner iron cell B, on which it rests, is also a
plane. The speculum is kept in this cell by the ring G G, and it may
be removed from, and replaced in, the telescope, without altering
its adjustment.
]
We will now consider the methods of mounting specula of larger size, and
will take as an instance the mounting of some of the largest specula in
existence which must act so as to prevent flexure in any position of the
speculum. The speculum is, in the case of the Melbourne telescope, of
the weight of something like two tons. When it is inclined at any
considerable angle to the horizon, it is apt to bend over at the top,
and thus destroy its proper curvature; and when horizontal, if not
equally supported, it will also bend, and unless some measures are taken
to prevent this flexure it will so entirely alter its figure by its own
weight as to render minute observations of any delicate stars absolutely
impossible.
Mr. Lassell was the first to suggest an arrangement for preventing this
flexure. Through the back of the speculum case—the case which holds and
supports the speculum, which we shall have to speak about presently—he
inserts a large number of very small levers, the centres of which are
fixed to the exterior part of this case, the forward part of each
resting against a small aperture made in the back of the speculum. The
ends of the levers furthest from the speculum are crowned with small
weights, the weights varying on different parts of the speculum. Now so
long as the speculum is perfectly horizontal, _i.e._ so long as the
zenith is being observed, these levers will have no action whatever; but
the moment the reflector is brought into any other position, as, for
instance, when we wish to observe a star near the horizon, the more the
mirror is inclined to the horizon the greater will be the power of these
small levers, and at length their total effect comes into action when a
star close to the horizon is being observed. Then the whole weight of
the mirror is carried by these levers acting at points all over its
back.
In the Melbourne reflector, which has recently been finished, Mr. Grubb
manages this somewhat differently, as will be seen by Figs. 73-76.
In Fig. 73 the speculum is in a vertical position. It is supported in a
frame, B B, all round it, which consists of a slightly flexible hoop of
metal a little larger than the speculum. This in its turn is supported
by a large fixed hoop, A A, having a hook-shaped section. This hoop is
attached to the tube of the telescope C C. The hoop, B B, is rather
larger than the part of A on which it hangs, so that it can adjust
itself to the form of the mirror; and not only is the mirror supported
in the hoop B B, like as in a strap in the position shown, but in every
other position of the tube the speculum still hangs evenly supported.
[Illustration:
FIG. 73.—Support of the mirror when vertical.
]
As we have already seen, there is another point to consider. Not only
must we be able to support the mirror when inclined to the horizon, but
we must support it bodily at the end of the tube when it is horizontal.
We will next examine an arrangement adopted by Mr. Grubb, similar to
that adopted by others, for supporting the Melbourne speculum, and we
cannot do better than quote Mr. Grubb’s own explanation of it. He says:—
“To understand it, suppose the speculum to be divided into
forty-eight portions, as in Fig. 74, each of them being exactly
equal in area, and consequently in weight. Now, if the centre of
gravity of each of these pieces rested on points which would bear up
with a force = the weight of each segmental piece, it is evident
that there would be no strain in the mass from segment to segment.
[Illustration:
FIG. 74.—Division of the speculum into equal areas.
]
“This is exactly what is accomplished by this system; in fact, if
when the speculum is resting on these supports it could be divided
up into segments corresponding to those lines, they would have no
inclination to leave their places, showing a perfect absence of
strain across those lines. Suppose now the points representing the
centres of gravity of these segments were supported on levers and
triangles, so as to couple them together, as at A, Fig. 75, and each
of these couplings to be supported from a point _a_, representing
the centre of gravity of the sum of the segments supported by that
particular couple, and it is evident that there can be no strain
between the components of these couples. Again, let these points,
_a_, be coupled together by the system shown at B, Fig. 75, and
their centres of gravity, _b_, coupled as at C, and it is evident
that the whole weight of the speculum ultimately condensed by this
system into these points is supported on forty-eight points of equal
support being the centres of gravity of the forty-eight segments at
Fig. 75. In Fig. 76 is seen the whole system complete. It consists
of three screws passing through the back of the speculum box (which
serve for levelling the mirror), the points of which carry levers
(_primary system_) supporting triangles on their extremities
(_secondary system_), from the vertices of which are hung two
triangles and one lever (_tertiary system_). All the joints of this
apparatus are capable of a small rocking motion, to enable them to
take their positions when the speculum is laid upon them.
[Illustration:
FIG. 75.—Primary, secondary, and tertiary systems of levers shown
separately.
]
[Illustration:
FIG. 76.—Complete system consolidated into three screws.
]
“In the system of levers made by Lord Rosse for his six-feet
speculum, the primary, secondary, and tertiary systems were piled up
one over the other, so that the distance from the support of the
primary to the back of the speculum was about fifteen inches. This,
as will be readily seen on consideration, introduced a new strain
when the telescope was turned off the zenith, and had to be
counterpoised by another very complicated system of levers. But in
the Melbourne telescope, by the substitution of cast-steel for
cast-iron, and by hanging the tertiary system from the secondary,
and allowing it (_the tertiary_) to act in some places through the
secondary, the whole system is reduced to three and a half inches in
height, and the distance from the support of the primary lever to
the back of the speculum is only one and three-quarter inch, by
which means this cumbersome apparatus is entirely done away with.
“The ultimate points of the tertiary system are gunmetal cups, which
hold truly ground cast-iron balls with a little play, and when the
speculum is laid on these it can be moved about a little by a
person’s finger with such ease as to seem to be floating in some
liquid.”
It may perhaps be thought that it would be better to support these great
specula on a flat surface, and it might be, if we could do so without
extreme difficulty; but Lord Rosse has stated that if we attempt to
support a large speculum on a surface extremely flat, a thread placed
across that surface, or even a piece of dust, is quite enough to bend
the mirror and render it absolutely useless. That will show the extreme
importance of the support of the speculum.
Let us then assume that we have the speculum and the tube perfectly
adjusted. The next thing, in all constructions except the Herschelian,
is to apply the second small reflector, concave in the case of the
Gregorian, convex in the case of the Cassegrainian, and plane in the
case of the Newtonian.
This small mirror is generally supported by a thin strip of metal firmly
fastened to the side of the tube, with power of movement parallel to the
axis of the telescope, in the case of the Gregorian and Cassegrainian,
for the purpose of focussing. In the Newtonian, the reflecting diagonal
prism or plane mirror, inclined at an angle of 45° to the axis, is
preferably supported in the manner suggested by Mr. Browning. See Figs.
77 and 78.
In these B B B represent strips of strong chronometer spring steel,
placed edgewise towards the speculum; by these the prism or small mirror
D is suspended.
The mirror thus mounted, does not produce such coarse rays on bright
stars as when it is fixed to a single stout arm; it is also less liable
to vibration, which is very injurious to distinct vision, or to flexure,
which interferes with the accuracy of the adjustments.
[Illustration:
FIG. 77.—Support of diagonal plane mirror (Front view).
]
[Illustration:
FIG. 78.—Support of diagonal plane mirror (Side view).
]
The most usual form of reflector is the Newtonian, large numbers of
which kind are now made; and just as the object-glasses of refractors
require adjusting, so do not only the large mirror, but also the “flat”
or diagonal mirror of this form. In the Newtonian the flat must be
adjusted first; to do this, first place the large mirror in its cell in
the tube, and secure it by turning it in the bayonet joint, _with the
cover on the mirror_. Then remove the glasses from one of the eyepieces,
insert it into the eyetube, and fix the diagonal mirror loosely in its
position.
Then, looking through the eyetube, move the diagonal mirror, by means of
the motions which are provided, until the reflected image of the cover
of the speculum is seen in the _centre_ of it.
This is accomplished by first loosening the milled-headed screw behind
the mirror, and turning the mirror until the image of the speculum cover
appears central in one direction. The screw at the back of the mirror
enables the reflected image to be brought central in the other
direction.
Next comes the turn of the large mirror. Take off the cover by screwing
off the side opening and place the eye at the eyetube after having
removed the eyepiece; the reflection of the diagonal mirror will be seen
in the reflected image of the speculum. The adjusting screws, at the
back of the speculum, must then be moved until the diagonal mirror is
seen in the centre of the speculum. The adjustment should then be
complete.
This may be judged of by bringing a star to the centre of the field, and
sliding the focussing-tube in or out, when the circle of light should
expand equally, and its centre should remain central in the field. As
another test a bright star should be viewed with a high power, and the
image examined; if it is round and the circles of light round it are
concentric without rays in any one direction, then all is correct; but
if a flare is seen, it is evidence that the part of the diagonal mirror
towards which the flare extends must be moved from the eye by the
setting-screws at the back.
CHAPTER XII.
THE MODERN TELESCOPE.
The gain to astronomy from the discovery of the telescope has been
twofold. We have first, the gain to physical astronomy from the
magnification of objects, and secondly, the gain to astronomy of
position from the magnification, so to speak, of _space_, which enables
minute portions of it to be most accurately quantified.
Looking back, nothing is more curious in the history of astronomy than
the rooted objection which Hevel and others showed to apply the
telescope to the pointers and pinnules of the instruments used in their
day; but doubtless we must look for the explanation of this not only in
the accuracy to which observers had attained by the old method, but in
the rude nature of the telescope itself in the early times, before the
introduction of the micrometer. We shall show in a future chapter how
the modern accuracy has step by step been arrived at; in the present one
we have to see what the telescope does for us in the domain of that
grand physical astronomy which deals with the number and appearances of
the various bodies which people space.
Let us, to begin with, try to see how the telescope helps us in the
matter of observations of the sun. The sun is about ninety millions of
miles away; suppose, therefore, by means of a telescope reflecting or
refracting, whichever we like, we use an eyepiece which will magnify say
900 times, we obviously bring the sun within 100,000 miles of us; that
is to say, by means of this telescope we can observe the sun with the
naked eye as if it were within 100,000 miles of us. One may say, this is
something, but not much; it is only about half as far as the moon is
from us. But when we recollect the enormous size of the sun, and that if
the centre of the sun occupied the centre of our earth the circumference
of the sun would extend considerably beyond the orbit of the moon, then
one must acknowledge we have done something to bring the sun within half
the distance of the moon. Suppose for looking at the moon we use on a
telescope a power of 1,000, that is a power which magnifies a thousand
times, we shall bring the moon within 240 miles of us, and we shall be
able to see the moon with a telescope of that magnifying power pretty
much as if the moon were situated somewhere in Lancashire—Lancaster
being about 240 miles from London.
It might appear at first sight possible in the case of all bodies to
magnify the image formed by the object-glass to an unlimited extent by
using a sufficiently powerful eyepiece. This, however, is not the case,
for as an object is magnified it is spread over a larger portion of the
retina than before; the brightness, therefore, becomes diminished as the
area increases, and this takes place at a rate equal to the square of
the increase in diameter. If, therefore, we require an object to be
largely magnified we must produce an image sufficiently bright to bear
such magnification; this means that we must use an object-glass or
speculum of large diameter. Again, in observing a very faint object,
such as a nebula or comet, we cannot, by decreasing the power of the
eyepiece, increase the brightness to an unlimited extent, for as the
power decreases, the focal length of the eyepiece also increases, and
the eyepiece has to be larger, the emergent pencil is then larger than
the pupil of the eye, and consequently a portion of the rays of the cone
from each point of the object is wasted.
[Illustration:
FIG. 79.—A portion of the constellation Gemini seen with the naked
eye.
]
We get an immense gain to physical astronomy by the revelations of the
fainter objects which, without the telescope, would have remained
invisible to us; but, as we know, as each large telescope has exceeded
preceding ones in illuminating power, the former bounds of the visible
creation have been gradually extended, though even now we cannot be said
to have got beyond certain small limits, for there are others beyond the
region which the most powerful telescope reveals to us; though we have
got only into the surface we have increased the 3,000 or 6,000 stars
visible to the naked eye to something like twenty millions. This
space-penetrating power of the telescope, as it is called, depends on
the principle that whenever the image formed on the retina is less than
sufficient to appear of an appreciable size the light is apparently
spread out by a purely physiological action until the image, say of a
star, appears of an appreciable diameter, and the effect on the retina
of such small points of light is simply proportionate to the amount of
light received, whether the eye be assisted by the telescope or not; the
stars always, except when sufficiently bright to form diffraction rings,
appearing of the same size. It, therefore, happens that as the apertures
of telescopes increase, and with them the amount of light, (the
eyepieces being sufficiently powerful to cause all the light to enter
the eye,) smaller and smaller stars become visible, while the larger
stars appear to get brighter and brighter without increasing in size,
the image of the brightest star with the highest power, if we neglect
rays and diffraction rings, being really much smaller than the apparent
size due to physiological effects, and of this latter size every star
must appear.
[Illustration:
FIG. 80.—The same region, as seen through a large telescope.
]
The accompanying woodcuts of a region in the constellation of Gemini as
seen with the naked eye and with a powerful telescope will give a better
idea than mere language can do of the effect of this so-called
space-penetrating power.
[Illustration:
FIG. 81.—Orion and the neighbouring constellations.
]
With nebulæ and comets matters are different, for these, even with small
telescopes and low powers, often occupy an appreciable space on the
retina. On increasing the aperture we must also increase the power of
the eyepiece, in order that the more divergent cones of light from each
point of the image shall enter the pupil, and therefore increase the
area on the retina, over which the increased amount of light, due to
greater aperture, is spread; the brightness therefore is not increased,
unless indeed we were at the first using an unnecessary high power. On
the other hand, if we lengthen the focus of the object-glass, and
increase its aperture, the divergence of the cones of light is not
increased and the eyepiece need not be altered, but the image at the
focus of the object-glass is increased in size by the increase of focal
length, and the image on the retina also increases as in the last case.
We may, therefore conclude that no comet or nebula of appreciable
diameter, as seen through a telescope having an eyepiece of just such a
focal length as to admit all the rays to the eye, can be made brighter
by any increase of power, although it may easily be made to appear
larger.
[Illustration:
FIG. 82.—Nebula of Orion.
]
Very beautiful drawings of the nebula of Orion and of other nebulæ, as
seen by Lord Rosse in his six-foot reflector, and by the American
astronomers with their twenty-six inch refractor, have been given to the
world.
The magnificent nebula of Orion is scarcely visible to the naked eye;
one can just see it glimmering on a fine night; but when a powerful
telescope is used, it is by far the most glorious object of its class in
the Northern hemisphere, and surpassed only by that surrounding the
variable star η Argûs in the Southern. And although, of course, the
beauty and vastness of this stupendous and remote object increase with
the increased power of the instrument brought to bear upon it, a large
aperture is not needed to render it a most impressive and awe-inspiring
object to the beholder. In an ordinary 5-foot achromatic, many of its
details are to be seen under favourable atmospheric conditions.
Those who are desirous of studying its appearance, as seen in the most
powerful telescopes, are referred to the plate in Sir John Herschel’s
“Results of Astronomical Observations at the Cape of Good Hope,” in
which all its features are admirably delineated, and the positions of
150 stars which surround θ in the area occupied by the Nebula, laid
down. In Fig. 82 it is represented in great detail, as seen with the
included small stars, all of which have been mapped with reference to
their positions and brightness. This then comes from that power of the
telescope which simply makes it a sort of large eye. We may measure the
illuminating power of the telescope by a reference to the size of our
own eye. If one takes the pupil of an ordinary eye to be something like
the fifth of an inch in diameter, which in some cases is an extreme
estimate, we shall find that its area would be roughly about
one-thirtieth part of an inch. If we take Lord Rosse’s speculum of six
feet in diameter the area will be something like 4,000 inches: and if we
multiply the two together we shall find, if we lose no light, we should
get 120,000 times more light from Lord Rosse’s telescope than we do from
our unaided eye, everything supposed perfect.
Let us consider for a moment what this means; let us take a case in
point. Suppose that owing to imperfections in reflection and other
matters two-thirds of the light is lost so that the eye receives 40,000
times the amount given by the unaided vision, then a sixth magnitude
star—a star just visible to the naked eye—would have 40,000 times more
light, and it might be removed to a distance 200 times as great as it at
present is and still be visible in the field of the telescope, just as
it at present is to the unaided eye. Can we judge how far off the stars
are that are only just visible with Lord Rosse’s instrument? Light
travels at the rate of 185,000 miles a second, and from the nearest star
it takes some 3½ years for light to reach us, and we shall be within
bounds when we say that it will take light 300 years to reach us from
many a sixth magnitude star.
But we may remove this star 200 times further away and yet see it with
the telescope, so that we can probably see stars so far off that light
takes 60,000 years to reach us, and when we gaze at the heavens at night
we are viewing the stars not as they are at that moment, but as they
were years or even hundreds of years ago, and when we call to our
assistance the telescope the years become thousands and tens of
thousands—expressed in miles these distances become too great for the
imagination to grasp; yet we actually look into this vast abyss of space
and see the laws of gravitation holding good there, and calculate the
orbit of one star about another.
Whether the telescope be of the first or last order of excellence, its
light-grasping powers will be practically the same; there is therefore a
great distinction to be drawn between the illuminating and defining
power. The former, as we have seen, depends upon size (and subsidiarily
upon polish), the latter depends upon the accuracy of the curvature of
the surface.
[Illustration:
FIG. 83.—Saturn and his moons (general view with a 3¾-inch
object-glass.)
]
If the defining power be not good, even if the air be perfect, each
increase of the magnifying power so brings out the defects of the image,
that at last no details at all are visible, all outlines are blurred, or
stellar character is lost.
The testing of a glass therefore refers to two different qualities which
it should possess. Its quality as to material and the fineness of its
polish should be such that the maximum of light shall be transmitted.
Its quality, as to the curves, should be such that the rays passing
through every part of its area shall converge absolutely to the same
point, with a chromatic aberration not absolutely _nil_, but sufficient
to surround objects with a faint violet light.
[Illustration:
FIG. 84.—Details of the ring of Saturn observed by Trouvelot with the
26-inch Washington Refractor.
]
In close double stars therefore, or in the more minute markings of the
sun, moon, or planets, we have tests of its defining power; and if this
is equally good in the instruments examined, the revelations of
telescopes as they increase in power are of the most amazing kind.
A 3¾-inch suffices to show Saturn with all the detail shown in Fig. 83,
while Fig. 84 shows us the further minute structure of the rings which
comes out when the planet is observed with an aperture of 26 inches.
In the matter of double stars, a telescope of 2 inches aperture, with
powers varying from 60 to 100, should show the following stars double:—
Polaris.
α Piscium.
μ Draconis.
γ Arietis.
ρ Herculis.
ζ Ursæ Majoris.
α Geminorum.
γ Leonis.
ξ Cassiopeæ.
A 4-inch aperture, powers 80-120, reveals the duplicity of—
β Orionis.
ε Hydræ.
ε Boötis.
ι Leonis.
α Lyræ.
ξ Ursæ Majoris.
γ Ceti.
δ Geminorum.
σ Cassiopeæ.
ε Draconis.
A 6-inch, powers 240-300—
ε Arietis.
32 Orionis.
λ Ophiuchi.
20 Draconis.
κ Geminorum.
ι Equulei.
ξ Herculis.
ξ Boötis.
An 8-inch—
δ Cygni.
γ^2 Andromedæ.
Sirius.
19 Draconis.
μ^2 Herculis.
μ^2 Boötis.
The “spurious disk,” which a fixed star presents, as seen in the
telescope, is an effect which results from the passage of the light
through the object-glass; and it is this appearance which necessitates
the use of the largest apertures in the observation of close double
stars, as the size of the star’s disk varies, roughly speaking, in the
inverse ratio of the aperture of the object-glass.
In our climate, which is not so bad as some would make it, a 6- to an
8-inch glass is doubtless the size which will be found the most
constantly useful; a larger aperture being frequently not only useless,
but hurtful. Still, 4 or 3¾ inches are apertures by all means to be
encouraged; and by object-glasses of these sizes, made of course by the
_best_ makers, views of the sun, moon, planets, and double stars may be
obtained, sufficiently striking to set many seriously to work as amateur
observers, and with a prospect of securing good, useful results.
Observations should always be commenced with the lowest power, gradually
increasing it until the limit of the aperture, or of the atmospheric
condition at the time, is reached. The former may be taken as equal to
the number of hundredths of inches which the diameter of the
object-glass contains. Thus, a 3¾-inch object-glass, if really good,
should bear a power of 375 on double stars where light is no object; the
planets, the Moon, &c., will be best observed with a much lower power.
(See chapter on eyepieces.)
Care should be taken that the object-glass is properly adjusted. And we
may here repeat that this may be done by observing the image of a large
star out of focus. If the light be not equally distributed over the
image, or the diffraction rings are not circular, the screws of the cell
should be carefully loosened, and that part of the cell towards which
the rings are thrown very gently tapped with wood, to force it towards
the eyepiece, or the same purpose may be effected by means of the
setscrews always present on large telescopes, until perfectly equal
illumination is arrived at. This, however, should only be done in
extreme cases; it is here especially desirable that we should let well
alone.
The convenient altitude at which Orion culminates in these latitudes
renders it particularly eligible for observation; and during the first
months of the year our readers who would test their telescopes will do
well not to lose the opportunity of trying the progressively difficult
tests, both of illuminating and separating power, afforded by its
various double and multiple systems, which are collected together in
such a circumscribed region of the heavens that no extensive movement of
their instruments—an important point in extreme cases—will be necessary.
Beginning with δ, the upper of the three stars which form the belt,
the two components will be visible in almost any instrument which may
be used for seeing them, being of the second and seventh magnitudes,
and well separated. The companion to β, though of the same magnitude
as that to δ, is much more difficult to observe, in consequence of its
proximity to its bright primary, a first-magnitude star. Quaint old
Kitchener, in his work on telescopes, mentions that the companion to
Rigel has been seen with an object-glass of 2¾-inch aperture; it
should be seen, at all events, with a 3-inch. ζ, the bottom star in
the belt, is a capital test both of the dividing and space-penetrating
power, as the two bright stars of the second and sixth magnitudes, of
which the close double is composed, are exactly 2½˝ apart, while there
is a companion to one of these components of the twelfth magnitude
about ¾˝ distant. The small star below, which the late Admiral Smyth,
in his charming book, “The Celestial Cycle,” mentions as a test for
his object-glass of 5·9 inches in diameter, is now plainly to be seen
in a 3¾. The colours of this pair have been variously stated; Struve
dubbing the sixth magnitude—which, by the way, was missed altogether
by Sir John Herschel—“olivaceasubrubicunda.”
That either our modern opticians contrive to admit more light by means
of a superior polish imparted to the surfaces of the object-glass, or
that the stars themselves are becoming brighter, is again evidenced by
the point of light preceding one of the brightest stars in the system
composing σ. This little twinkler is now always to be seen in a 3¾-inch,
while the same authority we have before quoted—Admiral Smyth—speaks of
it as being of very difficult vision in his instrument of much larger
dimensions. In this very beautiful compound system there are no less
than seven principal stars; and there are several other faint ones in
the field. The upper very faint companion of λ is a delicate test for a
3¾-inch, which aperture, however, will readily divide the closer double
of the principal stars which are about 5˝ apart.
These objects, with the exception of ζ, have been given more to test the
space-penetrating than the dividing power; the telescope’s action on 52
Orionis will at once decide this latter quality. This star, just visible
to the naked eye on a fine night, to the right of a line joining α and
δ, is a very close double. The components, of the sixth magnitude, are
separated by less than two seconds of arc, and the glass which shows a
_good wide black division_ between them, free from all stray light, the
spurious disk being perfectly round, _and not too large_, is by no means
to be despised.
Then, again, we have a capital test object in the great nebula to which
reference has already been made.
The star, to which we wish to call especial attention, is situate (see
Fig. 82) opposite the bottom of the “fauces,” the name given to the
indentation which gives rise to the appearance of the “fish’s mouth.”
This object, which has been designated the “trapezium,” from the figure
formed by its principal components, consists, in fact, of six stars, the
fifth and sixth (γ´ and α´) being excessively faint. Our previous
remark, relative to the increased brightness of the stars, applies here
with great force; for the fifth escaped the gaze of the elder Herschel,
armed with his powerful instruments, and was not discovered till 1826,
by Struve, who, in his turn, missed the sixth star, which, as well as
the fifth, has been seen in modern achromatics of such small size as to
make all comparison with the giant telescopes used by these astronomers
ridiculous.
Sir John Herschel has rated γ´ and α´ of the twelfth and fourteenth
magnitudes—the latter requires a high power to observe it, by reason of
its proximity to α. Both these stars have been seen in an ordinary
5-foot achromatic, by Cooke, of 3¾-inches aperture, a fact speaking
volumes for the perfection of surface and polish attained by our modern
opticians.
Let us now try to form some idea of the perfection of the modern
object-glass. We will take a telescope of eight inches aperture, and ten
feet focal length. Suppose we observe a close double star, such as ξ
Ursæ, then the images of these two stars will be brought to a focus side
by side, as we have previously explained, and the distance by which they
will be separated will be dependent on the focal length of the
object-glass. If we refer once again to Fig. 39 we shall see that this
distance depends on the focal length and on the angle subtended by the
images of the stars at the object-glass, which is of course the same as
the angle made by the real stars at the object-glass, which is called
their angular distance, or simply their distance, and is expressed in
seconds of arc.
If we take a telescope ten feet long and look at two stars 1° apart, the
angle will be 1°; and at ten feet off the distance between the two
images will be something like 2⅒ inches, and therefore, if the angle be
a second, the lines will be the 1/3600th part of that, or about 1/1700th
part of an inch apart, so that in order to be able to see the double
star ξ Ursæ, which is a 1˝ star, by means of an eight-inch object-glass,
all the surfaces, the 50 square inches of surface, of both sides of the
crown, and both sides of the flint glass, must be so absolutely true and
accurate, that after the light is seized by the object-glass, we must
have those two stars absolutely perfectly distinct at the distance of
the seventeen hundredth part of an inch, and in order to see stars ½˝
apart, their images must be distinct at one-half of this distance or at
1/3400th part of an inch from each other.
We know that both with object-glasses and reflectors a certain amount of
light is lost by imperfect reflection in the one case, and by reflection
from the surfaces and absorption in the other; and in reflectors we have
generally two reflections instead of one. This loss is to the distinct
disadvantage of the reflector, and it has been stated by authorities on
the subject, that, light for light, if we use a reflector, we must make
the aperture twice as large as that of a refractor in order to make up
for the loss of light due to reflection. But Dr. Robinson thinks that
this is an extreme estimate; and with reference to the four-foot
reflector which has recently been constructed, and of which mention has
already been made, he considers that a refractor of 33·73 inches
aperture would be probably something like its equivalent if the glass
were perfectly transparent, which is not the case, and when the
thickness of such a lens came to be considered, it was calculated that
instead of its being equal to the four-foot reflector, it would only be
equal to one of 37¼ of similar construction, and that even a refractor
of 48 inches aperture, if such could be made, would not come up to the
same sized reflector just referred to in illuminating power.
On the assumption, therefore, that no light is lost in transmission
through the object-glass, Dr. Robinson estimates that the apertures of a
refractor and a reflector of the Newtonian construction must bear the
relation to each other of 1 to 1·42. In small refractors the light
absorbed by the glass is small, and therefore this ratio holds
approximately good, but we see from the example just quoted how more
nearly equal the ratio becomes on an increase of aperture, until at a
certain limit the refractor, aperture for aperture, is surpassed by its
rival, supposing Dr. Robertson’s estimate to be correct. But with
specula of silvered glass the reflective power is much higher than that
of speculum metal; the silvered glass, being estimated to reflect about
90 per cent.[8] of the incident light, while speculum metal is estimated
to reflect about 63 per cent.; but be these figures correct or not, the
silvered surface has undoubtedly the greater reflective power; and,
according to Sir J. Herschel, a reflector of the Newtonian construction
utilizes about seven-eighths of the light that a refractor would do.
Speaking generally, refractors of sizes usually obtainable are
preferable to reflectors of equal and even greater aperture for ordinary
work; as in addition to the want of illuminating power of reflectors,
the absence of rigidity of the mounting of the speculum militates
against its comfort of manipulation.
In treating of the question of the future of the telescope, we are
liable to encroach on the domain of opinion and go beyond the facts
vouched for by evidence, but there are certain guiding principles which
are well worthy of discussion. There are the two classes of telescopes,
the refractors and reflectors, each possessing advantages over the
other. We may set out with observing that the light-grasping power of
the reflector varies as the square of the aperture multiplied by a
certain fraction representing the proportion of the amount of reflected
light to that of the total incident rays. On the other hand, the power
of the refractor varies as the square of the aperture multiplied by a
certain fraction representing the proportion of transmitted light to
that of the total incident rays. Now in the case of the reflector the
reflecting power of each unit of surface is constant whatever be the
size of the mirror, but in that of the refractor the transmitting power
decreases with the thickness of the glass, rendered requisite by
increased size, although for small apertures the transmitting power of
the refractor is greater than the reflecting power of the reflector;
still it is obvious that on increasing the size a stage must be at last
reached when the two rivals become equal to each other. This limit has
been estimated by Dr. Robinson to be 35·435 inches, a size not yet
reached by our opticians by some 10 inches, but object-glasses are
increasing inch by inch, and it would be rash to say that this size
cannot be reached within perhaps the lifetime of our present workers,
but up to the present limit of size produced, refractors have the
advantage in light-grasping power.
The next point worthy of attention is the question of permanence of
optical qualities. Here the refractor undoubtedly has the advantage. It
is true that the flint glass of some objectives gets attacked by a sort
of tarnish, still, that is not the case generally, while, on the other
hand, metallic mirrors often become considerably tarnished after a few
years of use, and although repolishing is not a matter of any great
difficulty in the hands of the maker, still it is a serious drawback to
be obliged to return mirrors every few years to be repolished. There
are, however, some exceptions to this, for there are many small mirrors
in existence whose polish is good after many years of continuous use,
just as on the other hand there are many object-glasses whose polish has
suffered in a few years, but these are exceptions to the rule. The same
remarks apply to the silvered glass reflectors, for although the
silvering of small mirrors is not a difficult process, the matter
becomes exceedingly difficult with large surfaces, and indeed at present
large discs of glass, say of four or six feet diameter, cannot be
produced. If, however, a process should be discovered of manufacturing
these discs satisfactorily and of silvering them, there are objections
to them on the grounds of the bad conductivity of glass, whereby changes
of temperature alter the curvature to a fatal extent, and there is also
a great tendency for dew to be deposited on the surface.
The next point to be considered is the general suitability for
observatory work, and this depends upon the quality of the work
required, whether for measuring positions, as in the case of the transit
instrument, where permanency of mounting is of great importance, or for
physical astronomy, when a steady image for a time is only required. For
the first purpose the refractor has decidedly the advantage, as the
object-glass can be fixed very nearly immovably in its cell, whereas its
rival must of necessity, at least with present appliances, have a small,
yet in comparison considerable, motion.
Again, the refractor has the advantage over the other in not being of so
large aperture when of equal power, so that the disturbing effects of
air currents is considerably less, but the method of making the tubes of
open lattice-work materially reduces this objection.
We have mentioned the difficulty of mounting mirrors, especially of
large size, but this has now been got over very perfectly. This
difficulty does not occur in the mounting of object-glasses of sizes at
present in use, but when we come to deal with lenses of some 30 inches
diameter, the present simple method will in all probability be found
insufficient.
On the other hand the cost of mirrors is of course much less than that
of object-glasses, a matter of considerable importance. The late M.
Merz, on being asked as to price of a 30-inch object-glass, estimated
that, if it were possible to make it, its cost would be between £8,500
and £9,000.
There is one great point of advantage in the use of the reflector in
physical work,—the absence of secondary spectrum; but it is by no means
certain that stellar photography will not be more easy with refractors.
-----
Footnote 8:
Sir John Herschel, in his work on the telescope, gives the following
table of reflective powers:—
After transmission through one surface of glass not in contact 0·957
with any other surface
After transmission through one common surface of two glasses 1·000
cemented together
After reflection on polished speculum metal at a perpendicular 0·632
incidence
After reflection on polished speculum metal at 45° obliquity 0·690
After reflection on pure polished silver at a perpendicular 0·905
incidence
After reflection on pure polished silver at 45° obliquity 0·910
After reflection on glass (external) at a perpendicular 0·043
incidence
The effective light in reflectors (irrespective of the eyepieces) is
as follows:—
Herschelian (Lord Rosse’s speculum metal) A. 0·632
Newtonian (both mirrors ditto) B. 0·436
Newtonian (small mirror or glass prism) C. 0·632
Gregorian or Cassegrainian D. 0·399
{ A. 0·905
The same telescopes, all the metallic { B. 0·824
reflections being from pure silver { C. 0·905
{ D. 0·819
BOOK III.
_TIME AND SPACE MEASURERS._
CHAPTER XIII.
THE CLOCK AND CHRONOMETER.
I. THE RISE AND PROGRESS OF TIME-KEEPING.
When we dealt with the astronomical instruments of Hipparchus, we saw
that although the astrolabe which that great observer used was the germ
of our modern instruments, the time recorded by Hipparchus and those who
lived after him down to the later times of the Roman Empire was, as they
measured it, a time which would be entirely useless for us.
The ancients contented themselves with dividing the interval between
sunrise and sunset, regardless whether this was in summer or winter,
into twelve equal hours. Now, as in summer the sun is longer above the
horizon than in winter in these northern latitudes, we have more time
during which the sun is above the horizon in summer than in winter, and
if that period of time is to be divided into twelve hours, the hours
would be much longer in summer than in other seasons.
As we are informed by Herodotus, tables were made by which these varying
lengths of hours might be indicated by the shadows of a pole, which they
called a gnomon or style. This was placed in a given locality, and the
hour of the day was determined by the position of the shadow of the
gnomon; and we need scarcely say that as Hipparchus observed he was
compelled to find the position of the sun in order to determine the
absolute longitude of a star at night. The ancients were limited to such
ideas of time as could be got from slaves, who watched the risings and
settings of the constellations, and who tried to bring to their own
minds and those of their masters some idea of the lapse of time; and
this even a few centuries ago was ordinarily depended upon in several
countries.
Then, a little later, we come to the time being measured by monks
repeating psalms—a certain number perhaps in the hour; and there were
the water and sand clocks dating from Aristophanes, which were the
predecessors of our sand-glasses. Candles were also at one time used
with divisions on them to show how long they had been burning. But when
we come to clocks proper, the history of which is very imperfectly
known, we find an enormous improvement upon this state of things;
because the clock, being dependent upon a constant mechanical action
produced by the fall of a weight, could not be got to imitate these
varying hours.
Still the clock had to fight its own battle for all that; and the first
clocks were altered from week to week, or from month to month, so that
the time-keeper, which did its best to be constant, was made inconstant
to represent the ever-varying hours.
Doubtless the history of the first clocks—by which we do not mean the
sand clocks or water clocks of the ancients, but such as those used by
Archimedes when he attached wheels together—is lost in obscurity; and
whether clocks, as we have them, were suggested in the sixth (Boethius,
A.D. 525) or ninth century matters little for our inquiry; but beyond
all doubt the first clock of considerable importance that was put up in
England was the one erected in Old Palace Yard in the year 1288, as the
result of a fine imposed upon the Lord Chief Justice of that time.
[Illustration:
FIG. 85.—Ancient Clock Escapement.
]
If we have a falling weight as a time-measurer we must also have some
opposing force—a regulator in fact, so that the weight becomes the
source of power, and the regulator the time-measurer; therefore, in
addition to the fall of the weight, we find in the earliest clocks a
regulating power to prevent the weight falling too fast. So we have the
two contending powers, first the weight causing the motion and then the
regulator.
The first thing which was introduced as a regulator was a fly-wheel.
There was a fly-wheel of a certain weight, and the force which was
applied to the clock had to turn the wheel against the resistance of the
air; but that did not answer well, and the first tolerable arrangement
was suggested by Henry de Wyck, who constructed a bell and a clock in
1364, in which the fall of the weight was prevented by an oscillating
balance, similar to that shown in Fig. 85.
[Illustration:
FIG. 86.—The Crown Wheel.
]
Here we see what is called the crown wheel (S S, shown in plan, Fig.
86), on which the escapement depends, and into the teeth of which work
two pallets, P_{1} P_{2}, which are placed on a vertical axis pivoted
above and below. Now if we suppose a weight attached to the cord passing
over a drum, so as to propel the intermediate wheels and pull them
round, the crown wheel tends to rotate, but is prevented from moving
until the pallets give way. Let us see how the clock goes. When the
bottom tooth, presses against the pallet P_{1}, in order to make it get
out of the way and enable the wheel to go on, it twists the rod and
moves the horizontal bar M M, on which are several saw-like teeth, on
the intervals of which, as in the modern steelyard, weights are placed,
so that the wheel pushes away the pallet and makes the horizontal beam
describe a part of a circle. And what happens is this:—the upper pallet
is turned out of its position and driven into the upper teeth of the
wheel, and driven out by the further revolution of the wheel, so that
the fall of the weight depends on the oscillations of the horizontal
beam which carries the weights. The clock was regulated by the distance
of the weights from the pivots on which the balance swung. Such was the
form of clock used by Tycho Brahe, but with little success, for it was
extremely irregular in its action, and Tycho still had to compare the
position of one star with another instead of trusting to his clock.
There is no necessity to say much regarding the train of wheels between
the weight or spring and the escapement. Their office is simply to
create a great difference in velocity of rotation between the wheel
turned by the weight or spring and the escape wheel, so that a slow
motion with great force may be transformed into a quick motion with
small force. The train of wheels is so arranged, by the consideration of
the number of teeth in the wheels, that one wheel shall go round once an
hour, and another once a minute, so that the first may carry the
minute-hand and the other the second-hand. The hour-hand wheel is also
geared to the minute-wheel, so that it shall turn once in twelve hours
or twenty-four hours, according to the purposes for which the clock is
required. Weights are usually used when space is no object, being more
regular in their action than springs; but the latter are used for
chronometers and watches, and other portable time-keepers.
The general arrangement of the clock train is shown in Fig. 87, where W
is the weight, hung by a cord passing over the barrel B, on the axis of
wheel G. The teeth of the wheel G gear into the pinion P_{1}, which
again is carried on the axis of the wheel C, and so on up the last
wheel—the escape-wheel, which generally is cut to thirty teeth, so that
it goes round once a minute and carries a second-hand. The pinion P_{1}
is so arranged by the number of teeth between it and the escape-wheel
that it goes round once an hour or to sixty turns of the escape-wheel.
[Illustration:
FIG. 87.—The Clock Train.
]
[Illustration:
FIG. 88.—Winding Arrangements.
]
To wind up the clock the barrel B, Fig. 88, is turned round by the key
on the square; the pawl L fastened to the wheel G allows the barrel to
be turned in one direction without turning the wheel. It is obvious,
however that directly we begin to wind up, the pressure on the pawl
tending to turn the wheel G is removed, and the clock stops—a very
objectionable thing in astronomical and other clocks supposed to keep
good time. The following is one of the devices for keeping the clock
going during winding,—in this case everything is the same as before,
with the exception of an additional rachet-wheel R_{2}, Fig. 88,
carrying the pawl L; this wheel is loose on the axis but attached to the
wheel G through the spring S. The weight therefore acts on the pawl L,
and tends to drive the wheel R_{2}, which again presses round the wheel
G by means of the spring S, and, as the whole moves round, the teeth of
the wheel R_{2} pass the pawl K K fixed to some part of the clock-frame.
When now we commence to wind, the pressure on the pawl L and wheel R_{2}
is removed, and the spring S S, which is always kept bent by the action
of the weight, endeavours to open; and since the wheel R_{2} is
prevented from going backwards by the pawl K, the wheel G is continually
urged onwards by the spring, and the clock kept going for the short
period of winding.
II. THE PENDULUM.
The clock, as left by Henry de Wyck, was only an exceedingly irregular
time-keeper, and some mechanical contrivance that should beat or mark
correct intervals of time was urgently required. The contrivance for
beating correct intervals of time—the pendulum—was thought of by
Galileo, who showed that its oscillations were isochronous, although
their lengths might vary within small limits. The pendulum then was just
the very thing required, and Huyghens, in 1658, applied it to clocks.
In the next form of clock, therefore, we find the pendulum introduced as
a regulator. There was a crown wheel like the one in the balance clock,
only instead of being vertical it was horizontal. This wheel was allowed
to go round and the weight was allowed to fall by means of alternating
pallets; it was in fact like that shown in Fig. 86, with the balance
weights and the rod carrying them removed, and instead thereof there was
a rod, attached at right angles to the end of that carrying the pallets,
and hanging downwards, which, by means of a fork at its lower end, swung
a pendulum to an extent equal to the go of the balance first used. Thus
the pendulum was adapted by Huyghens. We have here something extremely
different from the rough arrangement in which the weight was controlled
by the horizontal oscillating bar carrying the weights, for the balance
would go faster or slower as the crown wheel pressed harder or softer
against the pallets, and so, if the weight acted at all irregularly the
clock would go badly. But with the pendulum the control of the weight
over it is small, for the bob can be made of considerable weight,
because it swings from its suspending spring without friction, and such
a heavy weight at the end of a long rod is scarcely altered in its rate
by variations of pressure on the pallets.
Galileo and Huyghens who followed him found that the oscillations of a
simple pendulum are isochronous at all places where the force of gravity
is equal, and that the time of oscillation depends on the length of the
pendulum—the shorter the pendulum the shorter time of oscillation, and
_vice versâ_. The time of oscillation varying as the square root of the
length.
In 1658, then, the pendulum was applied to clocks, as the balance had
been before that time. But Huyghens was not slow to perceive that the
circular arc of a rigid pendulum would not be sufficiently accurate for
an astronomical time-keeper, when used with a clock like that employed
by Tycho Brahe and the Landgrave of Hesse for their astronomical
observations. Huyghens next showed that with a clock of that kind,
requiring a large swing of pendulum, the oscillations were not quite
isochronous, but varied in time according as the arc increased or
diminished. It was clear therefore that this simple form of pendulum
would not do well for the large and varying arc required to be
described, but that the theoretical requirements would be satisfied if
the pendulum, instead of being suspended from a rigid rod, were
suspended by a cord or spring or some elastic substance which would
mould itself against two curved pieces of metal, C C, Fig. 89, attached
one on either side of the suspending spring. In swinging, the spring
would wrap, as it were, gradually round either curved surface, and so
virtually alter the point of suspension, and with it, of course, the
virtual length of the pendulum; so that the extreme point of the
pendulum U, instead of describing a circular arc K B as before, would,
by means of the portions of metal at the top, have a cycloidal motion D
L, the pendulum becoming virtually shorter as the spring wrapped round
the pieces of metal, so that it becomes isochronous for any length of
swing. But it was very soon found that the theoretically perfect clock
did not after all go as well as the clock it was to replace. And it
would now be difficult to say what would have happened if a few years
afterwards clocks had not been made much more simple and perfect by the
introduction of an entirely new escapement which permitted a very small
swing.
[Illustration:
FIG. 89.—The Cycloidal Pendulum.
]
If we wish a clock to go perfectly well, we have only to consider a very
few things—First, the weight should be as small as possible; secondly,
within reason, the pendulum should be as solidly suspended and as heavy
as possible; and, thirdly, the less connection there is between the
pendulum which controls the clock, and the weight which drives the
clock, the better.
The latter point is provided for in the dead beat arrangement of Graham,
and in the “gravity” and other forms of escapement, about which more
presently. At present we have been dealing with pendulums as if they
were simple pendulums, which are almost mathematical abstractions.
Everything that we have said assumes that there is a mass depending from
such a fine line that the mass of the line shall not be considered; but
if we examine the pendulum of some clocks we see that the rod is of
steel, and that its weight or bob is elongated, and consists of a long
cylinder of glass filled with mercury, and carried in a sort of stirrup
of steel; this is very different from our simple pendulum—it is a
compound pendulum. In a compound pendulum we have first of all the axis
of suspension, which is the axis where the pendulum is supported on the
top, and below that, near the centre of gravity of the pendulum, we have
what is called the centre of oscillation. It will at once be perceived
that as the rate of the pendulum depends upon its length, the particles
in the upper part of the pendulum will be trying to go more rapidly than
they can go, seeing that they are connected in one series of particles,
and that the particles at the lowest portion are carried with greater
velocity than they would be if they were left to themselves, because
they are connected rigidly with the upper ones. Therefore we have to
find a point, which oscillates at the same rate as it would if all the
other particles were absent.
This is called the centre of oscillation, and it is on the distance of
this from the point of suspension that the rate depends.
What is the use of the mercury? It is to compensate for the expansion of
the rod by temperature. We shall at once see the reason of this from the
fact that the pendulum gets longer by being heated, and the rate of the
pendulum depends on the square root of its length; that is, if we
multiply the length by four, the square root of which is two, we shall
only multiply the rate by two, or double the time of oscillation.
Therefore, since temperature causes all metals to vary in length, and
metals are the most useful things we can employ for the support of the
weights, we find that we have to consider further the alteration of the
length of the pendulum due to the variation of the length of the metal
we employ. Hence, in addition to the necessity of an arrangement which
gives the shortest possible swing, we require also a method for
compensating for changes of temperature.
[Illustration:
FIG. 90.—Graham’s, Harrison’s, and Greenwich Pendulums.
]
We have not space to go through the history of compensating pendulums,
but we may direct attention to some of the best results which have been
obtained in this matter. We will first examine the mercurial pendulum,
Fig. 90, which we have referred to. In this case the compensation is
accomplished as follows: Mercury is inclosed in a glass cylinder M M;
shown in the left hand side of the figure; and as the mercury expands
more than the glass, it will rise to a higher level on being heated; and
the lengthening of the steel rod R R will be counteracted by a similar
lengthening due to the expansion of mercury, so that the centre of
oscillation is carried down by the steel rod, and up by the mercury, and
it is therefore not displaced if the proper ratio is maintained between
the length of the steel rod and the column of mercury in the glass
vessel. The mercury in the glass will lengthen fifteen times as much as
the steel rod, if we have equal lengths of each, so that in order that
they may expand equally the rod must be fifteen times as long as the
mercury column. This would keep the top of the mercury at the same
distance from the point of suspension, but we want to keep the centre of
oscillation, which is about half way down the column, at the same
distance, so we double the height of the mercury, making it
two-fifteenths of the length of the steel rod, so that the surface is
over-compensated, but the centre of oscillation is exactly corrected. An
astronomer can alter the amount of mercury as he pleases, making it now
more, now less, till the stars tell him he has done the right thing, and
the pendulum is compensated, and the clock keeps correct time at all
temperatures.
The little sliding cup C is to carry small weights for final delicate
adjustment, the addition of a weight thus obviously tending to increase
the rate of the pendulum.
This is Graham’s mercurial pendulum, invented by him in 1715. There is
another compensating pendulum, called Harrison’s gridiron pendulum, from
the bars of metal sustaining the pendulum being arranged gridiron
fashion, Fig. 90. At the top is a knife edge or spring for the centre of
suspension, and the pendulum bob is suspended by a system of rods, the
five black ones being made of a less expansible metal than the other
four; consequently, as the five black ones expand and tend to lower the
bob, the intermediate ones expand also and tend to raise it; the length
of the black rods exceeding that of the others, these latter must be
made of a more expansible metal to make up for their smaller length.
Thus the acting length of the shaded rods is two-thirds of the acting
length of the black ones (each pair is considered as one rod because
they act as such), so that a metal is used for the former which expands
more than that used for the latter in the proportion of about three to
two, and brass is found to answer for the most expansible metal, and
steel for the less. These rods are packed side by side, and look very
ornamental. If _l_ be the length of the brass rods, and _l´_ that of the
steel rods, and _e_ the coefficient of expansion of the brass, and _e´_
that of the steel, then _l_: _l´_:: _e´_: _e_. The pendulum is then
compensated, and the bob remains at the same distance from the centre of
suspension at all temperatures.
For the pendulum of the clock at the Royal Observatory a modification of
the gridiron form has been adopted; for it was found on trial with a
mercurial pendulum that the steel rod gained in temperature more rapidly
than the mercury, and lost heat quicker, so that the pendulum did not
compensate immediately on a change of temperature. The form adopted is
as follows (Fig. 90):—A steel rod is suspended as usual, and is
encircled by a zinc tube resting on the nut for rating the pendulum; the
zinc tube is again encircled by a steel tube resting on the top of the
zinc tube and carrying at its lower end a cylindrical leaden bob
attached at its centre to the steel tube; slots and holes are cut in the
tubes to expose the inner parts to the air, so that each will experience
the change of temperature at the same time. It is of course possible
that the tubes forming the pendulum rod are not of exactly the right
length to perfectly compensate; a final delicate adjustment is therefore
added. On the crutch axis, and held by a collar to it, are two compound
bars of brass and steel, _h_ and _i_, Fig. 96. The collar fits loosely
on the axis, so that the rods, which carry small weights at their
extremities, can be easily shifted to make any angle with the
horizontal; then, since brass expands more than steel for the same
degree of heat, the bars will bend on being heated or cooled, and if the
brass be uppermost the weights at the ends of the rods will be lowered
with an increase of temperature, and will tend to increase the rate of
the pendulum, and _vice versâ_. So long as the rods are horizontal and
in the same straight line their centre of gravity is in the crutch axis,
and they are therefore balanced in every position; they therefore only
retard the pendulum by their inertia; but when the ends are bent down
the centre of gravity is lowered, and they have a tendency to come to a
horizontal position and to balance each other like a scale beam, and so
swing with the pendulum and overcome its retardation.
It is obvious that they would, if alone, swing in a shorter time than
the pendulum and so, being connected, they increase its rate.
When the rods are vertical they have no compensating action, for the
centre of gravity is simply thrown sidewise, and acts as a continuous
force tending to make the pendulum oscillate further on one side than on
the other; and in the intermediate positions of the rods their action
varies, and a consideration of the position of their centre of gravity
will give the intensity of the compensating action. In order to make a
small change in the rate of the clock without stopping it to turn the
screw at the bottom of the pendulum, the following contrivance is
adopted.
A weight _k_ slides freely on the crutch rod, but is tapped to receive
the screw cut on the lower portion of the spindle _l_, the upper end of
which terminates in a nut _m_ at the crutch axis. By turning this nut
the position of the small weight on the crutch rod is altered, and the
clock rate correspondingly changed. To make the clock lose, the weight
must be raised.
There is also another method of compensation, depending on differential
expansion. Attached to an ordinary pendulum just above the bob, and at
right angles to it, is a composite rod, made of copper and iron, the
lower half being copper; then, as the pendulum rod lengthens and lets
down the bob, the copper expands more than the iron, and causes the rod
to bend, like a piece of wood wetted on one side, and by this bending or
warping the weights at either end are raised as the bob is lowered, so
the centre of oscillation keeps at the same height at all temperatures.
We have dealt with clocks and pendulums somewhat in the order of their
invention. We may add that the great majority of clocks of modern
manufacture of any pretention to time-keepers are constructed with the
dead beat escapement of Graham or a modification of it, combined with a
mercurial or gridiron pendulum. For the best Observatory clocks of the
more expensive kind other more elaborate forms of escapement are
sometimes used, as, for example, that in the clock at the Royal
Observatory, Greenwich, which we shall refer to in detail further on, on
account of other new points in its construction.
Now, having a clock good enough to use with the transit instrument, it
is necessary to take the utmost precautions with reference to it. The
Russian astronomers have inclosed their clock in a stone case, and
placed it many yards below the ground, endeavouring thus to get rid of
the action of temperature, which changes the length of the steel
pendulum rod. But that is not all; after we have corrected our clock as
well as we can from the point of view of temperature, it is still found
that there may be a variation, amounting to something considerable, due
to another cause. If the barometer changes an inch or an inch and a half
by change of pressure of the air, the rate of the pendulum will alter,
and the cause of the variation it is impossible to prevent without
putting the clock in a vacuum, so that changes of the barometer must be
allowed for.
There are, however, methods of compensating the pendulum for changes of
pressure if desirable: one way of doing this is to pass the suspending
spring of the pendulum through a slit in a metal plate, which then
becomes virtually the point of suspension; this plate is then raised or
lowered by an aneroid barometer, or by a float in an ordinary cistern
barometer so that the length of the pendulum is virtually altered with
the pressure of the atmosphere. At Greenwich the Astronomer-Royal has
adopted the following expedient: A magnet at the lower end of the
pendulum passes at each swing near a magnet which is raised or lowered
by means of a float in the cistern of a barometer. The magnet then has a
greater or less influence on the pendulum magnet according as the
pressure of the air varies, and so adds a variable amount to the effect
of gravity and therefore to the rate of oscillation.
[Illustration:
FIG. 91.—Greenwich Clock: arrangement for Compensation for Barometric
Pressure.
]
This principle is carried out as follows:—Two bar magnets, each about
six inches long, are fixed vertically to the bob of the clock pendulum;
one in front, _a_, Fig. 91, the other at the back. The lower pole of the
front magnet is a north pole; the lower pole of the back magnet is a
south pole. Below these a horse-shoe magnet, _b_, having its poles
precisely under those of the pendulum magnets, is carried transversely
at the end of the lever _c_, the extremity of the opposite arm of the
lever being attached by the rod _d_, to the float _e_ in the lower leg
of a syphon barometer. The lever turns on knife edges. A plan of the
lever (on a smaller scale) is given, as well as a section through the
point A. Weights can be added at _f_ to counterpoise the horse-shoe
magnet. The rise or fall of the mercurial barometer correspondingly
raises or depresses the horse shoe magnet, and, increasing or decreasing
the magnetic action between its poles and those of the pendulum magnets,
compensates, by the change of rate produced, for that arising from
variation in the pressure of the atmosphere. The shorter leg of the
barometer in which the float rests has an area of four times that of the
barometer tube at the upper surface of the mercury, so that for a large
change of barometric height the magnet is only moved a small distance, a
change of one inch of the barometer lowering the surface in the short
leg 2/10 inch; the distance between the pendulum magnets and the
horse-shoe magnets is 3¾ inches.
III. ESCAPEMENTS.
The invention of the pendulum, its application, and the improvements
thereon having been described, it remains to treat of the equally
important improvements on the escapement. The first change for the
better appears to have been due to Hooke, who in 1666 brought before the
Royal Society the crutch, or anchor escapement, whereby the arc through
which the pendulum vibrated was so much reduced that Huyghens’s
cycloidal curves became unnecessary, and the power required to drive the
clock was materially reduced.
This escapement, common in ordinary eight-day clocks, is different from
that previously described in the way in which the crown wheel or escape
wheel is regulated.
We have come back to a vertical escape wheel as it was in the clock used
by Tycho; but instead of using two pallets on a rod which regulated the
wheel, we have here an anchor escapement (Fig. 92) in connection with
the pendulum; and what happens is this—when the pendulum is made to
oscillate, these pallets P P gradually move in and out of the teeth of
the wheel, and let a tooth pass at every swing; and it is obvious that
when the wheel and anchor are nicely adjusted, an extremely small motion
of the anchor, and consequently a small oscillation of the pendulum,
allows the escape wheel to turn round, and the clock to go.
The greater regularity of this form of escapement is due to a smaller
oscillation of the pendulum being required than with the form first
described; for it is found that the motion of a pendulum when vibrating
through not more than six degrees is practically cycloidal, and it is
only with larger arcs that the circle materially differs from the
theoretical curve required.
The pendulum is kept in vibration by the escape wheel, or rather by its
teeth pressing against the inclined surfaces of the pallets, and forcing
them outwards, and so giving the pendulum an impulse prior to each tick.
[Illustration:
FIG. 92.—The Anchor Escapement.
]
This anchor escapement, which was invented by “Clement, of London,
clockmaker,” forms, as it were, the basis of our modern clocks, and,
with the exception of the dead beat, which was due to Graham some years
afterwards, is in almost exclusive use at the present date.
We see that as soon as a tooth has escaped on one side, a tooth on the
other begins immediately to retard the action of the pendulum by
pressing against the inclined surface of the other pallet, and as the
pendulum swings on, the tooth gives way, and the motion of the wheel is
reversed; then when the pendulum begins to return, it is assisted again
by the tooth, so that the pendulum is always under the influence of the
escape wheel, some times accelerated, and sometimes retarded. The
principle of Graham’s dead beat is to get rid of the retarding action of
the escape wheel, so that there should be no necessity for so much
accelerating power, and the pendulum should be out of the influence of
the escape wheel during a large portion of its vibration. This he
accomplished by doing away with a large portion of the inclined surface
of the pallet (Fig. 93), so that the teeth have no accelerating action
on the pendulum until just as they leave the ends of the pallets where
they are inclined; the greater portion of both the pallets on which the
escape wheel works being at right angles to its direction of motion, the
teeth have no tendency to force the pallet outwards. In Fig. 93 the
tooth V has fallen on the pallet D, the tooth T having just been
released, and as the pendulum still swings on in the direction of the
arrow, the pallet D will be pushed further under the tooth C but without
pressing the wheel backwards, and without retardation other than that of
friction. When the pendulum returns and the pallet just gets past the
position shown, it gets an impulse, and this is given as nearly as
possible as much before the pendulum reaches its vertical position as
after it passes it, its action is therefore neither to increase nor
diminish the rate. In this escapement not only is the arc of oscillation
considerably lessened and the motion of the pendulum brought near to the
cycloidal form, but in addition to this there is this important point,
that the weight is acting upon the pendulum for the least possible time.
[Illustration:
FIG. 93.—Graham’s Dead Beat.
]
[Illustration:
FIG. 94.—Gravity Escapement (Mudge).
]
We will now describe the more elaborate forms of escapement, and we will
take first the gravity escapement, as it is called. The principle of its
action consists in there being a small impulse given to the pendulum at
each oscillation, by means of two small rods hanging, one on each side
of it, and tending by their own weight to force the pendulum into a
vertical position; these rods are alternately pushed outwards by the
escapement before the pendulum in its swing arrives at them, and then
they are allowed to press against it on its return towards the vertical,
so that the pendulum has a constant force acting on it at each
oscillation, unconnected with the clock movement. This is carried out in
the escapement invented by Mudge, as shown in Fig. 94. The pendulum rod
is supposed to be hanging just in front of the rods hanging from the
pivots Y_{1} Y_{2}, and on swinging it presses against the pins at the
lower ends of the rods and so lifts the pallets S_{1} S_{2} out of the
teeth of the escape wheel. In the position shown the pendulum is moving
to the right, having been gently urged from the left by the weight of
the pallet rod Y_{2} S_{2}, and the pallet S_{1} has been lifted
outwards by the tooth acting on its inclined surface. On the pendulum
rod reaching the pin the rod is moved outwards and the end of the pallet
S_{1} pushed out of the tooth when the wheel moves on, at the same time
pushing outwards the pallet S_{2}. As the pendulum returns towards the
left again the rod Y_{1} follows it, giving it a gentle impulse by its
own weight until it returns nearly to the vertical or to the
corresponding position in which Y_{2} S_{2} is shown. On the pendulum
swinging on and releasing T_{2} the pallet S_{1} is again pushed
outwards by the inclined plane to the position shown in the diagram. In
this escapement there was danger of the pallets being thrown too
violently outwards so that the teeth were not caught by the flat
surfaces at the ends, and Mr. Bloxam improved on it by letting the
pallets be thrown outwards by a small wheel on the axis of the escape
wheel so that the action was less rapid; he accomplished this in the
following manner. On the end of the axis of the last wheel are a number
of arms A A, Fig. 95, say nine, about 1½ inches long, which are
prevented from revolving by studs L_{1} L_{2} on the inside of each
hanging rod P_{1} P_{2}; then, as each rod is pushed outwards by the
pendulum, an arm escapes from a stud and the clock goes on one second.
Each rod is pushed outwards by the clock almost sufficiently far for the
arm to escape, but not quite, so that the pendulum just releases the arm
at the end of its swing in the same manner as in Mudge’s escapement,
Fig. 94; but instead of the teeth of the escape wheel pushing the rods
outwards there is the small wheel T_{1} T_{2}, having the same number of
teeth as there are arms on the axis and close to them, and the
projecting pieces H_{1} H_{2} at right angles to each swinging rod rest
against the teeth of this wheel, one resting against the teeth at the
top and the other at the bottom, so that they catch against the teeth
after the manner of a ratchet, and the rods are pushed outwards by this
wheel as it revolves. The arms and ratchet wheel are so set that, during
the motion of an arm A, to a stud, a tooth of the ratchet wheel is
pushing outwards the rod carrying that stud. The action is as
follows:—The pendulum having just swung up to a rod and released the arm
pressing against its stud, the arms and ratchet wheel revolve, and the
tooth of the ratchet wheel, which had been pressing outwards the
swinging rod, passes on free of the projecting piece, which can now move
backwards to the next tooth; so the rod, being no longer supported,
presses against the pendulum rod on its return oscillation. The arms and
ratchet wheel revolve until an arm on the opposite side comes in contact
with the stud on the other rod, and in revolving the ratchet wheel
throws outwards this rod just so far that the arm is not released. The
pendulum is assisted by the weight of the first rod to the vertical
position, when the projecting piece of the rod comes in contact with the
next tooth of the ratchet wheel where it rests until the oscillation is
completed, and the second arm is released. It is then forced outwards,
and the next arm on that side presses against the stud, when a
repetition of the foregoing takes place. In this way the clock is kept
going without any direct action of the clock train on the pendulum.
[Illustration:
FIG. 95.—Gravity Escapement (Bloxam).
]
Another very beautiful escapement is that devised by the
Astronomer-Royal and carried out in the clock erected in 1871 at
Greenwich.[9] In this case the pendulum is free except during a portion
of every alternate second, when it releases the escapement and receives
an impulse, so that there is a tick only at every other second.
[Illustration:
FIG. 96.—Greenwich Clock Escapement.
]
The details of the escapement may be seen in Fig. 96, which gives a
general view of a portion of the back plate of the clock movement,
supposing the pendulum removed; _a_ and _b_ are the front and back
plates respectively of the clock train; _c_ is a cock supporting one end
of the crutch axis; _d_ is the crutch rod carrying the pallets, and _e_
an arm carried by the crutch axis and fixed at _f_ to the left-hand
pallet arm; _g_ is a cock supporting a detent projecting towards the
left and curved at its extreme end; at a point near the top of the
escape wheel this detent carries a pin (jewel) for locking the wheel,
and at its extreme end there is a very light “passing spring.” The
action of the escapement is as follows:—Suppose the pendulum to be
swinging from the right hand. It swings quite freely until a pin at the
end of the arm _e_ lifts the detent; the wheel escapes from the jewel
before mentioned, and the tooth next above the left-hand pallet drops on
the face of the pallet (the state shown in the figure), and gives
impulse to the pendulum; the wheel is immediately locked again by the
jewel, and the pendulum, now detached, passes on to the left; in
returning to the right, the light passing spring, before spoken of,
allows the pendulum to pass without disturbing the detent; on going
again to the left, the pendulum again receives impulse as already
described. The right-hand pallet forms no essential part of the
escapement, but is simply a safety pallet, designed to catch the wheel
in case of accident to the locking-stone during the time that the
left-hand pallet is beyond the range of the wheel. The escape wheel
carrying the seconds hand thus moves once only in each complete or
double vibration of the pendulum, or every two seconds.
IV. THE CHRONOMETER.
We have now given a description of the astronomical clock—the modern
astronomical instrument which it was our duty to consider. There is
another time-keeper—the chronometer—which we have to dwell upon. In the
chronometer, instead of using the pendulum, we have a balance, the
vibration of which is governed by a spiral spring, instead of by
gravity, as the pendulum is. By such means we keep almost as accurate
time as we do by employing a pendulum, the balance being corrected for
temperature on principles, one of which we shall describe.
We must premise by saying that fully four-fifths of the compensation
required by a chronometer or watch-balance is owing to the change in
elasticity of the governing spiral spring, the remainder, comparatively
insignificant, being due to the balance’s own expansion or contraction.
The segments R_{1}, R_{2} of the balance (see Fig. 97) are composed of
two metals, say copper and steel, the copper being exterior; then as the
governing spiral spring loses its elasticity by heat, the segments
R_{1}, R_{2} curve round and take up positions nearer the axis of
motion, the curvature being produced by the greater expansion of copper
over steel; and thus the loss of time due to the loss of elasticity of
the spiral spring is compensated for.
This balance may be adjustable by placing on the arms small weights, W
W, which may be moved along the arms, and so increase or diminish the
effect of temperature at pleasure.
[Illustration:
FIG. 97.—Compensating Balance.
]
Of the number of watch and chronometer escapements we may mention the
detached lever—the one most generally used for the best watches, the
form is shown in Fig. 98. P P are the pallets working on a pin at S as
in the dead-beat clock escapement; the pallets carry a lever L which can
vibrate between two pins B B. R is a disc carried on the same axis with
the balance, and it carries a pin I, which as the disc goes round in the
direction of the arrow, falls into the fork of the lever, and moves it
on and withdraws the pallet from the tooth D, which at once moves
onwards and gives the lever an impulse as it passes the face of the
pallet. This impulse is communicated to the balance through the pin I,
the balance is kept vibrating in contrary directions under the influence
of the hair-spring, gaining an impulse at each swing. On the same axis
as R is a second disc O with a notch cut in it into which a tongue on
the lever enters; this acts as a safety lock, as the lever can only move
while the pin I is in the fork of the lever.
[Illustration:
FIG. 98.—Detached Lever Escapement.
]
The escapement we next describe is that most generally used in
chronometers. S S, Fig. 99, is the escape wheel which is kept from
revolving by the detent D. On the axis of the balance are two discs,
R_{1}, R_{2}, placed one under the other. As the balance revolves in the
direction of the arrow, the pin P_{2} will come round and catch against
the point of the detent, lifting it and releasing the escape-wheel,
which will revolve, and the tooth T will hit against the stud P_{1},
giving the balance an impulse. The balance then swings on to the end of
its course and returns, and the stud P_{2} passes the detent as follows:
a light spring Y Y is fastened to the detent, projecting a little beyond
it, and it is this spring, and not the detent itself, that the pin P_{2}
touches: on the return of P_{2} it simply lifts the spring away from the
detent and passes it, whereas in advancing the spring was supported by
the point of the detent, and both were lifted together.
[Illustration:
FIG. 99.—Chronometer Escapement.
]
[Illustration:
FIG. 100.—The Fusee.
]
In watches and chronometers and in small clocks a coiled spring is used
instead of a weight, but its action is irregular, since when it is fully
wound up it exercises greater force than when nearly down. In order to
compensate for this the cord or chain which is wound round the barrel
containing the spring passes round a conical barrel called a _fusee_
(Fig. 100): B is the barrel containing the spring and A A the fusee. One
end of the spring is fixed to the axis of the barrel, which is prevented
from turning round, and the other end to the barrel, so that on winding
up the clock by turning the fusee the cord becomes coiled on the latter,
and the more the spring is wound the nearer the cord approaches the
small end of the fusee, and has therefore less power over it; while as
the clock goes and the spring becomes unwound, its power over the axis
becomes greater. The power, therefore, acting to turn the fusee remains
pretty constant.
-----
Footnote 9:
By Messrs. E. Dent and Co. of the Strand.
CHAPTER XIV.
CIRCLE READING.
One of the great advantages which astronomy has received from the
invention of the telescope is the improved method of measuring space and
determining positions by the use of the telescope in the place of
pointers on the old instruments. The addition of modern appliances to
the telescope to enable it to be used as an accurate pointer, has played
a conspicuous part in the accurate measurement of space, and the results
are of such importance, and they have increased so absolutely _pari
passu_ with the telescope, that we must now say something of the means
by which they have been brought about.
For astronomy of position, in other words for the measurement of space,
we want to point the telescope accurately at an object. That is to say,
in the first instance we want circles, and then we want the power of not
only making perfect circles, but of reading them with perfect accuracy;
and where the arc is so small that the circle, however finely divided,
would help us but little, we want some means of measuring small arcs in
the eyepiece of the telescope itself, where the object appears to us, as
it is called, in the field of view; we want to measure and inspect that
object in the field of view of the telescope, independently of circles
or anything extraneous to the field. We shall then have circles and
micrometers to deal with divisions of space, and clocks and chronographs
to deal with divisions of time.
We require to have in the telescope something, say two wires crossed,
placed in the field of view—in the round disc of light we see in a
telescope owing to the construction of the diaphragm—so as to be seen
together with any object. In the chapter on eyepieces it was shown that
we get at the focus the image of the object; and as that is also the
focus of the eyepiece, it is obvious that not only the image in the air,
as it were, but anything material we like to put in that focus, is
equally visible. By the simple contrivance of inserting in this common
focus two or more wires crossed and carried on a small circular frame,
we can mark any part of the field, and are enabled to direct the
telescope to any object.
In the Huyghenian eyepiece, Fig. 60, the cross should be between the two
convex lenses, for if we have an eyepiece of this kind the focus will be
at F, and so here we must have our cross wires; but, if instead of this
eyepiece we have one of the kind called Ramsden’s eyepiece, Fig. 62,
with the two convex surfaces placed inwards, then the focus will be
outside, at F, and nearer to the object-glass: therefore we shall be
able to change these eyepieces without interfering with the system of
wires in the focus of the telescope. We hence see at once that the
introduction of this contrivance, which is due to Mr. Gascoigne, at once
enormously increases the possibility of making accurate observations by
means of the telescope.
[Illustration:
FIG. 101.—Diggs’ Diagonal Scale.
]
Hipparchus was content to ascertain the position of the celestial bodies
to within a third of a degree, and we are informed that Tycho Brahe, by
a diagonal scale, was able to bring it down to something like ten
seconds. Fig. 101 will show what is meant by this. Suppose this to be
part of the arc of Tycho’s circle, having on it the different divisions
and degrees. Now it is clear that when the bar which carried the pointer
swept over this arc, divided simply into degrees, it would require a
considerable amount of skill in estimating to get very close to the
truth, unless some other method were introduced; and the method
suggested by Diggs, and adopted by Tycho, was to have a series of
diagonal lines for the divisions of degrees; and it is clear that the
height of the diagonal line measured from the edge of the circle could
give, as it were, a longer base than the direct distance between each
division for determining the subdivisions of the degree, and a slight
motion of the pointer would make a great difference in the point where
it cuts the diagonal line. For instance, it would not be easy to say
exactly the fraction of division on the inner circle at which the
pointer in Fig. 101 rests, but it is evident that the leading edge of
the pointer cuts the diagonal line at three-fourths of its length, as
shown by the third circle; so the reading in this case is seven and
three-quarters; but that is, after all, a very rough method, although it
was all the astronomer had to depend upon in some important
observations.
[Illustration:
FIG. 102.—The Vernier.
]
The next arrangement we get is one which has held its own to the present
day, and which is beautifully simple. It is due to a Frenchman named
Vernier, and was invented about 1631. We may illustrate the principle in
this way. Suppose for instance we want to subdivide the divisions marked
on the arc of a circle, Fig. 102 _a b_, and say we wish to divide them
into tenths, what we have to do is this—First, take a length equal to
nine of these divisions on a piece of metal, _c_, called the vernier,
carried on an arm from the centre of the circle, and then, on a separate
scale altogether, divide that distance not into nine, as it is divided
on the circle, but into ten portions. Now mark what happens as the
vernier sweeps along the circle, instead of having Tycho’s pointer
sweeping across the diagonal scale.
Let us suppose that the vernier moves with the telescope and the circle
is fixed; then when division 0 of the vernier is opposite division 6 on
the circle we know that the telescope is pointing at 6° from zero
measured by the degrees on this scale; but suppose, for instance, it
moves along a little more, we find that line 1 of the vernier is in
contact with and opposite to another on the circle, then the reading is
6° and ⅒°; it moves a little further, and we find that the next line 2,
is opposite to another, reading 6° and 2/10°, a little further still,
and we find the next opposite. It is clear that in this way we have a
readier means of dividing all those spaces into tenths, because if the
length of the vernier is nine circle divisions the length of each
division on the vernier must be as nine is to ten, so that each division
is one-tenth less than that on the circle.
We must therefore move the vernier one-tenth of a circle division, in
order to make the next line correspond. That is to say, when the
division of the vernier marked 0 is opposite to any line, as in the
diagram, the reading is an exact number of degrees; and when the
division 1 is opposite, we have then the number of degrees given by the
division 0 plus one-tenth; when 2 is in contact, plus two-tenths; when 3
is in contact, plus three-tenths; when 4 is in contact, plus
four-tenths, and so on, till we get a perfect contact all through by the
0 of the vernier coming to the next division on the circle, and then we
get the next degree. It is obvious that we may take any other fraction
than to for the vernier to read to, say 1/60, then we take a length of
59 circle divisions on the vernier and divide it into 60, so that each
vernier division is less than a circle division by 1/60. This is a
method which holds its own on most instruments, and is a most useful
arrangement.
But most of us know that the division of the vernier has been objected
to as coarse and imperfect; and Sharp, Graham, Bird, Ramsden, Troughton,
and others found that it is easy to graduate a circle of four or five
feet in diameter, or more, so accurately and minutely that five minutes
of arc shall be absolutely represented on every part of the circle. We
can take a small microscope and place in its field of view two cross
wires, something like those we have already mentioned, so as to be seen
together with the divisions on the circle, and then, by means of a screw
with a divided head, we can move the cross wires from division to
division, and so, by noting the number of turns of the screw required to
bring the cross wires from a certain fixed position, corresponding to
the pointer in the older instruments, to the nearest division, we can
measure the distance of that division from the fixed point or pointer,
as it were, just as well as if the circle itself were much more closely
divided. We can have matters so arranged that we may have to make, if we
like, ten turns of the screw in order to move the cross wires from one
graduation to the next, and we may have the milled head of the screw
itself divided into 100 divisions, so that we shall be able to divide
each of the ten turns into 100, or the whole division into 1,000 parts.
It is then simply a question of dividing a portion of arc equal to five
minutes into a thousand, or, if one likes, ten thousand parts by a
delicate screw motion.
We are now speaking of instruments of precision, in which large
telescopes are not so necessary as large circles. With reference to
instruments for physical and other observations, large circles are not
so necessary as large telescopes, as absolute positions can be
determined by instruments of precision, and small arcs can, as we shall
see in the next chapter, be determined by a micrometer in the eyepiece
of the telescope.
CHAPTER XV.
THE MICROMETER.
It will have been gathered from the previous chapter that the perfect
circles nowadays turned out by our best opticians, and armed in
different parts by powerful reading microscopes, in conjunction with a
cross wire in the field of view of the telescope to determine the exact
axis of collimation, enable large arcs to be measured with an accuracy
comparable to that with which an astronomical clock enables us to
measure an interval of time.
We have next to see by what method small arcs are measured in the field
of view of the telescope itself. This is accomplished by what are termed
micrometers, which are of various forms. Thus we have the wire
micrometer, the heliometer, the double-image micrometer, and so on.
These we shall now consider in succession, entering into further details
of their use, and the arrangements they necessitate when we come to
consider the instrument in conjunction with which they are generally
employed.
The history of the micrometer is a very curious one. We have already
spoken of a pair of cross wires replacing the pinnules of the old
astronomers in the field of view of the telescope, so that it might be
pointed to any celestial object very much more accurately than it could
be without such cross wires. This kind of micrometer was first applied
to a telescope by Gascoigne in 1639. In a letter to Crabtree he
writes:[10] “If here (in the focus of the telescope) you place the scale
that measures ... _or if here a hair be set_ that it appear perfectly
through the glass ... you may use it in a quadrant for the finding of
the altitude of the least star visible by the perspective wherein it is.
If the night be so dark that the hair or the pointers of the scale be
not to be seen, I place a candle in a lanthorn, so as to cast light
sufficient into the glass, which I find very helpful when the moon
appeareth not, or it is not otherwise light enough.”
This then was the first “telescopic sight,” as these arrangements at the
common focus of the object-glass and eyepiece were at first called. It
is certain that we may date the micrometer from the middle of the
seventeenth century; but it is rather difficult to say who it was who
invented it. It is frequently attributed to a Frenchman named Auzout,
who is stated to have invented it in 1666; but we have reason to know
that Gascoigne had invented an instrument for measuring small distances
several years before. Though first employed by Gascoigne, however, they
were certainly independently introduced on the Continent, and took
various forms, one of them being a reticule, or network of small silver
threads, suggested by the Marquis Malvasia, the arc interval of which
was determined by the aid of a clock. Huyghens had before this proposed,
as specially applicable to the measures of the diameters of planets and
the like, the introduction of a tapering slip of metal. The part of the
slip which exactly eclipsed the planet was noted; it was next measured
by a pair of compasses, and having the focal length of the telescope,
the apparent diameter was ascertained.
[Illustration:
FIG. 103.—System of Wires in a Transit Eyepiece.
]
Malvasia’s suggestion was soon seized upon for determinations of
position. Römer introduced into the first transit instrument a
horizontal and a number of vertical wires. The interval between the
three he generally used was thirty-four seconds in the equator, and the
time was noted to half seconds. The field was illuminated by means of a
polished ring placed outside of the object-glass. The simple system of
cross wires, then, though it has done its work, is not to be found in
the telescope now, either to mark the axis of collimation, or roughly to
measure small distances. For the first purpose a much more elaborate
system than that introduced by Römer is used. We have a large number of
vertical wires, the principal object of which is, in such telescopes as
the transit, to determine the absolute time of the passage of either a
star or planet, or the sun or moon, over the meridian; and one or more
horizontal ones. These constitute the modern transit eyepiece, a very
simple form of which is shown in the above woodcut.
THE WIRE MICROMETER.
The wire micrometer is due to suggestions made independently by Hooke
and Auzout, who pointed out how valuable the reticule of Malvasia would
be if one of the wires were movable.
[Illustration:
FIG. 104.—Wire Micrometer. _x_ and _y_ are thicker wires for measuring
positions on a separate plate to be laid over the fine wires.
]
The first micrometer in which motion was provided consisted of two
plates of tin placed in the eyepiece, being so arranged and connected by
screws that the distances between the two edges of the tin plates could
be determined with considerable accuracy. A planet could then be, as it
were, grasped between the two plates, and its diameter measured; it is
very obvious that what would do as well as these plates of tin would be
two wires or hairs representing the edges of these tin plates; and this
soon after was carried out by Hooke, who left his mark in a very decided
way on very many astronomical arrangements of that time. He suggested
that all that was necessary to determine the diameter of Saturn’s rings
was to have a fixed wire in the eyepiece, and a second wire travelling
in the field of view, so that the planet or the ring could be grasped
between those two wires.
The wire-micrometer. Fig. 104, differs little from the one Hooke and
Auzout suggested, A A is the frame, which carries two slides, C and D,
across the ends of each of which fine wires, E and B, are stretched;
then, by means of screws, F and G, threaded through these movable slides
and passing through the frame A A, the wires can be moved near to, or
away from, each other. Care must be taken that the threads of the screw
are accurate from one end to the other, so that one turn of the screw
when in one position would move the wire the same distance as a turn
when in another position. In this micrometer both wires are movable, so
as to get a wide separation if needful, but in practice only one is so,
the other remaining a fixture in the middle of the field of view. There
is a large head to the screw, which is called the micrometer screw,
marked into divisions, so that the motion of the wire due to each turn
of the screw may be divided, say into 100 parts, by actual division
against a fixed pointer, and further into 1,000 parts by estimation of
the parts of each division. Hooke suggested that, if we had a screw with
100 turns to an inch, and could divide these into 1,000 parts, we should
obviously get the means of dividing an inch into 100,000 parts; and so,
if we had a screw which would give 100 turns from one side of the field
of view of the telescope to the other, we should have an opportunity of
dividing the field of view of any telescope into something like 100,000
parts in any direction we chose.
The thick wires, _x_, _y_, are fixed to the plate in front of, but
almost touching, the fine wires, and in measuring, for instance, the
distance of two stars the whole instrument is turned round until these
wires are parallel to the direction of the imaginary line joining them.
This was the way in which Huyghens made many important measures of the
diameters of different objects and the distances of different stars.
Thus far we are enabled to find the number of divisions on the
micrometer screw that corresponds to the distance from one star to
another, or across a planet, but we want to know the number of seconds
of arc in the distance measured.
In order to do this accurately we must determine how many divisions of
the screw correspond to the distance of the wires when on two stars,
say, one second apart. Here we must take advantage of the rate at which
a star travels across the field when the telescope is fixed, and we
separate the wires by a number of turns of the screw, say twenty, and
find what angle this corresponds to, by letting a star on or near the
equator[11] traverse the field, and noticing the time it requires to
pass from one wire to the next. Suppose it takes 26⅔ seconds, then, as
fifteen seconds of arc pass over in one second of time, we must multiply
26 by 15, which gives 400, so that the distance from wire to wire is 400
seconds of arc; but this is due to twenty revolutions of the screw, so
that each revolution corresponds to 400/20˝, or twenty seconds, and as
each revolution is divided into 100 parts, and 20/100˝ = ⅕˝ therefore
each division corresponds to ⅕˝ of arc.
We shall return to the use of this most important instrument when we
have described the equatorial, of which it is the constant companion.
THE HELIOMETER.
[Illustration:
FIG. 105.—A B C. Images of Jupiter supposed to be touching; B being
produced by duplication, C duplicate image on the other side of A.
A B, Double Star; A, A´ & B, B´, the appearance when duplicate image
is moved to the right; A´, A & B´, B, the same when moved to the
left.
]
[Illustration:
FIG. 106.—Object-glass cut into two parts.
]
[Illustration:
FIG. 107.—The parts separated, and giving two images of any object.
]
There are other kinds of micrometers which we must also briefly
consider. In the heliometer[12] we get the power of measuring distances
by doubling the images of the objects we see, by means of dividing the
object-glass. The two circles, A and B, Fig. 105, represent the two
images of Jupiter formed, as we shall show presently, and touching each
other; now, if by any means we can make B travel over A till it has the
position C, also just touching A, it will manifestly have travelled over
a distance equal to the diameters of A and B, so that if we can measure
the distance traversed and divide it by 2, we shall get the diameter of
the circle A, or the planet. The same principle applies to double stars,
for if we double the stars A and B, Fig. 105, so that the secondary
images become A´ and B´, we can move A´ over B, and then only three
stars will be visible; we can then move the secondary images back over A
and B till B´ comes over A, and the second image of A comes to A´. It is
thus manifest that the images A´ and B´ on being moved to A´ and B´ in
the second position have passed over double their distance apart. Now
all double-image micrometers depend on this principle, and first we will
explain how this duplication of images is made in the heliometer. It is
clear that we shall not alter the power of an object-glass to bring
objects to focus if we cut the object-glass in two, for if we put any
dark line across the object-glass, which optically cuts it in two, we
shall get an image, say of Jupiter, unaltered. But suppose instead of
having the parts of the object-glass in their original position after we
have cut the object-glass in two, we make one half of the object-glass
travel over the other in the manner represented in Fig. 107. Each of
these halves of the object-glass will be competent to give us a
different image, and the light forming each image will be half the light
we got from the two halves of the object-glass combined; but when one
half is moved we shall get two images in two different places in the
field of view. We can so alter the position of the images of objects by
sliding one half of the object-glass over the other, that we shall, as
in the case of the planet Jupiter, get the two images exactly to touch
each other, as is represented in Fig. 105; and further still, we can
cause one image to travel over to the other side. If we are viewing a
double star, then the two halves will give four stars, and we can slide
one half, until the central image formed by the object-glasses will
consist of two images of two different stars, and on either side there
will be an image of each star, so that there would appear to be three
stars in the field of view instead of two. We have thus the means of
determining absolutely the distance of any two celestial objects from
each other, in terms of the separation of the centres of the two halves
of the object-glass.
But as in the case of the wire micrometer we must know the value of the
screw, so in the case of the heliometer we must know how much arc is
moved over by a certain motion of one half of the object-glass.
[Illustration:
FIG. 108.—Double images seen through Iceland spar.
]
[Illustration:
FIG. 109.—Diagram showing the path of the ordinary and extraordinary
rays in a crystal of Iceland spar, producing two images apparently
at E and O.
]
THE DOUBLE-IMAGE MICROMETER.
Now there is another kind of double-image micrometer which merits
attention. In this case the double image is derived from a different
physical fact altogether, namely, double refraction. Those who have
looked through a crystal of Iceland spar, Fig. 108, have seen two images
of everything looked at when the crystal is held in certain positions,
but the surfaces of the crystal can be cut in a certain plane such that
when looked through, the images are single. For the micrometer therefore
we have doubly refracting prisms, cut in such a way as to vary the
distance of the images. Generally speaking, whenever a ray of light
falls on a crystal of Iceland spar or other double refracting substance,
it is divided up into two portions, one of which is refracted more than
the other. If we trace the rays proceeding from a point S, Fig. 109, we
find one portion of the light reaching the eye is more refracted at the
surfaces than the other, and consequently one appears to come from E and
the other from O, so that if we insert such a crystal in the path of
rays from any object, that object appears doubled. There is, however, a
certain direction in the crystal, along which, if the light travel, it
is not divided into two rays, and this direction is that of the optic
axis of the crystal, A A, Fig. 110; if therefore two prisms of this spar
are made so that in one the light shall travel parallel to the axis, and
in the other at right angles to it, and if these be fastened together so
that their outer sides are parallel, as shown in Fig. 111, light will
pass through the first one without being split up, since it passes
parallel to the axis, but on reaching the second one it is divided into
two rays, one of which proceeds on in the original course, since the two
prisms counteract each other for this ray, while the other ray diverges
from the first one, and gives a second image of the object in front of
the telescope, as shown in Fig. _b_. The separation of the image depends
on the distance of the prisms from the eyepiece, so that we can pass the
rays from a star or planet through one of these compound crystals and
measure the position of the crystal and so the separation of the stars,
and then we shall have the means of doing the same that we did by
dividing our object-glass, and in a less expensive way, for to take a
large object-glass of eight or ten inches in diameter and cut it in two
is a brutal operation, and has generally been repented of when it has
been done.
[Illustration:
FIG. 110.—Crystals of Iceland Spar showing, A A´, the optic axis.
]
It is obvious that a Barlow lens, cut in the same manner as the
object-glass of the heliometer, will answer the same purpose; the two
halves are of course moved in just the same manner as the halves of the
divided object-glass. Mr. Browning has constructed micrometers on this
principle.
[Illustration:
FIG. 111.—Double Image Micrometer. FIG. _a_, _p q_, single image
formed by object-glass. FIG. _b_, _p_{1} q_{1}_, _p_{2} q_{2}_,
images separated by the double refracting prism. FIG. _c_, same,
separated less, by the motion of the prism.
]
There is yet another double-image micrometer depending on the power of a
prism to alter the direction of rays of light. It is constructed by
making two very weak prisms, _i.e._, having their sides very nearly
parallel, and cutting them to a circular shape; these are mounted in a
frame one over the other with power to turn one round, so that in one
position they both act in the same direction, and in the opposite one
they neutralise each other; these are carried by radial arms, and are
placed either in front of the object-glass or at such a distance from it
inside the telescope that they intercept one half of the light, and the
remaining portion goes to form the usual image, while the other is
altered in its course by the prism and forms another image, and this
alteration depends on the position of the movable prism.
-----
Footnote 10:
Grant’s _History of Physical Astronomy_, p. 454.
Footnote 11:
More accurately the time of transit is to be multiplied by the cosine
of the star’s declination.
Footnote 12:
So called because the contrivance was first used to measure the
diameter of the sun.
BOOK IV.
_MODERN MERIDIONAL OBSERVATIONS._
CHAPTER XVI.
THE TRANSIT CIRCLE.
We are now, then, in full possession of the stock-in-trade of the modern
astronomer—the telescope, the clock, and the circle,—and we have first
to deal with what is termed astronomy of position, that branch of the
subject which enables us to determine the exact position of the heavenly
bodies in the celestial sphere at any instant of time.
Before, however, we proceed with modern methods, it will be well, on the
principle of _reculer pour mieux sauter_, to refer back to the old ones
in order that we can the better see how the modern instruments are
arranged for doing the work which Tycho, for instance, had to do, and
which he accomplished by means of the instruments of which we have
already spoken.
First of all let us refer to the Mural Quadrant, in which we have the
germ of a great deal of modern work, its direct descendant being the
Transit Circle of the present time.
We begin then by referring to the hole in the wall at which Tycho is
pointing (see Fig. 112), and the circle, of which the hole was the
centre, opposite to it, on which the position of the body was observed,
and its declination and right ascension determined. This then was
Tycho’s arrangement for determining the two co-ordinates, right
ascension and declination, measured from the meridian and equator. It is
to be hoped that the meaning of right ascension and declination is
already clear to our readers, because these terms refer to the
fundamental planes, and distances as measured from them are the very A B
C of anything that one has to say about astronomical instruments.
We know that Tycho had two things to do. In the first place he had to
note when a star was seen through the slit in the wall, which was
Tycho’s arrangement for determining the southing of a star, the sun, or
the moon; and then to give the instant when the object crossed the sight
to the other observer, who noted the time by the clocks. Secondly, he
had to note at which particular portion of the arc the sight had to be
placed, and so the altitude or the zenith distance of the star was
determined; and then, knowing the latitude of the place, he got the two
co-ordinates, the right ascension and declination.
How does the modern astronomer do this? Here is an instrument which,
without the circle to tell the altitude at the same time, will give some
idea of the way in which the modern astronomer has to go to work. In
this we have what is called the Transit Instrument, Fig. 113; it is
simply used for determining the transit of stars over the meridian. It
consists essentially of a telescope mounted on trunnions, like a cannon,
having in the eyepiece, not simple cross wires, but a system of wires,
to which reference has already been made, so that the mean of as many
observations as there are wires can be taken; and in this way Tycho’s
hole in the wall is completely superseded. The quadrant is represented
by a circle on the instrument called the transit circle, of which for
the present we defer consideration.
[Illustration:
FIG. 112.—Tycho Brahe’s Mural Quadrant.
]
[Illustration:
FIG. 113.—Transit Instrument (Transit of Venus Expedition).
]
[Illustration:
FIG. 114.—Transit Instalment in a fixed Observatory.
]
Now there are three things to be done in order to adjust this instrument
for observation. In the first place we must see that the line of sight
is exactly at right angles to the axis on which the telescope turns, and
when we have satisfied ourselves of that, we must, in the second place,
take care, not only that the pivots on which the telescope rests are
perfectly equal in size, but that the entire axis resting on these
pivots is perfectly horizontal. Having made these two adjustments, we
shall at all events be able, by swinging the telescope, to sweep through
the zenith. Then, thirdly, if we take care that one end of this axis
points to the east, and the other to the west, we shall know, not only
that our transit instrument sweeps through the zenith, but sweeps
through the pole which happens to be above the horizon—in England the
north pole, in Australia the south pole. That is to say, by the first
adjustment we shall be able to describe a great circle; by the second,
this circle will pass through the zenith; and by the third, from the
south of the horizon to the north, through the pole. Of course, if the
pole star were at the pole, all we should have to do would be to adjust
the instrument (having determined the instrument to be otherwise
correct) so as simply to point to the pole star, and then we should
assure ourselves of the east and west positions of the axis. Some
details may here be of interest.
The first adjustment to be made is that the line of sight or collimation
shall be at right angles to the axis on which the instrument moves: to
find the error and correct it, bring the telescope into a horizontal
position and place a small object at a distance away, in such a position
that its image is bisected by the central wire of the transit, then lift
the instrument from its bearings or Ys, as they are called, and reverse
the pivots east for west, and again observe the object. If it is still
bisected, the adjustment is correct, but if not, then half the angle
between the new direction in which the telescope points and the first
one as marked by the object is the collimation error, which may be
ascertained by measuring the distance from the object to the central
wire, by a micrometer in the field of view, and converting the distance
into arc. To correct it, bring the central wire half way up to the
object by motion of the wire, and complete the other half by moving the
object itself, or by moving the Ys of the instrument. This of course
must be again repeated until the adjustment is sensibly correct.
The second adjustment is to make the pivots horizontal. Place a striding
level on the pivots and bring the bubble to zero by the set screws of
the level, or note the position of it; then reverse the level east for
west, and then if the bubble remains at the same place the axis of
motion is horizontal, but, if not, raise or lower the movable Y
sufficiently to bring the bubble half way to its original position, and
complete the motion of the bubble, if necessary, by the level screw
until there is no alteration in the position of the bubble on reversing
the level.
[Illustration:
FIG. 115.—Diagram explaining third adjustment, H, R, plane of the
horizon; H, Z, A, P, B, R, meridian; A and B places of circumpolar
star at transit above and below pole P.
]
The third adjustment is to place the pivots east and west. Note by the
clock the time of transit of a circumpolar star, when above the pole,
over the central wire, and then half a day later when below it, and
again when above it; if the times from upper to lower transit, and from
lower to upper are equal, then the line of collimation swings so as to
bisect the circle of the star round the pole, and therefore it passes
through the pole, and further it describes a meridian which passes
through the zenith by reason of the second adjustment. This is therefore
the meridian of the place, and therefore the pivots are east and west.
If the periods between the transits are not equal, the movable pivot
must be shifted horizontally, until on repeating the process the periods
are equal.
In practice these adjustments can never be made quite perfect, and there
are always small errors outstanding, which when known are allowed for,
and they are estimated by a long series of observations made in
different manners and positions. The error of the first adjustment is
called the collimation error, that of the second the level error, and
that of the third the deviation error. When the errors of an instrument
are known the observations can be easily corrected to what they would
have been had the instrument been in perfect adjustment.
* * * * *
Now what does the modern astronomer do with this instrument when he has
got it? It is absolutely without circles, but the faithful companion of
the Transit Instrument is the Astronomical Clock—and the two together
serve the purpose of a circle of the most perfect accuracy, so that by
means of these two instruments we shall be able to determine the right
ascensions of all the stars merely by noting the time at which the
earth’s rotation brings them into the field of view. The clock having
been regulated to sidereal time, a term fully explained in the sequel,
it will show 0_h._ 0_m._ 0_s._ when the first point of Aries passes the
meridian, and instead of dividing the day into two periods of twelve
hours each, the clock goes up to twenty-four hours. If now a star is
observed to pass the centre of the field of view (that is the meridian)
at 1_h._ by the clock, or one hour after the first point of Aries, it
will be known to be in 1_h._ of right ascension; or if it passes at
12_h._ it will be 12_h._ right ascension, or opposite to the first point
of Aries, and so on up to the twenty-four hours, the clock keeping exact
time with the earth. The transit instrument thus gives us the right
ascension of a star, or one co-ordinate: and now we want the other—the
declination.
THE TRANSIT CIRCLE.
This is given by the Transit Circle, which is a transit instrument with
a circle attached, to ascertain the angle between the object and the
pole or equator.
[Illustration:
FIG. 116.—The Mural Circle.
]
The combination of the circle with the transit, forming the transit- or
meridian-circle, is of comparatively recent date, and the earlier method
was to use a circle with a telescope attached, fixed to a pivot moving
on bearings in a wall, and called therefore the Mural Circle, Fig. 116.
Since it is supported only on one side it cannot move so truly in the
meridian as the transit, but, having a large circle, it gives accurate
readings.
[Illustration:
FIG. 117.—Transit Circle, showing the addition of circles to the
transit instrument.
]
[Illustration:
FIG. 118.—Perspective view of Greenwich Transit Circle.
]
Fig. 117 shows in what respect the Transit Circle is an advance upon the
transit instrument and the mural circle, for in addition to the transit
instrument we have the circle. This is a perspective view of the
transit, and the telescope is represented sweeping in the vertical plane
or meridian. In addition to the instrument resting with its pivots on
the massive piers, we have the circle attached to the side of the
telescope. We see at once that by means of this circle we are able to
introduce the other co-ordinate of declination. If the clock goes true
with the earth—if they both beat in unison and keep time with each
other—and further if the clock shows 0_h._ 0_m._ 0_s._ when the first
point of Aries passes the centre of the field, that is through the
meridian plane, then, if we observe a star at the moment it passes over
the meridian, the clock will give its right ascension and the circle its
declination, when the latitude of the place is known.
The construction of the transit circle will repay a more detailed
examination. A system of weights suspended over pulleys (Fig. 118)
reduces the weight of the instrument on the pivots, in order that their
form shall not be altered by too much friction, and on the right-hand
side of one of the piers the eyepieces of the microscopes for reading
the circle are shown. This is shown better in section in Fig. 119. One
of the solid stone piers is pierced through diagonally, as shown at (m)
(m), so that light proceeding from a gas-lamp (q) placed opposite the
pivot of the telescope is allowed to fall through the openings, and is
condensed by means of the lens (n) on the graduations of the circle of
five minutes each, already referred to. By the side of each illuminating
hole is another hole (o) (o) through which the reading microscopes, six
in number, two of which are shown at (q) (p), having their eye-ends
arranged in a circle at the end of the pier, are focussed on to the
graduations of the circle. There is also another reading microscope,
besides the six just mentioned, of less power for reading the degrees,
or larger divisions of the circle. Hence from the side of the pier close
to the lamp the observer can read the circle with accuracy, and measure
the angle, to which we have alluded, made by the telescope when pointed
to any particular star. We have now seen how the circle is illuminated,
and now we will inquire further as to the arrangements that are
necessary in order to bring this instrument into use.
[Illustration:
FIG. 119.—Plan of the Greenwich Transit Circle.
]
We must defer giving more explanation of the practical working of the
instrument until we have considered the clock used in connection with
it, and we shall then show how the observations are made. One important
point to which attention should be given is the method of illuminating
the wires in the eyepiece. This is the arrangement. There is a lamp at
the end of one of the pivots which is hollow, the light falls on a
mirror, placed in the centre of the telescope, of such a shape and in
such a position that it will not intercept the light from the
object-glass falling through the diaphragms on to the eyepiece. The
mirror is ring-shaped, something like the brim of a hat, and is carried
on two pivots, so that it can be placed diagonally in the tube, or at
right angles to it; it is arranged just outside the cone of rays from
the object-glass, so that when the mirror is diagonally placed the light
will be grasped directly from the lamp at the end of the axis and
reflected down and mixed up with the light coming from the star into the
eyepiece.
In this way of course the wires can be rendered visible at night, and
without such a method they would be invisible. This arrangement gives a
bright field and dark wires; but there is also a method of reversing
matters; for near the edge of the ring-shaped reflector are fixed prisms
for reflecting the light, and when the reflector is placed square with
the axis of the telescope the small prisms on the reflector send the
light down through apertures in the diaphragms, so that the mirror in
this position no longer sends the light down with the rays from the
star, but through holes in the diaphragms themselves, to two small
reflecting prisms, one on each side of the wires in the eyepiece. What
has that light to do? It has simply to do this, it has to fall sideways
on the wires themselves in such a manner that it does not fall on the
eye except by reflection from the wires. In this way we have the means
of getting a bright system of wires on a dark field, in which the wires
and objects to be measured are the only things to be seen.
As with the pivots of the transit circle, and in fact of any
astronomical instrument, so with the circles, certain fundamental points
have to be borne in mind; and, although it is absolutely impossible to
ensure perfection, still, to go as near to it as possible, the
astronomer has to observe a great many times over in all sorts of
positions in order to bring the error down to its minimum.
First, the circle must be placed exactly at right angles to the axis of
the telescope, so that it is in the plane of the meridian. Secondly, the
error of centering must be found. For instance, if the Greenwich circle
were to be read by only one microscope, an error in the pivot or any
part of the axis round which the circle turns would vitiate the
readings; but we could get rid of that error, due to a fault of the
axis, or to a want of centering, by means of two readings, at the
extremities of a diameter; but even then we should not get rid of the
possible error due to graduation, for even if the divisions on the
circle were accurate at first, they would not long remain so, for the
metal of which these circles are made is liable, like other metals, to
certain changes due to temperature; and if a circle is very large the
weight of the circle itself, supposing its form perfect when horizontal,
will, when vertical, sag it down and deflect it out of shape, so that at
Greenwich the method adopted is to use six reading microscopes. Fig.
120, which shows the Cambridge Transit Circle, indicates the arrangement
of the five microscopes in use there, set round the circumference of the
circle, much in the same manner as in the case of the Greenwich
instrument, where there are holes through the pier in which the
microscopes are placed with the eye-ends arranged in a circle at the
side of it.
[Illustration:
FIG. 120.—Cambridge (U.S.) meridian circle.
]
When, therefore, the transit is pointed to any particular star, not only
is the time noted in order to determine the right ascension of the star,
in a careful and elaborate way, but the readings of the circle are made
by every one of these microscopes—reading from the next five minutes
division of the circle which happens to be visible,—and there is an
additional microscope giving the rough reading of the larger divisions
of the circle from a certain zero.
And what, then, is this zero? There is no doubt about the reading of the
zero of right ascension, it is the intersection of the two fundamental
planes at the first point of Aries; but what zero shall be used in the
case of the vertical circle?
[Illustration:
FIG. 121.—Diagram illustrating how the pole is found.
]
Let the circle, H, Z, R, Fig. 121, represent a great circle of the
heavens, the meridian in fact, and let the centre of this circle
represent the centre of the transit instrument. Now what we want is, not
only to be able to measure degrees of arc along this circle, but to
determine some starting-point for those degrees. One arrangement is to
observe the reflection of the wires in the eyepiece of the transit
circle, from the surface of mercury in a vessel which is placed below
the telescope, turned with its object-glass downwards; the vessel
containing the mercury is out of sight, between the two piers, but in
Fig. 118 are seen the two parallel bars, with weights at the ends,
carrying it, by which it may be brought into any position for the
purpose referred to, so that the light from the wires in the eyepiece
may pass through the tube and be reflected back by the mercury (the
surface of which is of course perfectly horizontal), up through the tube
again to the eyepiece. When the telescope is absolutely in the vertical
position the images of the cross wires will be superposed over the cross
wires themselves; and then an observation will give the actual reading
of the circle when the instrument is pointing at 180° from the zenith;
deduct 180° from this reading, and we get the reading when the
instrument is pointing at the zenith—the zero required. This should be
0°, and the quantity by which it differs from 0° must be applied to the
observed position of stars, so that the distance of a star from the
zenith can be at once determined.
But this is not all. If we assume for the moment that the observer is at
the north pole, the pole star will be exactly over head, and therefore,
supposing the pole star to absolutely represent the pole of the heavens,
all the observer has to do is simply to take a reading of the pole star
on the arc of his circle—call it 0° O´ 0˝—and then use it as another
zero to reckon polar distance from, seeing that every particular star or
body we observe has so many degrees, minutes, seconds, or tenths of
seconds, from the pole star.
But we are not at the north pole. Still we are in a position where the
pole is well above the horizon, and from that fact we can determine the
polar distance, although the absolute place of the pole is not pointed
out by the pole star. Thus, if we suppose any star, A, Fig. 121, to be a
certain distance from the pole, and the earth carrying the instrument to
be in the centre of the circle H, Z, R, we can observe the zenith
distance of that star, Z, A, when it transits our meridian above the
pole, P; and we can then observe its distance, Z, B, when it transits
below the pole; and it is clear that the difference between those two
measures will give the distance A, B, or double the polar distance of
that star, and the mean of the readings will give the distance, Z, P,
the zenith distance of the pole, so that it is perfectly easy to
determine the distance between the pole and the zenith, which,
subtracted from ninety degrees, gives us the latitude of the place. It
is therefore perfectly easy by means of this instrument to determine
either the zenith or polar distance, and, knowing the polar distance, we
get the declination, or distance from the equator, by subtracting it
from ninety degrees.
In our case it is the north polar distance or declination of any object
in the heavens that we record; and if we take the precaution to do so
with this instrument at the time given by the clock, when the object
passes the meridian, we have the actual apparent place of that body in
the sky; and in this way all the positions of the stars and other
bodies, and their various changes, and the courses of the planets, have
been determined.
The transit circle is the most important instrument of astronomy, and
such is the perfection of the Greenwich instrument that nothing could be
more unfortunate for astronomy than that that instrument should be in
any way damaged. And though many of us are admirers of physical
astronomy, we have yet to find the instrument that is as important to
physical astronomy as the transit circle at Greenwich is to astronomy of
position.
The room in which these transit circles are worked—the transit room—is
required to be of special construction. A clear space from the southern
horizon through the zenith to the north must at any time be available;
this entails the cutting of a narrow slit in the roof and both walls,
without the intervention of any beams across the room. This slit is
closed by shutters or windows which are made to open in sections, so
that any part of the meridian can be observed at pleasure.
CHAPTER XVII.
THE TRANSIT CLOCK AND CHRONOGRAPH.
We have now to consider the way in which the transit instrument is used
and the functions which both it and the transit circle fulfil.
The connection between the transit instrument and the transit clock is
so intimate that either is useless without the other. In the one case we
should note the passage of a star across the meridian without knowing at
what time it took place; while, on the other hand, we should not learn
whether the clock showed true time or not, unless we could check its
indications in the manner rendered possible by transit observations. In
what has been already said of time we referred to it as measured by our
ordinary clocks, _i.e._ reckoning it from noon to midnight and midnight
to noon, and regulated entirely by the length of the solar day. It would
at first sight seem that it should be twelve o’clock by a clock so
regulated when the sun passes the meridian; but the earth’s orbit is not
circular, and the sun’s course is inclined to the equator, so that, as
determined by such a clock, sometimes he would get to the meridian a
little too late, and sometimes too early, so that we should be
continually altering our clocks if we attempted to keep time with the
sun.
One of the greatest boons conferred by astronomy upon our daily life is
an imaginary sun that keeps exact time, called the _Mean Sun_, so that
the mean sun is on the meridian at twelve o’clock each day by our
clocks, regulated by the methods we have now to discuss. Such clocks
regulated, as it is called, to mean time are sometimes a few minutes
before, and at others a few minutes behind the true sun, by an amount
called the Equation of Time, which is given in the almanacs. It would
therefore be difficult to regulate our standard clock by the sun, so we
do it through the medium of the stars, which go past our meridian with
the greatest regularity, since their apparent motion depends almost
wholly upon the equable rotation of the earth on its axis, while the
apparent motion of the sun is complicated by the earth’s revolution
round it.
This method at first sight is complex, and in fact we cannot obtain mean
time directly by such transits of stars. It is accomplished indirectly
by means of a clock set to star- or sidereal-time, and such a clock is
the astronomer’s companion, to which he always refers his observations,
and the indications of which alone are always in his mind. This he calls
the Sidereal Clock.
[Illustration:
FIG. 122.—Diagram illustrating the different lengths of solar and
sidereal day.
]
We have, then, next to consider the difference between the clock used
for the transit, or the sidereal clock, and an ordinary solar clock, or
between a solar and a sidereal day. Let S, Fig. 122, represent the sun,
and the arc a part of the orbit of the earth, the earth going in the
direction of the arrow. Let 2 represent the position of the earth one
day, and let 1 represent the position of the earth on the day before. A
line drawn from the sun through the earth’s centre will give us the
places _a_, _b_, on the earth at which it is midday on the side turned
towards the sun, and midnight on the side turned from the sun. Now when
a revolution of the earth with reference to the stars has been
accomplished the earth comes to the second position, 2; and _c_ is the
point of midday; and there is a certain angle here between _a_ and _c_,
through which the earth must turn before it is noon at _a_, due to the
change of position of the earth, or to the apparent motion of the sun
among the stars, by which the sun comes to the meridian rather later
than the stars each day. Now let us suppose that, while one observer in
England is observing the sun at midday, another is observing the stars
at the antipodes at midnight, the star is seen in the direction ⁎. We
are aware that the stars are so far away, that from any point of the
earth’s orbit they seem to be in absolutely the same place—they do not
change their positions in the same way as the sun appears to do amongst
them—an observer at _b_ therefore sees on his meridian the star ⁎ while
the observer at _a_ sees the sun on his meridian; supposing _b_ to
represent the same observer, on the second day, he will see the star due
south before the other observer at _a_ sees the sun due south. The
result of that is, that the sidereal day is shorter than the solar day,
and the sun appears to lose on the stars. If we wish to have a clock to
show 12 o’clock when the sun is southing, we shall want it to go slower
by nearly four minutes a day than one which is regulated by the stars
and is at 12 o’clock when our starting-point of right ascension—which is
the intersection of those two fundamental planes, the equator and the
ecliptic—passes over the meridian.
One of the uses of the clock showing sidereal time in connection with
the convenient fiction of the “Mean Sun,” is to give to the outside
world a constant flow of mean time regulated to the average southing of
the sun _in the middle of the period for which the sun is above the
horizon each day in the year_.
The stellar day, that is the time from one transit of a star to the
next, is shorter than a solar day by 3_m._ 56_s._, so what is called
sidereal time, regulated by the transits of well-known stars, in the
manner we shall presently explain, by no means runs parallel with mean
time so far as the clock indications go. Indeed when we look at a
sidereal clock, we see something different to the clock we are generally
accustomed to see. In the first place, we have twenty-four hours instead
of twelve, and then generally there is one dial for hours, another for
minutes, and another for seconds. That of course might happen in the
case of the mean-time clock; but the mean-time clock is not often
divided into twenty-four hours, although it formerly used to be, as the
dials in Venice still testify.
We now see the importance of an absolutely correct determination of the
right ascension of stars; for this right ascension, expressed in hours,
minutes, and seconds, is nothing more nor less than the time indicated
by the sidereal clock, by the side of the transit instrument, when a
star passes over, or transits, the central wire of that instrument.
Hence it is the sidereal clock which keeps time with the stars, and
which we keep correct by means of the transit instrument.
[Illustration:
FIG. 123.—System of wires in transit eyepiece.
]
Let us show how this was always done some twenty or thirty years ago,
and how it is sometimes done now. The transit room is kept so quiet that
one can hear nothing but the ticking of the sidereal clock; the star to
be observed is then carefully watched as it traverses the field of view
over the wires, and the time of transit over each wire is estimated to
the tenth of the time between each beat by the observer.
We reproduce in Fig. 123 a rough representation of what is seen in the
field of view of a transit instrument. Now if we could be perfectly sure
of making an accurate observation by means of the central wire, it is
not to be supposed that astronomers would ever have cared to use this
complicated system of wires in their eyepieces; but so great is the
difficulty of determining accurately the time at which a star passes a
wire, that we have in eyepieces introduced a system of several wires, so
that we may take the transit of the star first at one wire, then at
another, until every wire has been passed over.
We want one wire exactly in the middle to represent the real physical
middle of the eyepiece so far as skill can do it, and then there is a
similar number of wires on either side at exactly equal distances; so
that the average of all the observations made at each of the wires will
be much more likely to be accurate than a single observation at one
wire. In this way the astronomer gives himself a good many chances
against one to be right. If he lost his chance from any reason when
using only one wire, he would have to wait twenty-four more sidereal
hours before he could make his measure again, but by having five, or
seven, or twenty-five or more wires in the eyepiece of the telescope, he
increases his chances of correctness: and the way in which he works is
this: While the heavens themselves are taking the stars across the wires
he listens to the beating of the clock. If a star crosses one of the
wires exactly as the clock is beating, he knows that it has passed the
wire at some second, and he takes care to know what second that is; but
if, instead of being absolutely coincident with one of the beats of the
clock, it is half-way between one beat and another, or nearer to one
beat than another, he estimates the fraction of a second, and by
practice he has no difficulty at all in estimating divisions of time
equal to tenths of a second, and at each particular wire in the eyepiece
the transit of the star is thus minutely observed.
Then if the observations are complete and the mean of them is taken, it
should, after the necessary corrections for instrumental errors have
been applied, give the actual observation made at the central wire; if
the astronomer cannot make observations at every wire, he introduces a
correction in his mean to make up for the lost observations.
This is what is called the “eye and ear” method, because the observer is
placed with his eye to the telescope, and he depends upon his ear to
give him the exact interval at which each beat of the clock takes place,
and he requires an exact power of mentally dividing the distance between
each beat into ten equal parts, which are tenths of seconds. In this
method of observation every observer differs slightly in his judgment of
the instant that the star crosses the wire, and his estimation differs
from the truth by a certain constant quantity which he must always allow
for; this error is called his _personal equation_.
In this way then the transit instrument enables us, having true time, to
determine the right ascension of a heavenly body as it transits the
meridian, and, knowing the right ascension of a heavenly body, we have
only to watch its transit in order to know the true time; so if the
observer knows at what time a known star ought to transit, he has an
opportunity of correcting his clock.
So much for the eye and ear method of transit observation. There is
another which has now to a very large extent superseded it. This is
called the “chronographic method”; we owe it to Sir Charles Wheatstone,
who made it possible about 1840.
Figs. 124-7 are from drawings of the chronograph in use at Greenwich,
and by their means we hope to make the principle of the instrument
clear. In this chronograph, _g_ is a long conical pendulum which
regulates the driving clock in the case below it, through the gearing of
wheel-work, as it turns the cylinder, E, gently and regularly round. On
the cylinder is placed paper to receive the mark registering the
observations; along the side of the cylinder or roller run two long
screws, K and N, Fig. 125, which are also turned by the clock, and on
them are carried electro-magnets, A, B, Fig. 125, and prickers, 35, Fig.
126; as the screws turn, the magnets and prickers are moved along the
roller, and, as the roller turns, the pointer, 36, Fig. 127, traces a
fine line on the paper like the worm of a screw on the surface; and it
is close to this line, which serves as a guide to the eye, that the
prickers make a mark each time a current is sent through the
electro-magnets; this turns each of them into a magnet, and they then
attract a piece of iron which, in moving upwards, presses down its
pricker by means of a lever, and registers the instant the current is
sent.
The different wires are brought, first from the transit circle to work
one pricker, and then from the clock to work the other, the clock
sending a current and producing a prick on the roller every second.
[Illustration:
FIG. 124.—The Greenwich chronograph. General view.
]
The observer, instead of depending upon the eye and ear as he had to do
before, has then the means of impressing a mark at any instant upon the
same cylinder, in exactly the same way that the pendulum of the clock
impresses the mark of any second, so that as each wire in the eyepiece
of the transit instrument is passed by the star, he is able, by the same
method as the clock, to record on this same revolving surface each
observation, which can afterwards be compared with the marks
representing the seconds, and so the exact time of each observation is
read off more accurately and with less trouble than by the old method.
Let us suppose we are making a transit observation: the clock will be
diligently pricking sidereal seconds, while we, by a contact-maker held
in the hand, are as diligently recording the moments at which the star
passes each wire.
[Illustration:
FIG. 125.—Details of the travelling carriage which carries the magnets
and prickers. Side view and view from above.
]
[Illustration:
FIG. 126.—Showing how on the passage of a current round the soft iron
the pricker is made to make a mark on the spiral line on the
cylinder.
]
[Illustration:
FIG. 127.—Side view of the carriage carrying the magnets and the
pointer that draws the spiral.
]
This is done by pressing a stud, and sending a current at each transit;
so that we shall have a dot in every other space between the clock dots,
supposing the wires to be two seconds in time apart; supposing them to
be three seconds apart, our dots will be in every third space; supposing
them to be four seconds apart, our dots will be in every fourth space,
and so on; and tenths and hundredths of seconds are estimated, by the
position of each transit dot between those which record the seconds.
In this way one sees that we have on the barrel an absolute record, by
one of the pointers, of the seconds recorded by the clock, and, by the
other, of the exact times at which a star has been seen at each wire of
the transit instrument.
Now of course what is essential in this method is that there shall be a
power of determining not only the precise second or tenth of a second of
time, but also the minute at which contact takes place, otherwise there
would be a number of seconds dots without knowing to what minute they
corresponded; it would be like having a clock with only a second-hand
and no minute-hand.
The brass vertical sliding piece shown at the lower left-hand side in
Fig. 96, carries at its upper end two brass bars, each of which has, at
its right-hand extremity, between the jaws, a slender steel spring for
galvanic contact; the lower spring carries a semicircular piece
projecting downwards, which a pin on the crutch rod lifts in passing,
bringing the springs in contact at each vibration: the contact takes
place when the pendulum is vertical, and the acting surfaces of the
springs are, one platinum, the other gold; an arrangement that has been
supposed to be preferable to making both surfaces of platinum. By means
of the screws _n_ and _o_, which both act on sliders, the contact
springs can be adjusted in the vertical and horizontal directions
respectively. Other contact springs in connection with the brass bars
_p_ and _q_, on the other side of the back plate, are ordinarily in
contact, but the contact is broken at one second in each minute by an
arm on the escape-wheel spindle. The combination of these contacts
permits the clock to complete a galvanic circuit at fifty-nine of the
seconds in each minute, and omit the sixtieth.[13]
In this way we may suppress the sixtieth second, thus leaving a blank
that marks the minute; and all that the observer has to do after he has
made a record of the transit, is to go quietly to the barrel, and mark
the hour and minute in the vacant space. A barrel of this size will
contain the observations which would be made in some hours; so that at
the end of that time it may be taken off, and it will give, with the
least possible chance of error, a permanent record of the work of the
astronomer.
It is at once apparent that by the introduction of this application of
electricity, astronomy has been an enormous gainer; but so far we have
simply given a description of one instrument which has been suggested
for that purpose. A few words may be said on other forms.
In the instrument used in the Royal Observatory at Greenwich the
rotation of the roller is kept uniform, as we have seen, by a conical
pendulum; but there are other methods of attaining this end—there is the
fly-wheel and fan, similar to the arrangement for regulating the
striking part of a clock; there is the governor used for the
steam-engine, and others which give a fairly regular motion—for the
motion need not be absolutely uniform, because the dots, which form the
points from which to measure, are made by the standard clock.
The particular instant at which each minute occurs may be recorded in
another way. The two steel springs above described may be pressed
together, not by a pin in the crutch, but by cogs on a wheel attached to
the spindle of the escape-wheel of the clock (see Fig. 128); and then
all we have to do to stop the transmission of a current at the sixtieth
second is to remove one of the cogs.
[Illustration:
FIG. 128.—Wheel of the sidereal clock, and arrangement for making
contact at each second.
]
Another simple method for transmitting seconds’ currents has also been
occasionally tried. A wire runs down the whole length of the pendulum,
and ends in a projection of such a length that it swings through a small
globule of mercury in a cup below it, the pendulum being connected with
one wire from the chronograph and the mercury with the other; thus there
will be a making and breaking of contact each time the point of the
pendulum swings through the mercury. It is uncertain which method is the
better; one would prefer that which, under any circumstances, could
disturb the pendulum least: but as to which this is opinions differ.
We have now described the _modus operandi_ of making time observations
with the transit instrument, the final result of which is that the time
shown by the sidereal clock corresponds with the right ascension of the
“clock stars” as they transit the central wire.
The great use, as we have already stated, made of the sidereal clock
thus kept right by the stars is to correct the mean-time clock with a
view of supplying mean solar time to the outside world.
As the sidereal clock is regulated by the stars, it can be corrected by
them at any time by the clock stars given in the “Nautical Almanac,”
whose time of passing the meridian is calculated beforehand much more
accurately than a mean-time clock could be corrected by the sun; we
therefore correct our mean clock by the sidereal, the two agreeing at
the vernal equinox, when the sun is in the first point of Aries, and the
sidereal clock gaining about 3_m._ 56_s._ each day until it has gained a
whole day, and agrees again at the next vernal equinox.
[Illustration:
FIG. 129.—Arrangement for correcting mean solar time clock at
Greenwich.
]
At Greenwich there is, as we have already seen, a _standard, sidereal
clock_, that is, a clock keeping sidereal time; and regulated from this
is the _standard solar time clock_, giving the time by which all our
clocks and watches are governed. In practice at Greenwich the solar
clock is regulated as follows: in the computing room are two
chronometers, _c_ and _b_, Fig. 129, the one, _c_, regulated
electrically by the mean-time clock, and the other, _b_, regulated by
the sidereal clock—the error of the latter being known by transit
observations of stars on the Nautical Almanac list, the difference
between the observed time of transit and the right ascension of the star
being the error required. The proper difference between the two clocks
is then calculated and the error allowed for, which shows whether the
solar clock is fast or slow; to correct it the following method is
adopted: Carried on the pendulum of the solar clock is a slender bar
magnet, about five inches long, and below it, fastened to the
clock-case, is a galvanic coil; the magnet passes at each swing over the
upper end of the coil; if now a current is sent through this coil in one
direction repulsion takes place between the magnet and coil, and the
clock is slowed; if, on the other hand, the current is reversed, the
clock is made to gain. Now between the two chronometers is a commutator,
_d_, which, by moving the handle to one side or the other, sends the
current through the coil in such a manner that the clock is accelerated
or retarded sufficiently to set it right; when the handle of the
commutator is in the position shown in the drawing no action takes
place. As an instance of another method of regulating one clock from
another, we will quote what Professor Piazzi Smyth says of the clock
arrangements at Edinburgh.
_Correction of Mean-time Clock._—“First get its error on the observing,
_i.e._ sidereal clock. This is always done by _coincidence of beats_,
safe and certain to within one-tenth of a second, and with great ease
and comfort by means of the loud-beating hammer which strikes the
seconds of the sidereal clock on the outside of the case; one can then
watch the neck-and-neck race which takes place every six minutes between
the second of a sidereal clock and the second of a mean-time clock, the
former always winning while you look at the motion of the mean-time
seconds hand, and hear the seconds of the sidereal time.
Having got the error, say three (0·3)-tenths of a second slow, this is
the arrangement for correcting it. The pendulum is suspended by a spring
extra long, and a long arm goes across the clock pier, and the pendulum
spring passes through a fine slit in the middle of it, and the left end
(of said arm) turns on a pivot, while the right end rests on a cam,
which can be turned by a handle outside the clock-case. Turning the
handle one way raises the arm, and with that lengthens the acting length
of the pendulum spring, and turning the other way, lowers it and
shortens the pendulum, but so slightly that it takes fifteen minutes of
the quickened rate of the pendulum, when shortened, to add the required
0·3 seconds to the indications of the clock.”[14]
The sidereal clock is used in many ways besides the purpose of giving a
basis from which we can at any time get solar time, the distribution of
which forms the subject of our next chapter.
-----
Footnote 13:
_Nature_, April 1, 1875.
Footnote 14:
This plan was devised and executed by Mr. Sang, C.E., Edinburgh.
CHAPTER XVIII.
“GREENWICH TIME” AND THE USE MADE OF IT.
We have now described the method of obtaining and keeping true Greenwich
time by means of transit observations, and the next thing is to
distribute it either by controlling or driving other clocks
electrically, or by sending electric signals at known times for persons
to set their clocks right.
Nearly all, if not quite the whole, of the mean-time clocks in the
Observatory are driven by a current controlled by the standard clock, as
also is a seconds relay, _a_ Fig. 129. The clock controls, by currents
sent every second by the relay, one or two clocks in London, by special
wires.
So long ago as the year 1840 Sir Charles Wheatstone read a paper before
the Royal Society in which he described an apparatus for controlling any
number of clocks by one standard clock at a distance away. The principle
was, that at each beat of the standard clock an electric current was
sent from it through a wire to the clocks to be worked by it or
governed; and this current made an electro-magnet attract a piece of
iron each time it was sent; and this piece of iron moved backwards and
forwards two pallets, something like those of an ordinary clock, which
turned a wheel, and so worked the clock. Instead of a spring or weight
being used to work it regulated by the pallets, the pallets moved the
clock themselves, and of course keep time with the standard clock. Sir
Charles Wheatstone in this most valuable pioneer paper, indicates
several modifications of this plan. He proposed to the Astronomer-Royal
to test his method by using the then new telegraph line to Slough, but
the idea was not carried out.
This method of _driving_ clocks by electricity naturally required
considerable battery power, and in the more modern systems the clocks
are simply _controlled_, and not _driven_, by electric currents.
A very pretty method of regulating clocks by a standard clock is that in
use at Edinburgh. On the pendulum rod of the clock to be regulated, and
low down on the same, is a coil of fine covered wire wound round a short
tube. Two permanent magnets are placed in line with each other, with
their N or S ends close together and the other ends attached to the
clock-case, in such a manner that the coil, on swinging with the
pendulum, can slide over the magnets without touching. The terminal
wires of the coil are led up to near the point of suspension of the
pendulum, so as not to affect its swing, and the regulating current is
sent through a wire like a telegraph wire from the standard clock, and
from this wire round the coil and then to the earth, or back by another
wire. Currents are sent through the wires in contrary directions during
each successive second, so that the current in the coil flows in one
direction during its swing from, say, right to left, and in the contrary
direction when swinging from left to right; the effect of the current
flowing in one direction is to cause one magnet to repel the coil off
it, and the other to attract it over it, so that there is a tendency to
throw the coil from one side of its swing to the other, and back again
when the current is reversed. A little consideration will make it clear
that if the pendulum tries to go too fast the coil will tend to commence
its return swing before the current assisting the previous swing has
stopped, and it will therefore meet with resistance, and be brought back
to correct time.
The alternate currents during each second may be sent by having a wheel
of thirty long teeth on the axis of the seconds hand. Above the wheel,
and insulated from each other, are fixed two light springs which descend
side by side on either side of the teeth of the wheel, and at right
angles to each spring there projects sideways a little bar of agate with
sloping sides, which is lifted up by the teeth as they pass; one agate
is fastened a little lower down its spring than the other, so that they
are held one above the other, and half the distance between two teeth
apart: the wheel is so arranged that while at rest one of the teeth
presses against one of the agates and pushes the spring outwards, while
the other agate drops between two teeth. At the next tick of the clock
the wheel will move one-half a tooth’s distance and the other agate will
be raised and the first dropped. At the bottom of each spring is a
little platinum knob that is brought against a platinum plate as each
spring is raised, so as to make electric contact. Two batteries (single
cells of “sawdust-Daniell’s” answer admirably for short distances) are
used, the + pole of one being put in contact with the upper attachment
of one spring and the - pole of the other battery in contact with the
other spring. The other poles are put to earth, or connected to the
return wire from the governed clock. The plate against which the springs
are lifted is put in connection with the line wire going to the
regulated clock. Then, as either spring is lifted up during the swing of
the pendulum from side to side, a + or - current is sent through the
line wire from one of the batteries. It is not absolutely necessary to
use two batteries, one being sometimes sufficient, and in this case one
spring is thrown out of action, and a current sent only during every
other second in the same direction. The battery may in this case be
placed close to the regulated clock, or anywhere in the circuit, so long
as a current flows whenever the standard clock completes the circuit at
the other end. This method has the advantage that the amount of current
sent can be regulated at will by a person at the regulated clock, so
that it is possible by putting on more battery power to get sufficient
current through the wire to work a bell ringing at every other second,
or a galvanometer, showing when the seconds hand of the standard clock
is at the O^s, for there is one tooth cut from the wheel in such a
position that when the seconds hand is at O^s no current is sent for two
or more following seconds according as one or both springs are acting;
knowing this, the observer watches for the first missing current or
“dropped second,” and so finds if his clock is being correctly
regulated.
We see now the necessity for correcting the standard clock by gradually
increasing or decreasing the rate, for if it were done rapidly, the
controlled clocks would break away from the control, and not be slowed
and accelerated with the standard. At Greenwich the correction, usually
only a fraction of a second, is made a little before the hours of 10
A.M. and 1 P.M., since at those instants a distribution of time is made
throughout the country. This distribution is made as follows:—
An electric circuit is broken in two places at the standard clock, one
place of which is connected for some seconds on either side of each
hour, while the other is connected at each sixtieth second; both breaks
can therefore be only connected at the commencement of each hour, and
then only can the current pass. We will call this, therefore, the hourly
current: it acts on the magnet discharging the Greenwich time ball at
one o’clock daily, and on the magnet of the hourly relay shown in Fig.
129, which completes various circuits. One goes to the London Bridge
station of the South-Eastern Railway Co., and the other to the General
Post Office for further distribution. The bell and galvanometer in the
figure marked “S. E. R. hourly signal and Deal ball,” and “Post Office
Telegraphs” show the passage of these signals. We have now got the
hourly signal at the Post Office, and this is distributed by means of
the Chronopher, or rather Chronophers, for there are two, the old one
originally constructed by Mr. Yarley, and brought from Telegraph Street
on the removal to St. Martin’s-le-Grand, and a new one, much larger,
shown in the accompanying Fig. 130. It is to this that the Greenwich
wire is led, and the current transmitted to the different lines. The
lines are divided into four groups, (1) the metropolitan, (2) short
provincial, (3) medium provincial, (4) long provincial; the first being
wires passing to points in London only, the second to places within
about 50 miles of London, the third to more distant places, and the
fourth to the more distant places still, requiring signals. The ends of
each of the four groups are brought together, and each group has its
separate relay. These four relays—the left-hand four shown in Fig.
130—are all acted upon by the Greenwich signal and therefore act
simultaneously, each relay sending a portion of the current of its
battery through each wire of its group.
[Illustration:
FIG. 130.—The Chronopher.
]
The metropolitan group, being used only for time purposes, is always
connected with the relay, but to the country, signals are sent only
twice a day, namely, at 10 A.M. and at 1 P.M., and as the ordinary wires
are used for this purpose, they must be switched into communication with
Nos. 2, 3, and 4 relays. The action at each hour is as follows:—The
wires leading to the respective towns are connected with their speaking
instruments through a contact spring; these contact springs are shown in
the figure in a row, like the keys of a piano; along the keys runs a
flat bar which at a short time before 10 A.M. and 1 P.M. is turned on
its axis by the clockwork above, by so doing it presses back all the
keys from their respective studs, and so cuts off communication with the
speaking instruments, and puts the wires into communication with the
bar, which is divided into three insulated portions, each in
communication with a relay and battery; the batteries and relays become
connected with their respective groups, and a constant current flows
through all the wires to the distant stations serving as a warning. When
the Greenwich current arrives the relays reverse the currents, and this
gives the exact time. Shortly afterwards the clock turns back the rod
and the springs go into contact with their respective instruments, and
all goes on as before. One of the remaining relays of the apparatus
sends a current to Westminster clock tower for the rating of the clock
there, but it is in no way mechanically governed by the current. The
apparatus is entirely automatic, and to judge of the degree of accuracy
obtained an experiment was made. One of the distributing wires was
connected with a return wire to Greenwich, and the outgoing current to
the Post Office and the incoming one were passed round galvanometers,
when no sensible difference could be seen in the indications.
At 10 A.M. a considerable distribution goes on by hand. At this instant
a sound signal is heard from the chronopher, and the clerks immediately
transmit signals through the ordinary instruments to some 600 places;
these again act as centres distributing the time to railway stations and
smaller places.
The methods of signalling the time are various; at some places, as at
Edinburgh, Newcastle, Sunderland, Dundee, Middlesborough, and Kendal, a
gun is fired at 1 P.M. The history of the introduction of time-guns is a
somewhat curious one.
In August 1863, during the meeting of the British Association at
Newcastle, Mr. N. J. Holmes contrived the first electric time-gun. This
gun was fired by the electric current direct from the Royal Observatory
at Edinburgh, 120 miles distant. Time-guns were afterwards
experimentally fired at North Shields and Sunderland; the Sunderland gun
was after a time withdrawn; the Newcastle and North Shields time-guns
are regularly fired every day at 1 P.M. Four time-guns were mounted in
Glasgow, also to be fired by the electric current from Edinburgh; a
large 32-pounder was placed at Port Dundas, on the banks of the Forth
and Clyde Canal; a second small gun was placed near the Royal Exchange;
a third 18-pounder at the Bromielaw, for the benefit of Clyde ships in
harbour; and a fourth twenty-five miles further down the Clyde, at the
Albert Quay, Greenock, for the vessels anchored off the tail of the
bank. These four guns, and the two at Newcastle, were regularly fired
from the Royal Observatory, Edinburgh, for some weeks. A local jealousy
springing up amongst a few of the Glasgow College Professors and the
Edinburgh Observatory, against the introduction of mean-time into
Glasgow from the Royal Observatory Edinburgh, instead of deriving it
from the Glasgow Observatory clock (the longitude of which was
undetermined at that time), the originator of the guns, Mr. Holmes, was
cited before the police-court, charged under the Act with discharging
firearms in the public streets. The jealousy ended in the withdrawal of
the guns, and Glasgow, from then until now, has been without any
practical register of true time.[15]
Another system of time signalling is to expose a ball to view on the top
of a building, and drop it, as in the case of the ball automatically
dropped at Greenwich every day. We have already mentioned that one of
the wires from the Greenwich Observatory connects it with the London
Bridge Station, and this is used for dropping the time-ball at Deal. In
return for the hourly signals the Company give up the use of the wires
to Deal for two or three minutes about 1 P.M., when the Deal wire is
switched into communication with the Greenwich wire by a clock, just in
the same manner as at the Post Office, and communication is also made at
Ashford and Deal, in order that the current shall go to the time-ball.
In order that they shall know at Greenwich that the ball has fallen
correctly, arrangements are made so that the ball on falling sends a
return current back to Greenwich. It appears that erroneous drops are
rare, but, if such is the case, a black flag is immediately hoisted and
the ball dropped at 2 P.M.
Hourly signals are distributed on the metropolitan lines and to the
“British Horological Institute” for Clerkenwell; the leading London
chronometer makers also receive them privately.
We now come to deal with one of the practical uses of the clock and
transit instrument with reference to determining longitudes.
The earth rotates once every twenty-four hours, and if at any time a
star is directly south of Greenwich it is also due south of all places
on the meridian of Greenwich north of the equator, and north of all
places on the same meridian south of the equator; then, as the earth
rotates, the meridian of Greenwich will pass from under the star, and
others to the west will take its place, and in an hours time, at 1 P.M.,
a certain meridian to the west of Greenwich will be under the star, and
in that case all places on this meridian will be an hour west of
Greenwich, and so on through all the twenty-four hours, the meridian
being called so many hours, minutes, or seconds, west, as it passes
under any star that length of time after the meridian of Greenwich. It
is immaterial whether we reckon longitude in degrees or in time, for
since there are 360 degrees or twenty-four hours into which the equator
is divided, each hour corresponds to 15°. We also express the longitude
of a place by its distance east of Greenwich in hours, so instead of
calling a place twenty-three hours west, it is called one hour east.
Suppose we wish to find the longitude of any place, all that is required
to be known to an observer there is the exact time that a certain star
is on the meridian of Greenwich; he then observes the time that elapses
before the star comes to his meridian, and this time is the longitude
required.
This, of course, only shows the principle, for in practice it is not
absolutely necessary for the star to be on either meridian, provided its
distance on either side is known, when, of course, the difference
between the times when it actually crosses the meridian can be reckoned.
In practice a difficulty arises in finding out at a distance from
Greenwich what time it is there. It is of course twelve o’clock at
Greenwich when the sun crosses the meridian, and it is also twelve
o’clock at all the other places when the sun crosses their meridian: but
if a place is two hours west of Greenwich, the sun crosses the meridian
two hours later than it does at Greenwich, and consequently their clock
is two hours slower than Greenwich time, hence the term “local time,”
which is different for different places east or west of Greenwich. We
have taken above a star for our fixed point, but obviously the sun
answers the same purpose.
It will appear from this, that if we know the difference between the
local times of two places, we also know the longitude of one place from
the other, which is the same. A great number of ways have been tried in
order to make it known at one observing station what time it is at the
other. Rockets are sent up, gunpowder fired, and all kinds of signals
made at fixed times for this purpose; but these, of course, only answer
for short distances, so for long ones carefully adjusted chronometers
have to be carried from one station to the other to convey the correct
time; unless telegraph wires are laid from one place to another, as from
England to America; then it is easy to let either station know what time
it is at the other. For ships at sea chronometers answer well for a
short time, but they are liable to variation.
There are certain astronomical phenomena the instant of occurrence of
which can be foretold—and published in the nautical almanacs—such as the
eclipses of Jupiter’s moons, and the position of our own moon amongst
the stars. Suppose then an eclipse of one of Jupiter’s moons is to take
place at 1 P.M. Greenwich time, and it is observed at a place at 2 P.M.
of the observer’s local time, _i.e._, two hours after the sun has passed
his meridian, then manifestly the clock at Greenwich is at 1 P.M. while
his is at 2 P.M., and the difference of local time is one hour, and the
place is one hour, or 15°, east of Greenwich. If, however, the eclipse
was observed at 12 noon, then the place must be one hour west of
Greenwich. The local time being one hour slower than Greenwich shows
that the sun does not south till an hour after it does at Greenwich, or,
in reality, the place does not come under the sun till after the
meridian at Greenwich has passed an hour before, clearly showing it to
be west of Greenwich.
We shall now see how easy it is to find the longitude when the two
stations are electrically connected. Suppose we wish to determine the
difference of longitude of two places in England,—this can be determined
with the utmost accuracy in a short time if the observers have a
chronograph, of the kind just described, to record the transit of a star
at these two places. The observers at each station arrange that the
observer at Station A shall observe the transit of a certain star on his
chronograph, and the observer at Station B shall observe the transit of
the same star on his, and then with the faithful clock, beating seconds
and marking them on the surface of both chronographs simultaneously, the
difference of sidereal time between the transit of the same star over
Station A and Station B will be an absolute distance to be measured off
in as delicate a way as possible by comparison of the roller of each
chronograph, and will give exactly how much time elapses between the two
transits. This is the longitude required. There are various methods of
utilizing the same principle, as, for instance, one chronograph only may
be used, and both observers then register their transits on the same
cylinder. But when we have to deal with considerable distances, such as
between England and the United States, then we no longer employ this
method. From Valentia we telegraph to Newfoundland in effect “Our time
is so-and-so,” and then the observer at Newfoundland telegraphs to
Valentia “Our time is so-and-so.”
In this way the absolute longitude of the West of Ireland and America
and the different observatories of Europe has been determined with the
greatest accuracy.
So it appears there are two methods, the first showing one time, say
Greenwich time, at both places, and showing the difference in times of
transit of stars; or secondly, having the clock at each place going to
its own local time, so that a certain star transits at the same local
time at each place, and finding the difference between the two clocks.
-----
Footnote 15:
It was found, that between the passing of the spark into the gun, and
the ignition of the powder and discharge of the piece, one tenth of a
second elapsed.
CHAPTER XIX.
OTHER INSTRUMENTS USED IN ASTRONOMY OF PRECISION.
In former chapters we have described the transit circle as it now exists
as the result of the thought of Tycho, Picard, Römer, and Airy. This,
though the fundamental instrument in a meridional observatory, is by no
means the only one, and we must take a glance at the others.
In Römer’s “Observatorium Tusculaneum,” near Copenhagen, built in 1704,
there was not only a transit circle in the meridian of course, but a
transit instrument in the prime vertical, _i.e._ swinging in a vertical
plane at right angles to the former one, so that while the optical axis
of one always lies in a N.S. plane, that of the other lies in an E.W.
one. Römer did not use this instrument much; it remained for the great
Bessel to point out its value in determinations of latitude.
This instrument is, so to speak, self-correcting, because between the
transit of a star over its wires while pointing to the east of the
meridian, and that while pointing to the west its telescope can be
reversed in its =Y=s, or one position may be taken for one night’s
observations, and the other for the next, and so on.
In Struve’s form of this instrument the transit of stars can be observed
at an interval of one minute and twenty seconds, this time only being
required to raise it from the =Y=s, to rotate it through 180°, and lower
it again. This rapid reversal, and consequent elimination of
instrumental imperfections, enable observations of the most extreme
precision to be made in such delicate matters as the slight differences
of declination of stars due to aberration, nutation, and the like.
The intersection of the meridian with the prime vertical marks the
zenith. To determine this:—first, there is the zenith sector, invented
by Hooke; it consists of a telescope, carried by an axis on one side of
the tube, and at right angles to it, so that the telescope swings
exactly as a transit does, and it is provided with cross wires in the
same manner; instead, however, of having a whole circle, it has only two
segments of a circle; and as it is never required to swing the telescope
far from its vertical position, there is a diagonal reflector at the
eyepiece, so that the observer can look sideways, instead of upwards, in
an awkward position. Its use is to determine the zenith distance of
stars as they pass near that point. These distances are read off on the
parts of the circle by verniers or microscopes, as in the transit
circle. The zenith telescope, chiefly designed by Talcott, is the modern
equivalent of the sector, and both instruments are more used in
geodetical operations than in fixed observatories. At Greenwich,
however, there is an instrument for determining zenith distances of very
special construction. This is called the reflex zenith tube, shown in
Fig. 131. It is a sectional drawing of one of those instruments showing
the path of the rays of light. A, B, is an object-glass, fixed
horizontally, and below it is a trough of mercury, C, the surface of
which is always of course horizontal. The light from a star near the
zenith is allowed to fall through the object-glass, which converges the
rays just so much that they come to a focus at F, after having been
reflected from the surface of the mercury, and also by the diagonal
mirror or prism, G; at F, therefore, we have an image of the star, which
can be examined together with the cross-wires at the eyepiece, M. There
is in this instrument no necessity for the accurate adjustments that
there is in the case of the transit, the surface of the mercury being
always horizontal, and so giving an unaltering datum plane.
[Illustration:
FIG. 131.—Reflex Zenith Tube.
]
When the star is perfectly vertical, its image will fall on a certain
known part in the eyepiece; but, as it leaves the vertical, the angle of
incidence of its light on the mercury alters, and likewise that of
reflection, so that the position of the image changes, and this change
of position in the eyepiece is measured by movable cross-wires and a
micrometer screw, similar to that employed for reading the circle in the
transit circle.
At the present time γ Draconis is the star which passes very nearly
through the zenith of Greenwich, and observations of this star are
accordingly made at every available opportunity.
We now pass to an enlargement of the sphere of observation of the
transit circle in order that any object can be viewed at all times when
above the horizon; in this case the transit circle passes into the
alt-azimuth, or altitude and azimuth instrument, astronomical
theodolite, or universal instrument.
A reference to Fig. 132—a woodcut of an ordinary theodolite—will show
the new point introduced by this construction.
Imagine the upper part of the theodolite fixed with its telescope and
circle in the plane of the meridian—we have the transit circle; swing
the theodolite round through 90°—we have the prime vertical instrument.
Now instead of having the upper part fixed let it be free to rotate on
the centre of the horizontal circle—we have the alt-azimuth.
In the description of the instruments used in Tycho’s observatory
(Chapter IV.), we described another instrument by which Tycho and the
Landgrave of Hesse-Cassel endeavoured to make observations out of the
meridian; and we may remember that they almost had to give the matter up
in despair, because they could not find any clocks sufficiently good to
enable them to fix the position of the star.
[Illustration:
FIG. 132.—Theodolite.
]
[Illustration:
FIG. 133.—Portable Alt-azimuth.
]
If we refer again to Fig. 18, we see the method by which Tycho tried to
get the two co-ordinates. On the horizontal circle there are the
graduations for azimuth, or the measurement from the south along the
horizon, and on the vertical quadrant are the graduations for altitude.
Now let us turn to the modern equivalent of that instrument. Fig. 133
shows this in a portable form. The upper part of the instrument is, as
one sees, nothing more than a transit circle exactly equivalent to the
one described. We have a telescope carried on a horizontal axis,
supported by a pillar; we have the reading microscopes, and the like;
but the support of the horizontal axis, instead of being on the solid
ground, as it is in the transit circle, rests on a movable horizontal
circle, which is also read by microscopes arranged round it, so that all
errors may be eliminated. With this instrument we can get the altitude
of an object at any distance from the meridian, and at the same time
measure its distance east and west of it. The arrangements designed by
the Astronomer Royal for observations of the moon at Greenwich are more
elaborate. In the Greenwich alt-azimuth, the telescope is swung on
pivots between two piers, just as in the case of the transit, these
piers being fixed to the horizontal circle.
The great advantage of this instrument is that the true place of a
heavenly body can be determined whenever it is above the horizon; we
have neither to wait for a transit over the meridian nor over the prime
vertical. Nevertheless its use is not general in fixed observatories.
Reduce the dimensions of the horizontal circle and increase those of the
vertical one, and we have the _vertical circle_ designed by Ertel, and
largely used in foreign observatories.
BOOK V.
_THE EQUATORIAL._
CHAPTER XX.
VARIOUS METHODS OF MOUNTING LARGE TELESCOPES.
We have already gone somewhat in detail into the construction of the
transit circle, which is almost the most important of modern
astronomical instruments. We then referred to the alt-azimuth, in which,
instead of dealing with those meridional measurements which we had
touched upon in the case of the transit circle, we left, as it were, the
meridian for other parts of the sphere and worked with other great
circles, passing not through the pole of the heavens, but through the
zenith.
We now pass to the “optick tube,” as used in the physical branch of
astronomy, and we have first to trace the passage from the alt-azimuth
to the Equatorial, as the most convenient mounting is called.
This equatorial gives the observer the power of finding any object at
once, even in the day-time, if it be above the horizon; and, when the
object is found, of keeping it stationary in the field of view. But
although this form is the most convenient, it is not the one universally
adopted, because it is expensive, and because, again, till within the
last few years our opticians were not able to grapple with all its
difficulties.
Hence it is that some of the instruments which have been most nobly
occupied in investigations in physical astronomy have been mounted in a
most simple manner, some of them being on an alt-azimuth mounting. Of
these the most noteworthy example is supplied by the forty-feet
instrument erected by Sir William Herschel at Slough.
[Illustration:
FIG. 134.—The 40-feet at Slough.
]
Lord Rosse’s six-feet reflector again is mounted in a different manner.
It is not equatorially mounted; the tube, supported at the bottom on a
pivot, is moved by manual power as desired between two high side walls,
carrying the staging for observers, and so allowing the telescope a
small motion in right ascension of about two hours. Our amateurs then
may be forgiven for still adhering to the alt-azimuth mounting for mere
star-gazing purposes.
[Illustration:
FIG. 135.—Lord Rosse’s 6-feet.
]
[Illustration:
FIG. 136.—Refractor mounted on Alt-azimuth Tripod for ordinary
Stargazing.
]
We must recollect that, with the alt-azimuth, we are able to measure the
position of an object with reference to the horizon and meridian; but
suppose we tip up the whole instrument from the base, so that, instead
of having the axis of the instrument vertical, we incline it so as to
make the axis, round which the instrument turns in azimuth, absolutely
parallel to the earth’s axis.
Of course, if we were using it at the north pole or the south pole, the
axis would be absolutely vertical, as when it is used as an alt-azimuth,
or otherwise it would not be absolutely parallel to the axis of the
earth. On the other hand, if we were using it at the equator, it would
be essential that the axis should be horizontal, since to an observer at
the equator the earth’s axis is perfectly horizontal; but, for a middle
latitude like our own, we have to tip this axis about 51½° from the
horizontal, so as to be in proper relationship with, _i.e._ parallel to,
the earth’s axis. Having done this, we can, by turning the instrument
round this axis, called the polar axis, keep a star visible in the field
of view for any length of time we choose by exactly counteracting the
rotation of the earth, without moving the telescope about its upper, or
what was its horizontal, axis. The lower circle of the instrument will
then be in the plane of the celestial equator, and the upper one, at
right angles to it, will enable us to measure the distance from that
plane, or the declination of an object, while the lower circle will tell
us the distance of the object from the meridian in hours or degrees.
With the aid of good circles and good clocks, we can thus determine a
star’s position. Fig. 137 shows an Equatorial Stand, one of the first
kind of equatorials used by astronomers. We see at once the general
arrangements of the instrument. In the first place, we have a horizontal
base, D, and on it, and inclined to it, is a disc of metal, C; again on
this disc lies another disc, A, B, which can revolve round on C, being
held to it by a central stud, so that when A B is in the plane of the
earth’s equator its axis points to the pole and is parallel to the axis
of the earth. On the upper disc there are two supports for the axis of
the telescope, E, which is at right angles to the polar axis and is
called the declination axis of the telescope; round it the telescope has
a motion in a direction from the pole to the equator.
[Illustration:
FIG. 137.—Simple Equatorial Mounting.
]
In the equatorial mounting, clockwork is introduced, and after the
instrument has been pointed to any particular star or celestial body,
the clock is clamped to the circle moving round the polar axis, and so
made to drive it round in exactly the time the earth takes to make a
rotation. By a clock is meant an instrument for giving motion, not with
reference to time, but so arranged that, if it were possible to use it
continuously, the motion would exactly bring the telescope round once in
the twenty-four sidereal hours which are necessary for the successive
transits of stars over the meridian.
There is an objection to the form of instrument given above,—the
telescope cannot be pointed to any position near the pole, since the
stand comes in the way. This is obviated in the various methods of
mounting, which we shall now pass under review.
_The German Mounting._
This is the form now almost universally adopted for refractors and
reflectors under 20 inches aperture.
The polar axis has attached to it at right angles a socket through which
the declination axis passes, and this axis carries the telescope at one
end and a counterweight at the other. The polar axis lies wholly below
the declination axis, and both are supported by a central pillar
entirely of iron, or partly of stone and partly of iron.
By the courtesy of Messrs. Cooke and Sons, Mr. Howard Grubb, and Mr.
Browning, we are enabled to give examples of the various forms of this
mounting now in use in this country for instruments of less than 20
inches aperture.
In Fig. 138, we have the type form of Equatorial Refractor introduced
some 30 years ago by the late Mr. Thomas Cooke. The telescope is
represented parallel to the polar axis, which is inclosed in the casing
supported by the central pillar, and carries one large right ascension
circle above and another smaller one below, the former being read by
microscopes attached to the casing.
The socket or tube carrying the declination axis is connected with the
top of the polar axis. To this the declination circle is fixed, while an
inner axis fixed to the telescope carries the verniers.
[Illustration:
FIG. 138.—Cooke’s form for Refractors.
]
[Illustration:
FIG. 139.—Mr. Grubb’s form applied to a Cassegrain Reflector.
]
The clock is seen to the north of the pillar. While this is driving the
telescope, rods coming down to the eyepiece enable the observer to make
any small alterations in right ascension or declination; indeed in all
modern instruments everything except winding the clock is done at the
eyepiece, so that the observer when fairly at work is not disturbed. The
lamp to illuminate the micrometer wires is shown near the finder. The
friction rollers, which take nearly all the weight off the surfaces of
the polar axis, are connected with the compound levers shown above the
casing of the polar axis.
In Fig. 139 we have Mr. Grubb’s revision of the German form. The pillar
is composite, and the support of the upper part of the polar axis is not
so direct as in the mounting which has just been referred to. There are,
however, several interesting modifications to which attention may be
drawn. The lamp is placed at the end of the hollow polar axis, and
supplies light not only for the micrometer wires, but for reading the
circles; the central cavity of the lower support is utilised for the
clock, which works on part of a circle, instead of a complete one, as in
the instrument already described.
In the case of Newtonian reflectors the observer requires to do his work
at the upper end of the tube; this therefore should be as near the
ground as possible. This is accomplished by reducing the support to a
minimum. Figs. 140 and 141 show two forms of this mounting, designed by
Mr. Grubb and Mr. Browning.
The two largest and most perfectly mounted refractors on the German form
at present in existence are those at Gateshead and Washington, U.S. The
former belongs to Mr. Newall, a gentleman who, connected with those who
were among the first to recognise the genius of our great English
optician, Cooke, did not hesitate to risk thousands of pounds in one
great experiment, the success of which will have a most important
bearing upon the astronomy of the future.
[Illustration:
FIG. 140.—Grubb’s form for Newtonians.
]
[Illustration:
FIG. 141.—Browning’s mounting for Newtonians.
]
In the year 1860 the largest refractors which had been turned out of the
Optical Institute at Munich under the control, first, of the great
Fraunhofer, and afterwards of Merz, were those of 177 square inches area
at Poulkowa and Cambridge (U.S.). Our own Cooke, who was rapidly
bringing back some of the old prestige of Dollond and Tulley’s time to
England—a prestige which was lost to us by the unwise meddling of our
excise laws and the duty on glass,[16] which prevented experiments in
glass-making—had completed a 9⅓ inch for Mr. Fletcher and a 10 inch for
Mr. Barclay; while in America Alvan Clarke had gone from strength to
strength till he had completed a refractor of 18½ inches for Chicago.
The areas of these objectives are 67, 78·5, and 268 inches respectively.
Those who saw the great Exhibition of 1862 may have observed near the
Armstrong Gun trophy two circular blocks of glass some 26 inches in
diameter and about two inches thick standing on their edges. These were
two of the much-prized “discs” of optical glass manufactured by Messrs.
Chance of Birmingham.
At the close of the Exhibition they were purchased by Mr. Newall, and
transferred to the workshops of Messrs. Cooke and Sons at York.
The glass was examined and found perfect. In time the object-glass was
polished and tested, and the world was in possession of an astronomical
instrument of nearly twice the power of the 18½ inch Chicago
instrument—485 inches area to 268.
Such an achievement marks an epoch in telescopic astronomy, and the
skill of Mr. Cooke and the munificence of Mr. Newall will long be
remembered.
The general design and appearance of this monster among telescopes will
be gathered from the general view given in the frontispiece, for which
we are indebted to Mr. Newall. It is the same as that of the well-known
Cooke equatorials; but the extraordinary size of all the parts has
necessitated the special arrangement of most of them.
The length of the tube, including dew-cap and eye-end, is 32 feet, and
it is of a cigar shape, the diameter at the object-end being 29 inches,
at the centre of the tube 34 inches, and at the eye-end 22 inches. The
cast-iron pillar supporting the whole is 19 feet in height from the
ground to the centre of the declination axis, when horizontal; and the
base of it is 5 feet 9 inches in diameter. The trough for the polar axis
alone weighs 14 cwt., the weight of the whole instrument being nearly 6
tons.
The tube is constructed of steel plates riveted together, and is made in
five lengths screwed together with bolts. The flanges were turned in a
lathe, so as to be parallel to each other. It weighs only 13 cwt., and
is remarkably rigid.
Inside the outer tube are five other tubes of zinc, increasing in
diameter from the eye to the object-end; the wide end of each zinc tube
overlapping the narrow end of the following tube, and leaving an annular
space of about an inch in width round the end of each for the purpose of
ventilating the tube, and preventing, as much as possible, all
interference by currents of warm air with the cone of rays. The zinc
tubes are also made to act as diaphragms.
The two glasses forming the object-glass weigh 144 lb., and the brass
cell weighs 80 lb. The object-glass has an aperture of nearly 25 inches,
or 485 inches area, and in order as much as possible to avoid flexure
from unequal pressure on the cell, it is made to rest upon three fixed
points in its cell, and between each of these are arranged three levers
and counterpoises round a counter-cell, which act through the cell
direct on to the glass, so that its weight in all positions is equally
distributed among the twelve points of support, with a slight excess
upon the three fixed ones. The focal length of the lens is 29 feet.
Attached to the eye-end of the tube are two finders, each of 12·5 inches
area; they are fixed above and below the eye-end of the main tube, so
that one may be readily accessible in all positions of the instrument.
It is also supplied with a telescope having an object-glass of 33 inches
area. This is fixed between the two finders, and is for the purpose of
assisting in the observations of comets and other objects for which the
large instrument is not so suitable. This assistant telescope is
provided with a rough position circle and micrometer eyepieces.
Two reading microscopes for the declination circle are brought down to
the eye-end of the main tube; the circle—38 inches in diameter—is
divided on its face and edge, and read by means of the microscopes and
prisms.
The slow motions in declination and R. A. are given by means of tangent
screws, carrying grooved pulleys, over which pass endless cords brought
to the eye-end. The declination clamping handle is also at the eye-end.
The clock for driving this monster telescope is fixed to the lower part
of the pillar, and is of comparatively small proportions, the instrument
being so nicely counterpoised that a very slight power is required to be
exerted by the clock, through the tangent screw, on the driving-wheel
(seven feet in diameter), in order to give the necessary equatorial
motion.
The declination axis is of peculiar construction, necessitated by the
weight of the tubes and their fittings, and corresponding counterpoises
on the other end, tending to cause flexure of the axis. This difficulty
is entirely overcome by making the axis hollow, and passing a strong
iron lever through it having its fulcrum immediately over the bearing of
the axis near the main tube, and acting upon a strong iron plate rigidly
fixed as near the centre of the tube as possible, clear of the cone of
rays. This lever, taking nearly the whole weight of the tubes, &c., off
the axis, frees it from all liability to bend.
The weight of the polar axis on its upper bearing is relieved by
anti-friction rollers and weighted levers; the lower end of the axis is
conical, and there is a corresponding conical surface on the lower end
of the trough; between these two surfaces are three conical rollers
carried by a loose or “live” ring, which adjust themselves to equalize
the pressure.
The hour-circle on the bottom of the polar axis is 26 inches in
diameter, and is divided on the edge, and read roughly from the floor by
means of a small diagonal telescope attached to the pillar; a rough
motion in R. A. by hand is also arranged for, by a system of cogwheels,
moved by a grooved wheel and endless cord at the lower end of the polar
axis, so as to enable the observer to set the instrument roughly in R.
A. by the aid of the diagonal telescope. It is also divided on its face,
and read by means of microscopes. The declination and hour-circle will
probably be illuminated by means of Geissler tubes, and the dark and
bright field illuminations for the micrometers will be effected by the
same means.
[Illustration:
FIG. 142.—The Washington Great Equatorial.
]
So soon as the success of the Newall experiment was put beyond all
question by Cooke, Commodore B. F. Sands, the superintendent of the U.S.
Naval Observatory, sent a deputation, consisting of Professors S.
Newcomb, Asaph Hall, and Mr. Harkness, accompanied by Mr. Alvan Clarke,
to examine and report upon the Newall telescope, and the result was that
they commissioned Alvan Clarke to construct a large telescope for that
country.
In the Washington telescope the aperture of the object-glass is 26
inches—that is, one inch larger than the English type-instrument. The
general arrangements are shown in the accompanying woodcut.
It will be seen that the mounting is much lighter than in the English
instrument, and a composite pillar gives place for the clock in the
central cavity.
_The English Mounting._
In the _English mounting_ the telescope, like a transit instrument, has
on each side a pivot, and these pivots rest on a frame somewhat larger
than the telescope, pointing to the pole and supported by two pivots,
one at the bottom resting on bearings near the ground, and the other
carried by a higher pillar clear of the observer’s chair. The motions of
the telescope are similar to those given by the German mounting in all
essentials; the Greenwich equatorial is mounted in this manner. It is
carried in a large cylindrical frame, supported at both ends by two
pillars—above by a strong iron pillar, while the other end rests on a
firm stone pillar, going right to the earth, independently of the
flooring. This mounting, though preferred for the large instrument at
Greenwich, has been discarded generally, as the long polar axis is
necessarily a serious element of weakness; the telescope is supported on
its weakest part, and it is liable to great changes from contraction and
expansion of the frame.
_The Forked Mounting._
It is now getting more usual to mount Newtonians of large dimensions
equatorially, in spite of the immense weight to be carried. One of the
first methods was to use a polar axis in the same manner as for a
refractor, only that it bifurcated at the top, forming there a fork, and
between this fork the telescope is swung, after the same manner as a
transit. This method of mounting was adopted by M. Foucault in the case
of his first large silvered-glass reflector. The height of the
bifurcation is dependent on the distance between the centre of gravity
of the tube and the speculum, and if we use an extremely light tube, or
if,—as it is the fashion to abolish them now altogether for
reflectors,—we use a skeleton tube of iron lattice work, this
bifurcation of the polar axis need not be of any great length. The polar
axis being entirely below the telescope and being driven by the clock,
we have a perfect method of mounting a speculum of any weight we please.
This arrangement was first suggested and carried into effect by Mr.
Lassell for his four-foot Newtonian, which was mounted at Malta. The
polar axis was a heavy cone-shaped casting resting on its point below,
and moving on its largest diameter just below the base of the fork. Lord
Rosse has recently much improved upon the original idea.
As the observer must be at the mouth of the tube, he is in a very bad
position as far as comfort goes, especially as the eye-end changes its
position rapidly in consequence of the great length of the tube from its
centre of gravity outwards. The platform on which he stands is raised on
supports, extending from the floor and going up to the opening through
which the telescope points to the heavens, and the whole platform is
sometimes fixed to the dome of the observatory, so that it travels round
with it.
With Mr. Lassell’s four-foot the observer stood in a gigantic reading
box, about thirty feet high, with openings in it at different
elevations. This structure was supported on a circular platform movable
on rails round the base of the mounting. Almost continual variations,
both of the observing height and of the circular platform, were
necessary, as the distance from the centre of motion of the tube and the
eyepiece was no less than 34 feet.
In Lord Rosse’s recent adaptation of this form the observer is placed in
a swinging basket, at the end of an arm almost as long as the telescope
tube. He is here counterpoised, and moves round a railway which
surrounds the mounting at the height of the tip of the fork.
_The Composite Mounting._
[Illustration:
FIG. 143.—General view of the Melbourne Reflector.
]
There is still another form of mounting which promises to be largely
used for reflectors in the future, whether the tube be lightened by its
being constructed of only a framework of iron or not. This mounting is
neither German nor English, but in part imitates both of these methods:
hence I give it the name of Composite. There is a short polar axis
supported at both ends.
[Illustration:
FIG. 144.—The mounting of the Melbourne Telescope. C, polar axis (cube
1 yard square, cone 8 feet long); D, Clock sector; U, Counterpoise
weights (2¼ tons).
]
Within the last few years two large reflectors have been erected,
equatorially mounted in this composite manner—the great Melbourne
Equatorial, constructed by Mr. Grubb, and the new Paris Equatorial,
constructed by Mr. Eichens.
Of the former, Fig. 143 gives a general view, showing how the
construction of this instrument differs from other equatorials which we
have seen. Fig. 144 shows the mounting in more detail. C is the polar
axis, T P is the declination axis, and T the small portion of the tube
of the telescope, the remainder of the tube being represented by
delicate lattice work, which is as light as possible, and used merely
for supporting the reflector, by means of which the light is thrown back
again, according to the suggestion of Cassegrain, and comes through the
hole in the centre of the speculum into the eyepiece, which is seen at
_y_, so that the observer stands at the bottom of the telescope in
exactly the same way as if he were using a refractor.
In this enormous instrument, the tube and speculum of which alone weigh
nearly three tons, the system of counterpoises is so perfect that we
describe the method adopted in order to give an idea of the general
arrangement of the bearing and anti-frictional apparatus. The series of
weights hanging behind the support of the upper end of the polar axis
are intended to take a great part of the weight of that axis off the
lower support; beside which there are friction-rollers pressed upwards
against the axis by the weights inside the support.
All the bearings are constructed on the same principle as the Y bearings
of a theodolite—that is, the pivots rest on two small portions of their
arc, 90° or 100° apart.
If allowed to rest on these bearings without some anti-frictional
apparatus, the force required to move such an instrument would render it
simply unmanageable and destroy the bearings.
The plan adopted by Mr. Grubb is to allow the axis to rest in its
bearings with just a sufficient portion of its weight to insure perfect
contact, and to support the remainder by some anti-frictional apparatus.
Generally 1/50 to 1/100 of the weight is quite sufficient to allow the
axis to take its bearing, and the remainder 49/50 to 99/100 can thus be
supported on friction rollers, and reduced to any desired extent,
without injuring in the slightest degree the perfection of steadiness
obtained by the use of the Y’s. This is the plan used in the bearings of
the polar axis, and the result is that the instrument can be turned
round this axis by a force of 5 pounds at a leverage of 20 feet. The
bearings of the declination axis are supported on virtually the same
principle; but the details of that construction are necessarily much
more complicated, on account of the variability of direction of the
resolved forces with respect to the axis.
We may now turn to the four-foot silver-on-glass Newtonian now in course
of completion at the Paris Observatory.
The illustration which we give represents the telescope in a position
for observation. The wheeled hut under which it usually stands, a sort
of waggon seven metres high by nine long and five broad, is pushed back
towards the north along double rails. The observing staircase has been
fitted to a second system of rails, which permits it to circulate all
round the foot of the telescope, at the same time that it can turn upon
itself, for the purpose of placing the observer, standing either on the
steps or on the upper balcony, within reach of the eyepiece. This
eyepiece itself may be turned round the end of the telescope into
whatever position is most easily accessible to the observer.
[Illustration:
FIG. 145.—Great Silver-on-Glass Reflector at the Paris Observatory.
]
The tube of the telescope, 7·30 metres in length, consists of a central
cylinder, to the extremities of which are fastened two tubes three
metres long, consisting of four rings of wrought-iron holding together
twelve longitudinal bars also of iron. The whole is lined with small
sheets of steel plate. The total weight is about 2,400 kilogrammes. At
the lower extremity is fixed the cell which holds the mirror; at the
other end a circle, movable on the open mouth of the telescope, carries
at its centre a plane mirror, which throws to the side the cone of rays
reflected by the great mirror.
The weight of the mirror in its barrel is about 800 kilogrammes; the
eyepiece and its accessories have the same weight.[17]
It will be quite clear from what has been said that the manipulation of
these large telescopes at present entails much manual and even bodily
labour, and when we come in future to consider the winding of the clock,
the turning of the dome, and the adjustment of the observing chair, it
will be seen that the labour is enormous. To save this, in all the best
instruments everything is brought to the eye-end of the telescope,
movements both in right ascension and declination, reading of circles,
and adjustment of illumination. Mr. Grubb has suggested that everything
should be brought to this point, and that, by the employment of
hydraulic power, “the observer, without moving from his chair, might, by
simply pressing one or other of a few electrical buttons, cause the
telescope to move round in right ascension, or declination, the dome to
revolve, the shutters to open, and the clock to be wound.” He very
properly adds, “This is no mere Utopian idea. Such things are done, and
in common use in many of our great engineering establishments, and it is
only in the application that there would be any difficulty encountered.”
_The Driving Clock._
In a previous chapter it was stated that in all large telescopes used
for the astronomy of position, whether a transit circle or the
alt-azimuth, what we wanted to do was to note the transit of the star
across the field—the transit due to the motion of the earth; but that
when we deal with other phenomena, such, for instance, as those a large
equatorial is capable of bringing before us, we no longer want these
objects to traverse the field, we want to keep them, if possible,
absolutely immovable in the field of view of the eyepiece, so that we
may examine them and measure them, and do what we please with them.
Hence it was that we found driving clocks applied to equatorials; and
our description would not be complete did we fail to explain the general
principles of their construction. They are instruments for counteracting
the motion of the earth by supplying an exactly equal motion to the tube
of the telescope in an opposite direction.
Without such a clock we may get an image of the object we wish to
examine; but before we should be able to do anything with it, either in
the way of measurement or observation, it would have gone from us. A
glimpse of a planet or star with a large telescope will give a general
notion of the extreme difficulty which any observer would have to deal
with if he wanted to observe any heavenly body without a driving clock.
We can easily see at once that it would not do to have an ordinary clock
regulated by a pendulum for driving the telescope, it would be driven by
fits and starts, which would make the object viewed jump in the field at
each tick of the pendulum. The most simple clock is therefore one in
which the conical pendulum is used in the form of the governor of a
steam-engine, so that when the balls A A, Fig. 146, fly up by reason of
the clock driving too fast, they rub against a ring, B, or something
else that reduces their velocity.
[Illustration:
FIG. 146.—Clock Governor.
]
[Illustration:
FIG. 147.—Bond’s Spring Governor.
]
There is another form made by Alvan Clarke, in which a pendulum
regulates the clock, but not quite in the ordinary way. The drawing will
perhaps make it clear: A A, Fig. 147, is one of the wheels of the
clock-train driving a small weighted fan, B, which is regulated so as to
allow the clock to drive a little too fast. Now let us see how the
pendulum regulates it. On the axis of A A is placed an arm, C, which is
of such a length that it catches against the studs S S, and is stopped
until the pendulum, P, swings up against one of the studs, R, which
moves the piece D, like a pendulum about its spring at E, until the
stud, S, is sufficiently removed to let the arm, C, pass, so that the
clock is under perfect control. If, however, the arm C were fixed
rigidly to the axis of the wheel A A, there would be a jerk every time C
touched one of the studs. The wheel is therefore attached to the axis
through the medium of a spring, F, so that when the arm is stopped the
wheel goes on, but has its velocity retarded by the pressure of the
spring. The pendulum is kept going in the following manner:—There is a
pin fixed to the axis on the same side of the centre as C, which, as the
arm approaches either stud S, raises the piece D, but not sufficiently
to liberate the arm; the pendulum has then only a very little work to do
to raise D and disengage the arm, C; but as soon as it is free it starts
off with a jerk, due to the tension of the spring on the axis, and
leaves D by means of its stud, R, to exert its full force on the
pendulum and accelerate its return stroke, so that the pendulum is kept
in motion by the regulating arrangement itself.
The late Mr. Cooke of York constructed a very accurately-going driving
clock. This differs in important particulars from Bond’s form, though
the control of the pendulum is retained.
The following extracts from a description of it will show the principal
points in its construction:—
The regulator adopted is the vibrating pendulum, because amongst the
means at the mechanician’s command for obtaining perfect
time-keeping there is none other by which the same degree of
accuracy can be obtained. The difficulty in this construction is the
conversion of the jerking or intermittent motion produced by such
pendulums into a uniform rotatory motion which can be available with
little or no disturbing influence on the pendulum itself, when the
machine is subject to varying frictions and forces to be overcome in
driving large equatorials.
The pendulum is a half-second one, with a heavy bob, adjusted by
sliding the suspension through a fixed slit. It is drawn up and let
down by a lever and screw, the acting length of the pendulum being
thus regulated.
The arrangement of the wheels represents something like the letter
U. At the upper end of one branch is the scape-wheel. At the upper
end of the other branch is an air-fan. The large driving-wheel and
barrel are situated at the bottom or bend. All the wheels are geared
together in one continuous train, which consists of eight wheels and
as many pinions. The scape-wheel and the two following wheels have
an intermittent motion; all the others have a continuous and uniform
one.
The change from one motion to the other is made at the third wheel,
which, instead of having its pivot at the end of the arbor where the
wheel is fixed—fixed to the frame like the others—is suspended from
above by a long arm having a small motion on a pin fixed to the
frame; the pivot at the other end of the arbor is fixed to the frame
as the others are, but its bole and its pivot are arranged so as to
permit a very small horizontal angular motion round them, as a
centre, without interfering with the action of the gearing of the
wheel itself.
If the weight is applied to the clock, and the pendulum is made to
vibrate, the moment it begins to move, the scape-wheel moves its
quantity for a beat; the remontoire wheel, by the very small force
outwardly caused by the reaction of the break-spring, relaxes its
pressure against a friction-wheel, and sets at liberty the train of
the clock.
The spring is now driven back to the break-wheel, but before it can
produce more than the necessary friction to keep the train in
uniform motion, another beat of the clock again releases it. The
repetition of these actions produces a series of impulses on the
break-wheel of such a force and nature as to keep the train freely
governed by the pendulum.
The uniform rotatory motion obtained by this clock as far as
experiments can be made by applying widely different weights, and
comparing the times with a chronometer, is perfectly satisfactory.
A clock constructed on the same principle, connected, and giving
motion to a cylinder, will, it is presumed, make an excellent
chronograph.
[Illustration:
FIG. 148.—Foucault’s governor.
]
The form of governor most usually employed will be seen in figures
previously given. The governor raises a plate and thus becomes a
frictional governor, by which all overplus of power is used up in
frictions, or by that doubling the driving power no, or only a small,
difference should be brought about in the rate.
Other forms of driving clocks or governors invented by Foucault and Yvon
Villarceau are now being largely employed. In them the rapid motion of a
fan and other devices are introduced.
A driving clock adjusted to sidereal time requires adjustments for
observations of the sun and moon. This (as at _z_ in Fig. 144) is
sometimes done once for all by differential gearing thrown into action
by levers when required.
Mr. Grubb has lately made a notable improvement upon the usual form by
controlling the motion of the governor by a sidereal clock and an
electric current.
There are various methods of attaching the clock to the polar axis. One
is to make the clock turn a tangent screw, gearing into a screw-wheel on
the axis of the telescope, which can be thrown in and out of gear for
moving the telescope rapidly in right ascension. Another method is to
have a segment of a circle on the polar axis which can be clamped or
unclamped at pleasure by means of a screw attached to it. A strip of
metal is attached to each end of the segment and is wound round a drum
turned by the clock, so that the two are geared together just as wheels
are geared by an endless strap passing round them. This arrangement
gives a remarkably even motion to the telescope. When the strap is wound
up to the end of the segment, which is done in about two or three hours’
work, the drum is thrown out of gear and the arc pushed back to its
starting-place again.
_THE LAMP._
[Illustration:
FIG. 149.—Illuminating lamp for equatorial.
]
In the description of the transit circle we saw how the Astronomer-Royal
had contrived to throw light into the axis of the telescope, so that the
wires were either rendered visible in a bright field, or, the field
being kept dark, the wires were visible as bright lines in a dark field.
That is the difference between a bright field, and a dark field of
illumination. Now a bright field of illumination in the case of
equatorials is managed by an arrangement as follows.—A A, Fig. 149, is a
section of the tube of the telescope. Near the eyepiece is a small lamp,
D, swung on pins on either side which rest on a circular piece of brass
swinging on a pin at C, and a short piece of tube at E, through which
the light passes into the telescope and falls on a small diagonal
reflector, F. This reflects the rays downwards into the eyepiece. When
the telescope is moved into any position the lamp swings like a
mariner’s compass on its gimbals, and still throws its light into the
tube, and the light mixes up with that coming from the star, but spreads
all over the field of view instead of coming to a point, so that the
star is seen on a bright field, and the wires as black lines. Now if the
star which is observed is a very faint one, we defeat our own object,
for the light coming from the lamp puts out the faint star.
[Illustration:
FIG. 150.—Cooke’s illuminating lamp.
]
We have seen how the illumination of the wires, instead of the field, is
carried out in the Greenwich transit. The same method can be adopted in
the case of equatorials, the light from the diagonal reflector being
thrown on other diagonal reflectors or prisms on either side the wires
in the micrometer so as to illuminate them. Messrs. Cooke and Sons have
devised a lamp of very great ingenuity, Fig. 150. It is a lamp which
does for the equatorial, in any position, exactly what the fixed lamp
does for the transit circle. It is impossible to put it out of order by
moving the telescope. There is a prism at P reflecting the light into
the telescope tube, and at whatever different angle of inclination, or
whatever may be the size of the telescope on which this lamp is placed,
it is obvious that the lamp never ceases to throw its light into the
reflector inside the telescope; and any amount of light, or any colour
of light required can be obtained by turning the disc containing glass
of different colours or the other having differently sized apertures, in
order to admit more or less light, or give the light any colour.
In both these arrangements the lamp is hung on the side of the
telescope, while Mr. Grubb prefers to hang it at the end of the
declination axis, as shown in Figs. 139 and 140.
The function of the lamp then is to illuminate the wires of the
micrometer eyepiece, of which more presently; but Mr. George Bidder
places the micrometer itself outside the tube of the telescope, the
light of a lamp being thrown on the wires.
This is done as follows:—On the same side of the wires as the lamp is a
convex lens and reflector so arranged that the rays from the wires are
reflected through a hole in the tube, and again down the tube to the
eyepiece, where the images of the wires are brought to a focus at the
same place as the stars to be measured, so that any eyepiece can be
used. The wires show as bright lines in the field, and they are worked
about in the field just as real wires might be by moving the wires
outside the tube. A sheet of metal can be moved in front of the
distance-wires so as to obstruct the light from them at any part of
their length, and their bright images appear then abruptly to terminate
in the field of view, so that faint stars can be brought up to the
terminations of the wires and be measured without being overcome by
bright lines.
-----
Footnote 16:
It is not too much to say that the duty on glass entirely stifled, if
indeed it did not kill, the optical art in England. We were so
dependent for many years upon France and Germany for our telescopes,
that the largest object-glasses at Greenwich, Oxford, and Cambridge
are all of foreign make.
Footnote 17:
These details are given from the _Forces of Nature_ (Macmillan).
CHAPTER XXI.
THE ADJUSTMENTS OF THE EQUATORIAL.
As the equatorial is _par excellence_ the amateur’s instrument, and as
in setting up an equatorial it is important that the several adjustments
should be correctly made, they are here dwelt upon as briefly as
possible. They are six in number.
1. The inclination of the polar axis must be the same as that of the
pole of the heavens.
2. The declination circle must read 0° when the telescope is at right
angles to the polar axis.
3. The polar axis must be placed in the meridian.
4. The optic axis of the telescope, or line of collimation must be at
right angles to the declination axis, so that it describes a great
circle on moving about that axis.
5. The declination axis must be at right angles to the polar axis, in
order that the telescope shall describe true meridians about that axis.
6. The hour circle must read 0h. 0m. 0sec. when the telescope is in the
meridian.
When these are correctly made the line of collimation will, on being
turned about the declination axis, describe great circles through the
pole, or meridians, and when moved about the polar axis, true parallels
of declination; and the circles will give the true readings of the
apparent declination, and hour angles from the meridian.
To make these adjustments, the telescope is set up by means of a compass
and protractor, or otherwise in an approximately correct position, the
declination circle put so as to read nearly 90° when the telescope
points to the pole, and the hour circle reading 0h. 0m. 0sec. when the
telescope is pointing south.
First, then, to find the error in _altitude_ of the polar axis.
Take any star from the Nautical Almanac of known declination on or near
the meridian, and put an eyepiece with cross wires in it in the
telescope, and bring the star to the centre of the field as shown by the
wires. Then read the declination circle, note the reading down and
correct it for atmospheric refraction, according to the altitude[18] of
the star by the table given in the Nautical Almanac, turn the telescope
on the polar axis round half a circle so that the telescope comes on the
other side of the pier. The telescope is then moved on its declination
axis until the same star is brought to the centre of the field, and the
circle read as before and corrected. The mean of the two readings is
then found, and this is the declination of the star as measured from the
equator of the instrument, and its difference from the true declination
given by the almanac is the error of the instrumental equator and of
course, also of the pole at right angles to it.
It is obvious that if the declination circle were already adjusted to
zero, when the telescope was pointing to the equator of the instrument,
one observation of declination would determine the error in question;
and it is to eliminate the _index error_ of the circle, as it is called,
that the two observations are taken in such a manner that the index
error increases one reading just as much as it decreases the other, so
that the mean is the true instrumental declination.
_Index Error._—From what has just been stated it follows that half the
difference of the two readings is the index error, which can be at once
corrected by the screws moving the vernier, giving correction No. 2.
To correct the error in altitude of the pole, the circle is then set to
the declination of the star given by the almanac, corrected for
refraction, and the telescope brought above or below the star as the
error may be, and the polar axis carrying the telescope is moved by the
setting screws, until the star is in the centre of the field.
3rd Adjustment.—A single observation of any known star, about 6 hours to
the east or west will give the error of the polar axis east and west,
the difference between the observed and true declination being this
error, and it can be corrected in the same manner as the last. These
observations should be repeated, and stars in different parts of the
heavens observed, in order to eliminate errors of division of the circle
until the necessary accuracy is obtained.
For example:
Observed dec. of Capella 43° 50´ 30˝ Telescope west.
47° 0´ 0˝ Telescope east.
——— ——— ———
2) 90° 50´ 30˝
——— ——— ———
45° 25´ 15˝ 47° 0´ 0˝
Error due to refraction 0° 0´ 7˝ 43° 50´ 30˝
——— ——— ——— ——— ——— ———
Instrumental declination 45° 25´ 8˝ 2) 3° 9´ 30˝
True declination 45° 52´ 0˝ ——— ——— ———
——— ——— ——— Index error 1° 34´ 45˝
26´ 52˝
This indicates that the pole of the instrument is pointing below the
true pole, and index error 1° 34´ 45˝.
Observed declination of Pollux 6h. west 28° 19´ 18˝
Refraction 0° 0´ 46˝
——— ——— ———
28° 18´ 3˝
True declination 28° 20´ 10˝
——— ——— ———
0° 1´ 38˝
This shows the pole to be 1´ 38˝ east of true pole.
4th Adjustment.—For the estimation and correction of the third error,
that of collimation, an equatorial star is brought to the centre of the
field of the telescope, the time by a clock noted, and the hour circle
read. The polar axis is then turned through half a circle, and the star
observed with the telescope on the opposite side (say the west) of the
pier, the time noted, and the hour circle read. Subtract the first
reading from the second (plus twenty-four hours if necessary) and
subtract the time elapsed between them, and the result should be exactly
twelve hours, and half the difference between it and twelve hours is the
error in question. If it is more than twelve hours the angle between the
object end of the telescope and the declination axis is acute, and if
less then it is obtuse. This error can then be corrected by the proper
screws. A little consideration will show, that if the angle between the
object end of the telescope and the declination axis be acute, and the
telescope is on the east side of the pier, and pointing to a star, say
on the meridian, the hour circle will not read so much as it would do if
the line perpendicular to the declination axis were pointing to the
meridian. When the telescope is on the wrest side of the pier, the
circle will read higher for the same reason, and therefore the
difference between the angle through which the hour circle is moved and
180° is equal to double the angle between the line perpendicular to the
declination axis and the collimation axis of the telescope; allowance
being made for the star’s motion.
For example γ Virginis, Dec. 0° 46´·5.
Time by clock. Hour circle reading.
11h. 23m. 52s. 11h. 55m. 30s. Telescope east.
11h. 31m. 55s. 24h. 8m. 24s. Telescope west.
———— ———— ———— ———— ———— ——————
8m. 3s. 12h. 12m. 54s.
8m. 3s.
———— ——————
2) 4m. 51s.
———— ——————
Collimation error at 2m. 25·5s.
dec. 46´·5
angle between object glass and declination axis acute.
If this error is not corrected, it must be added when the telescope is
on the east side of the pier, and subtracted when on the west.[19]
5th Adjustment.—Place a striding level on the pivots of the declination
axis and bring the bubble to zero by turning the polar axis; read off
the hour circle and note it; then reverse the declination axis east and
west and replace the level; bring the bubble to zero and again read the
circle. The readings should show the axis to be turned through half a
circle, and the difference shows the error.
If the second reading minus the first be more than half a circle or 12
hours, it shows that the pivot at the east at the first observation is
too high, and therefore in bringing the declination axis level, the
first reading of the hour circle is diminished from its proper amount
and increased on the axis being reversed.
To adjust the error, find half the difference of circle readings and
apply it, with the proper sign, to each of the two circle readings,
which will then differ by exactly twelve hours; bring the circles to
read one of the corrected readings and alter the declination axis until
the bubble of the level comes to zero. If the pivots of the declination
axis are not exposed, so that the level can be applied, the following
method must be adopted:—Fasten a small level on any part of the
declination axis or its belongings, say on the top of the counterpoise
weight; bring the axis apparently horizontal and the bubble to zero;
turn the telescope on the declination axis, so that by the turning of
the counterpoise the level comes below it; if then the bubble is at
zero, the axis of the level is parallel to the declination axis, and
both are horizontal, and if not it is clear that neither of these
conditions holds; therefore bring the bubble to zero by the two motions
of the level with reference to the counterpoise and the motion of the
declination axis on the polar axis, so that the error is equally
corrected between them; repeat the proceeding until the level is
parallel with the axis, when it will show when the axis is horizontal as
well as the striding level.
For example:—
Hour circle reading when } 11h. 57m. 57s. Telescope east.
declination axis is horizontal. } 23h. 59m. 47s. Telescope west.
———— ———— ————
12h. 1m. 50s.
Error 0h. 1m. 50s.
Or this error can be found and corrected without a level by taking two
observations of a star of large declination in the same manner as in
estimating the collimation error, for example:—
Η URSÆ MAJORIS.
Time by clock. Hour circle reading.
12h. 8m. 57s. 0h. 28m. 44s. Telescope east.
12h. 18m. 53s. 12h. 46m. 42s. Telescope west.
———— ———— ———— ———— ———— ————
9m. 56s. 12h. 17m. 58s.
9m. 56s.
———— ————
2) 8m. 2s.
———— ————
Error of hour circle due to error of 4m. 1s.
inclination of axes[20]
6th Adjustment.—Bring the declination axis to a horizontal position with
a level and set the hour circle to zero, or obtain the sidereal time
from the nearest observatory, or again find it from the solar time by
the tables, and correct it for the longitude of the place (subtracting
the longitude reduced to time when the place is west and adding when
east of the time-giving observatory) and set a clock or watch to it.
Take the time of transit of a known star near the meridian and then the
sidereal time by the clock at transit minus the right ascension of the
star will give the hour angle past the meridian, and its difference from
the circle reading is the index error, which is easily corrected by the
vernier. If the star is east of the meridian the time must be subtracted
from the right ascension to give the circle reading.
In the above examples we have assumed, for the sake of better
illustration, that the hour circle is divided into twenty-four hours,
but more usually they are divided into two halves of twelve hours each.
A movement through half a circle, therefore, brings the hour circle to
the same reading again instead of producing a difference of twelve
hours, as in the above example.
When the equatorial is once properly in adjustment, not only can the
co-ordinates of a celestial body be observed with accuracy when the time
is known, but a planet or other body can easily be found in the
day-time. The object is found by the two circles—the declination circle
and the hour or right-ascension circle. The declination of the required
object being given, the telescope is set by the circle to the proper
angle with the equator. The R.A. of the object is then subtracted from
the sidereal time, or that time plus twenty-four hours, which will give
the distance of the object from the meridian, and to this distance the
hour-circle is set. The object should then be in the field of the
telescope, or at least in that of the finder. We subtract the star’s
R.A. from the sidereal time because the clock shows the time since the
first point of Aries passed the meridian, and the star passes the
meridian later by just its R.A., so that if the time is 2_h._, or the
first point of Aries has passed 2_h._ ago, a star of 1_h._ R.A., or
transiting 1_h._ after that point, will have passed the meridian 2_h._ -
1_h._ = 1_h._ ago; so if we set the telescope 1_h._ west of the meridian
we shall find the star. The moment the object is found the telescope is
clamped in declination, and the clock thrown into gear, so that the star
may be followed and observed for any length of time.
-----
Footnote 18:
The altitude of the star in this case is its declination plus the
co-latitude of the place, but this only applies when the star is on
the meridian. When the altitude of a star in another situation is
required, it is found sufficiently accurately by means of a globe. A
sextant, if at hand, will of course give it at once.
Footnote 19:
Since the velocity of the star varies as the cosine of the
declination, the error of collimation at the equator = 2m. 25·5s. cos.
0° 45´·5 = 2m. 25·08s.; and for non-equatorial stars, 2m. 25·08s. sec.
dec.
Footnote 20:
This error varies as the tangent of the declination, and therefore to
find the constant for the instrument, in case the parts do not admit
of easy adjustment, we divide 4m. 1s. by 1·18 the tan. of Dec. of η
Ursæ Majoris, giving 3 min. 28 sec.
CHAPTER XXII.
THE EQUATORIAL OBSERVATORY.
We have now considered the mounting and adjustment of the equatorial, be
it reflector or refractor. If of large dimensions it will require a
special building to contain it, and this building must be so constructed
that, as in the case of the Melbourne and Paris instruments, it can be
wheeled away bodily to the north, leaving the instrument out in the
open; or the roof must be so arranged that the telescope can point
through an aperture in it when moved to any position. This requirement
entails (1) the removal of the roof altogether, by having it made nearly
flat, and sliding it bodily off the Observatory, or (2) the more usual
form of a revolving dome, with a slit down one side, or (3) the
Observatory maybe drum-shaped, and may run on rollers near the ground.
The last form is adopted for reflectors whose axis of motion is low; but
with refractors having their declination axis over six or seven feet
from the ground, the walls of the Observatory can be fixed, as the
telescope, when horizontal, points over the top. The roof, which may be
made of sheet-iron or of wood well braced together to prevent it
altering in shape, is built up on a strong ring which runs on wheels
placed a few feet apart round the circular wall, or, instead of wheels,
cannon balls may be used, rolling in a groove with a corresponding
groove resting on them. A small roof, if carefully made, may be pulled
round by a rope attached to any part of it, but large ones generally
have a toothed circle inside the one on which the roof is built, or this
circle itself is toothed, so that a pinion and hand-winch can gear into
it and wind it round. If the roof is conical in shape the aperture on
one side can be covered by two glazed doors, opening back like
folding-doors; but if it is dome-shaped, the shutter is made like a
Venetian blind or revolving shop-window shutter, and slides in grooves
on either side of the opening.
[Illustration:
FIG. 151.—Dome.
]
[Illustration:
FIG. 152.—Drum.
]
[Illustration:
FIG. 153.—New Cincinnati Observatory—Front elevation, showing exterior
of Drum.
]
[Illustration:
FIG. 154.—Cambridge (U.S.) Equatorial, showing Observing Chair and
rails.
]
The equatorial and the building to contain it have now been described,
but there is another piece of apparatus which is required as much as any
adjunct to the equatorial, and that is the chair or rest for the
observer. Since the telescope may be sometimes horizontal, and at other
times vertical, the observer must be at one time in an upright position,
and at another lying down and looking straight up. A rest is required
which will carry the observer in these or in intermediate positions. A
convenient form of rest for small telescopes consists of a seat like
that of a chair, with a support moving on hinges at the back of the
seat; a rack motion fixes this at any inclination, so that the
observer’s back can be sustained in any position, between upright and
nearly horizontal. The seat with its back slides on two straight bars of
wood, sloping upwards from near the ground at an angle of about 30°, and
about 8ft. long; these are supported at their upper ends by uprights of
wood, and at their lower ends in the same manner by shorter pieces.
These four uprights are firmly braced together, and have castors at the
bottom. A rack is cut on one of the inclined slides, and a catch falls
into it, so as to fix the seat at any height to which it is placed.
In larger observatories a more elaborate arrangement is adopted, the
rails, on which the seat moves, are curved to form part of a circle,
having the centre of motion of the telescope for its centre; as the seat
with its back is moved up or down on the curved slides, its inclination
is changed, so that the observer is always in a favourable position for
observing. The seat on its frame runs on circular rails round the pier
of the telescope, so that the eyepiece can be followed round as the
telescope moves in following a star. A winch by the side of the
observer, acting on teeth on one of the rails, enables him to move the
chair along, and a similar arrangement enables him to raise or lower the
seat on the slides without removing from his place. A steady mounting
for the telescope, and a comfortable seat for the observer, are the two
things without which a telescope is almost useless.
The observing chair is well seen in the engravings of Mr. Newall’s and
the Cambridge telescopes. The eyepieces and micrometer can be carried on
the rest, close to the observer, when much trouble is saved in moving
about for things in the dark; and for the same reason there should be a
place for everything in the observatory, and everything in its place.
[Illustration:
FIG. 155.—Section of Main Building—United States Naval Observatory,
showing support of Equatorial.
]
The very high magnifying power employed upon equatorials in the finest
states of the air necessitates a very firm foundation for the central
pillar. The best position for such an instrument is on the ground, but
it is almost always necessary to make them high in order to be able to
sweep the whole horizon. The accompanying woodcut will give an idea of
the precautions that have to be taken under these circumstances. A solid
pillar must be carried up from a concrete foundation, and there must be
no contact between this and the walls or floors of the building, when
the dome thus occupies the centre of the observatory. The other rooms,
generally built adjoining the equatorial room, radiate from the dome,
east and west, not sufficiently high to interfere with the outlook of
the equatorial. In one of these the transit is placed; an opening is
made in the walls and roof, so that it has an unimpeded view when swung
from north through the zenith to south, and this is closed when the
instrument is not in use by shutters similar to those of the dome.
CHAPTER XXIII.
THE SIDEROSTAT.
At one of the very earliest meetings of the Royal Society, the
difficulties of mounting the long focus lenses of Huyghens being under
discussion, Hooke pointed out that all difficulties would be done away
with if instead of giving movement to the huge telescope itself, a plane
mirror were made to move in front of it. This idea has taken two
centuries to bear fruit, and now all acknowledge its excellence.
One of the most recent additions to astronomical tools is the
Siderostat, the name given to the instrument suggested by Hooke. By its
means we can make the sun or stars remain virtually fixed in a
horizontal telescope fixed in the plane of the meridian to the south of
the instrument, instead of requiring the usual ponderous mounting for
keeping a star in the field of view.
It consists of a mirror driven by clockwork so as to continually reflect
the beam of light coming from a star, or other celestial object, in the
same direction; the principle consisting in so moving the mirror that
its normal shall always bisect the angle subtended at the mirror by the
object and the telescope or other apparatus on which the object is
reflected.
[Illustration:
FIG. 156.—Foucault’s Siderostat.
]
It was Foucault who, towards the end of his life, thought of the immense
use of an instrument of this kind as a substitute for the motion of
equatorials; he, however, unfortunately did not live to see his ideas
realized, but the Commission for the purpose of carrying out the
publication of the works of Foucault directed Mr. Eichens to construct a
siderostat, and this one was presented to the Academy of Science on
December 13th, 1869, and is now at the Paris Observatory. Since that
date others have been produced, and they have every chance of coming
largely into use, especially in physical astronomy. Fig. 156 shows the
elevation of the instrument, the mirror of which, in the case of the
instrument at Paris, is thirty centimetres in diameter, and is supported
by a horizontal axis upon two uprights, which are capable of revolving
freely upon their base. The back of the mounting of the mirror has an
extension in the form of a rod at right angles to it, by which it is
connected with the clock, which moves the mirror through the medium of a
fork jointed at the bottom of the polar axis.
The length of the fork is exactly equal to the distance from the
horizontal axis of the mirror to the axis of the joint of the fork to
the polar axis, and the direction of the line joining these two points
is the direction in which the reflected ray is required to proceed. The
fork is moved on its joint to such a position that its axis points to
the object to be viewed, and, being carried by a polar axis, it remains
pointing to that object as long as the clock drives it, in the same
manner as a telescope would do on the same mounting. Then, since the
distance from the axis of the mirror to the joint of the fork is equal
to the distance from the latter point to the axis of its joint to the
sliding tube on the directing rod, an isosceles triangle is formed
having the directing rod at its base; the angles at the base are
therefore equal to each other.
Further, if we imagine a line drawn in continuation of the axis of the
fork towards the object, then the angle made by this line and that from
the axis of the mirror to the elbow joint of the fork (the direction of
the reflected ray) will be equal to the two angles at the base of the
isosceles triangle; and, since they are equal to each other, the angle
made by the directing rod and the axis of the fork (or the incident ray)
from the object, is equal to half the angle made by the latter ray and
the direction of the reflected ray; and if lines are drawn through the
surface of the mirror in continuation of the directing rod and the line
from the elbow joint to the axis of the mirror; and a line to the point
of intersection be drawn from the object, this last line will be
parallel to the axis of the fork, and the angle it makes with the
continuation of the directing rod, or normal to the surface of the
mirror, will be half the angle made by it and the line representing the
reflected ray. Therefore the angle made by the incident ray and the
required direction of the reflected ray is always bisected by the
normal, so that the reflected ray is constant in the required direction.
The clock is driven in the usual manner by a weight. A rod carries the
motion up to the system of wheels by which the polar axis is rotated. As
this axis rotates it carries with it the fork, which transmits the
required motion to the mirror. And as the fork alters its direction the
tube slides upon the directing rod, thus altering the inclination of the
mirror. In order to vary the position of the mirror without stopping the
instrument there are slow motion rods or cords proceeding from the
instrument which may be carried to any distance desirable.
[Illustration:
FIG. 157.—The Siderostat at Lord Lindsay’s Observatory.
]
The polar axis is set in the meridian similarly to an equatorial
telescope, the whole apparatus being firmly mounted upon a massive stone
pillar which is set several feet in the ground, and rests upon a bed of
concrete, if the soil is light. A house upon wheels, running upon a
tramway, is used to protect the instrument from the weather, and when in
use this hut is run back to the north, leaving the siderostat exposed.
In the north wall of the observatory is a window, and the telescope is
mounted horizontally opposite to it: so the observer can seat himself
comfortably at his work, and by his guide rods direct the mirror of the
siderostat to almost any part of the sky, viewing any object in the
eyepiece of his telescope without altering his position. In spectroscopy
and celestial photography its use is of immense importance, for in these
researches the image of an object is required to be kept steadily on the
slit of the spectroscope or on the photographic plate, and for this
purpose a very strongly-made and accurate clock is required to drive the
telescope and mounting, which are necessarily made heavy and massive to
prevent flexure and vibration. The siderostat, on the other hand, is
extremely light, without tube or accessories, and a light, delicate
clock is able to drive it with accuracy, while the heavy telescope and
its adjuncts are at rest in one position. The sun and stars can,
therefore, as it were, be “laid on” to the observer’s study to be viewed
without the shifting of the observatory roof and equatorial, or of the
observing chair, which brings its occupant sometimes into most uneasy
positions.
We figure to ourselves the future of the physical observatory in the
shape of an ordinary room with siderostat outside throwing sunlight or
rays from whatever object we wash into any fixed instrument at the
pleasure of the observer. There are, however, inconveniences attending
its use in some cases; for instance, in measuring the position of double
stars, the diurnal motion gradually changes their position in the field
of the telescope, so that a new zero must be constantly taken or else
the time of observation noted and the necessary corrections made.
CHAPTER XXIV.
THE ORDINARY WORK OF THE EQUATORIAL.
The equatorial enables us to make not only physical observations, but
differential observations of the most absolute accuracy.
First we may touch upon the physical observations made with the eyepiece
alone—star-gazing, in fact. The Sun first claims our attention: our
dependence on him for the light of day, for heat, and for in fact almost
everything we enjoy, urges us to inquire into the physics of this
magnificent object. Precautions must however be taken; more than one
observer has already been blinded by the intense light and heat, and
some solar eyepiece must be used. For small telescopes up to two inches,
a dark glass placed between the eye and the eyepiece is sufficiently
safe; for larger apertures, the diagonal reflector, or Dawes’ solar
eyepiece, already described, comes into requisition. Another method of
viewing the sun is to focus the sun’s image with the ordinary eyepiece
on a sheet of paper or card, or, better still, on a surface of plaster
of Paris carefully smoothed. The bright ridges or streaks, usually seen
in spotted regions near the edge, called the faculæ, and the mottled
surface, appearing, according to Nasmyth, like a number of interlacing
willow-leaves—the minute “granules” of Dawes, are best seen with a blue
glass; but for observing the delicately-tinted veils in the umbræ of the
spots a glass of neutral tint should be used.
The Moon is a fine object even in small telescopes. The best observing
time is near the quarters, as near full moon the sun shines on the
surface so nearly in the same direction as that in which we look, that
there is no light and shade to throw objects into view. Hours may be
spent in examining the craters, rilles, and valleys on the surface,
accompanied with a good descriptive map or such a book as that which Mr.
Neison has recently published.
The planets also come in for their share of examination. Mercury is so
near the sun as seldom to be seen. Venus in small telescopes is only
interesting with reference to her changes, like the moon, but in larger
ones with great care the spots are visible. Mars is interesting as being
so near a counterpart of our own planet. On it we see the polar snows,
continents and seas, partially obscured by clouds, and these appearances
are brought under our view in succession by the rotation of the planet.
With a good six-inch glass and a power of 200 when the air is pure and
the opposition is favourable, there is no difficulty in making out the
coast-lines, and the various tones of shade on the water surface may be
observed, showing that here the sea is tranquil, and there it is driven
by storms. Up to very lately it was the only planet of considerable size
further off the sun than Venus that was supposed to have no satellite;
two of these bodies have however been lately discovered by Hall with the
large Washington refractor of twenty-six inches diameter, and they
appear to be the tiniest celestial bodies known, one of them in all
probability not exceeding 10 miles in diameter. Jupiter and Saturn are
very conspicuous objects, and the eclipses, transits, and occultations
of the moons, and the belts of the former and rings of the latter, are
among the most interesting phenomena revealed to us by our telescopes,
while the delicate markings on the third satellite of Jupiter furnish us
with one of the most difficult tests of definition. Uranus and Neptune
are only just seen in small telescopes, and even in spite of the use of
larger ones, we are in ignorance of much relating to these planets. The
amateur will do well to attack all these with that charming book, the
Rev. T. W. Webb’s _Celestial Objects for Common Telescopes_, in his
hand.
To observe the fainter satellites of the brighter planets, or, indeed,
faint objects generally, near very bright ones, the bright object may be
screened by a metallic bar, or red or blue glass placed in the common
focus.
So much with regard to our own system. When we leave it we are
confounded with the wealth of nebulæ, star-clusters, and single or
multiple systems of stars, which await our scrutiny. With the stars, not
much can be done without further assistance than the eyepiece alone. The
colours of stars may however be observed, and for this purpose a
chromatic scale has been proposed, and a memoir thereon written, by
Admiral Smyth, for comparison with the stars. The colour of a star must
not be confused with the colours—often very vivid—produced by
scintillations, these rapid changes of brightness and colour depending
on atmospheric causes. Of the large stars, Sirius, Vega and Regulus are
white, while Aldebaran and Betelgueux are red. In many double and
multiple stars however the contrast of colours shows up beautifully; in
β Cygni for instance we have a yellow and blue star, in γ Leonis, a
yellow and a green star; and of such there are numerous examples.
Interesting as all these observations are, a new life and utility are
thrown into them when instead of using a simple eyepiece the wire
micrometer is introduced. This, as we have before stated, generally
consists of one wire, or two parallel wires, fixed, and one or two other
wires at right angles to these, movable across the field. This
micrometer is used in connection with a part of the eyepiece end of the
telescope, which has now to be described. This is a circle, the fineness
of the graduation of which increases with the size of the telescope,
read by two or four verniers. The circle is fixed to the telescope,
while the verniers are attached to the eyepiece, carrying the
micrometer, which is rotated by a rack and pinion.
The whole system of position circle (as it is called) and wire
micrometer, is in adjustment when (1) the single or double fixed wires
and the movable ones cross in the centre of the field, and (2) when with
a star travelling along the single fixed or between the two fixed wires,
the upper vernier reads 180 and the lower one reads zero.
This motion across the field gives the direction of a parallel of
declination; that is to say, it gives a line parallel to the celestial
equator, and, knowing that, one will be able at once, by allowing the
object to pass through the field of view, to get this datum line. For
instance, supposing the whole instrument is turned round on the end of
the telescope, so that one of the two wires _x_ and _y_, Fig. 104, at
right angles to the thin wires for measuring distance, shall lie on a
star during all its motion across the field of view; then those two
wires, being parallel to the star’s motion, will represent two parallels
of declination; and we use the direction of the parallels of declination
to determine the datum point at right angles to them, that is, the north
point of the field. We have then a _position micrometer_, that is, one
in which the field of view is divided into four quadrants, called north
preceding, north following, south preceding, and south following,
because if there be an object at the central point it will be preceded
and followed by those in the various quadrants. The movable wires lie on
meridians and the fixed ones on parallels when adjusted as above.
[Illustration:
FIG. 158.—Position Circle.
]
The position circle is often attached to, and forms part of, the
micrometer instead of being fixed to the telescope, and in screwing it
on from time to time, the adjustment of the zero changes, and the index
error must be found each time the micrometer is put on the telescope.
In practice it is usual to take the north and south line as the datum
line, and positions are always expressed in degrees from the north round
by east 90°, south 180°, and west 270°, to north again in the direction
contrary to that of the hands of a clock.
The angle from the east and west line being found by the micrometer, 90°
is either added or subtracted, to give the angular measurement from
north. But to make these measurements we want a clock; a clock which,
when we have got one of these objects in the middle of the field of
view, shall keep it there, and enable the telescope to keep any object
that we may wish to observe fixed absolutely in the field of view. But
in the case of faint objects this is not enough. We want not only to see
the object, but also the wires we have referred to. Now then the
illuminating-lamp and bright wires, if necessary, come into use.
The following, Fig. 159, will show how we proceed if we merely wish to
measure a distance, the value of the divisions of the micrometer screw
having been previously determined by allowing an equatorial star to
transit. It represents the position of the central and the movable wire
when the shadow thrown by the central hill of the the lunar crater
Copernicus is being measured to determine the height of the hill above
the floor of the crater. It has been necessary to let the fixed wire lie
along the shadow; this has been done by turning the micrometer; but
there is no occasion to read the vernier.
[Illustration:
FIG. 159.—How the Length of a Shadow thrown by a Lunar Hill is
measured.
]
Except on the finest of nights the stars shake in the field of view or
appear woolly, and even on good nights the readings made by a practised
eye often differ, _inter se_, more than would be thought possible. In
measuring distances we have supposed for simplicity that we find the
distance that one wire has to be moved from coincidence with the fixed
wire from one point to another, and theoretically speaking the pointer
should point to O on the screw head when the wires are over each other,
and then when the wires are on the points, the reading of the screw head
divided by the number of divisions corresponding to 1˝ will give the
distance of the points in seconds of arc. But in practice it is
unnecessary to adjust the head to O when the wires coincide, and the
unequal expansion of the metals of the instrument, due to changes of
temperature, would soon disarrange it. It is also somewhat difficult to
say when the wires exactly coincide, and an error in this will affect
the distance between the points. It is therefore found best to only
roughly adjust the screw head to O, and then open out the wires until
they are on the points and take a reading, say twenty-two; the screw is
then turned, in the opposite direction and the movable wire passed over
to the other side of the fixed one, and another reading taken, say
eighty-two; now the screw has to be moved in the direction which
decreases the readings on its head from one hundred downwards, as the
distance of the wires increases, so that we must subtract the reading
eighty-two from a hundred to give the number of divisions from the O
through which the screw is turned, and the reading in this direction we
will call the indirect reading, in contradistinction to the direct
reading taken at first. So far we have got a reading of twenty-two
direct and eighteen indirect, which means that we have moved the screw
from twenty-two on one side of O to eighteen on the other side, or
through forty divisions, and in doing so the movable wire has been moved
from the distance of the two points on one side of the fixed wire to the
same distance on the other, or through double the distance required.
Therefore forty divisions is the measure of twice the distance, and the
half of forty, or twenty divisions, is the measure of the distance
itself between the two points to which our attention has been directed,
whether stars, craters in the moon, spots on the sun, and the like.
Let us consider what is gained by this method over a measure taken by
coincidence of the wires as a starting-point, and opening out the wires
until they cut the points. In the method we have just described there
are two chances of error in taking the measurements—the direct and
indirect; but the result obtained is divided by two, so that the error
is also halved in the final result. Now by taking the coincidence of the
wires as the zero, or starting-point, the measure is open to two errors,
as in the last case—the error of measurement of the points, _plus_ the
error of coincidence of wires, an error often of considerable amount,
especially as the warmth of the face and breath causes considerable
alteration in the parts of the instrument, making a new reading of
coincidence necessary at each reading of distance. As the result is not
divided by two, as in the first case, the two errors remain undivided,
so we may say that there is the half of two errors in one case and two
whole errors in the other.
Here then we use the micrometer to measure distances; but from a very
short acquaintance with the work of an equatorial it will at once be
seen that one wants to do something else besides measure distances. For
instance, if we take the case of the planet Saturn, it would be an
object of interest to us to determine how many turns, or parts of a
turn, of the screw will give the exact diameter of the different rings;
but we might want to know the exact angle made by the axis with the
direction of the planet’s motion, across the field, or with, the north
and south line.
If we have first got the reading when the wires are in a parallel of
declination, and then bring Saturn back again to the middle of the field
and alter the direction of the wires until they are parallel to the
major axis of the ring, we can read off the position on the circle, and
on subtracting the first reading from this, we get the angle through
which we have moved the wires, made by the direction of the ring with
the parallel of declination, which is the angle required. We are thus
not only able to determine the various measurements of the diameter of
the outer ring by one edge of the ring falling on one of the fine wires,
and the other edge on the other wire, but, by the position circle
outside the micrometer we can determine exactly how far we have moved
that system, and thus the angle formed by the axis of the ring of the
planet at that particular time.
[Illustration:
FIG. 160.—The Determination of the Angle of Position of the axis of
Saturn’s Ring.
]
The uses of the position micrometer as it is called are very various. In
examination of the sun it is used to ascertain the position of spots on
the surface, and the rate of their motion and change. The lunar craters
require mapping, and their distances and bearing from certain fixed
points measuring, for this then the position micrometer comes into use.
The varying diameters and the inclinations of the axes of the planets
and the periods of revolution of the satellites are determined, and the
position of their orbits fixed, in like manner. When a comet appears it
is of importance to determine not only the direction of its motion among
the stars, but the position of its axis of figure, and the angles of
position and dimensions of its jets. The following diagram gives an
example of the manner in which the position of its axis of figure is
determined. First the nucleus is made to run along the fixed wire, so
that it may be seen that the north vernier truly reads zero under this
condition; if it does not its index error is noted. The system of wires
is then rotated till one of the wires passes through the nucleus and
fairly bisects the dark part behind the nucleus.
[Illustration:
FIG. 161.—Measurement of the Angle of Position of the Axis of Figure
of a Comet, _a a_, positions of fixed wire when the north vernier is
at zero; _d d_ position of movable wire under like conditions; _a´
a´_, _d´ d´_, positions of these wires which enable the angle of
position of the comet’s axis to be measured. The angle _a a´_ or _d
d´_ is the angle required.
]
It need scarcely be said that these observations are also of importance
with reference to the motion of the binary stars, those compound bodies,
those suns revolving round each other, the discovery of which we owe to
the elder Herschel. We may thus have two stars a small distance apart;
at another time we may have them closer still; and at another we may
have them gradually separating, with their relative position completely
changed. By means of the wire micrometer and the arrangement for turning
the system of wires into different positions with regard to the parallel
of declination, we have a means of determining the positions occupied by
the binary stars in all parts of their apparent orbit, as well as their
distances in seconds of arc. It is found, however, by experience that
the errors of observation made in estimating distances are so large,
relatively to the very small quantities measured, that it is absolutely
necessary to make the determination of the orbit depend chiefly on the
positions. And this is done in the following way.
[Illustration:
FIG. 162.—Double Star Measurement, _a a_, _b b_, first position of
fixed, double wire when the vernier reads 0°, and the star runs
between the wires; _c c_, _d d_, first position of movable wires.
_a´ a´_, _b´ b´_, new position of fixed double wire which determines
the angle of position; _c´ c´_, _d´ d´_, new positions of the
movable wires which measure the distance.
]
It is possible, by knowing the position angles at different dates, to
find the angular velocity, and since the areas described by the radius
vector are equal in equal times, the length of the radius vector must
vary inversely as the square root of the angular velocity, and by taking
a number of positions on the orbit of known angular velocity, we can set
off radii vectores, and construct an ellipse, or part of one, by drawing
a curve through the ends of the radii vectores; and from the part of the
ellipse so constructed it is possible to make a good guess at the
remainder. The angular size of this ellipse is obtained from the average
of all the measures of distance of the stars. This ellipse is then the
apparent ellipse described by the star, and the form and position of the
true ellipse can be constructed from it from the consideration of the
position of the larger star (which must _really_ be the focus), with
reference to the focus of the _apparent_ ellipse; for if an ellipse be
seen or projected on a plane other than its own, its real foci will no
longer coincide with the foci of the projected ellipse.
The methods adopted in practice, for which we must refer the reader to
other works on the subject, are, however, much more laborious and
lengthy than the above outline, which is intended merely to show the
possibility, or the faint outline of a method of constructing the real
ellipse. When the real ellipse or orbit is known, it is then of course
possible to predict the relative positions of the two components. Let us
consider in some little detail the actual work of measuring a double
star.
A useful form for entering observations upon, as taken, is the
following, which is copied from one actually used.
TEMPLE OBSERVATORY.
No. 1. _April 12, 1875·276._
DOUBLE STARS.
STRUVE 1338.
R.A.—9h. 13m. 28s. DECL. 38° 41´ 20˝.
Magnitudes—6·7, 7·2.
POSITION.
Zero, 109·8.
[Illustration]
DISTANCE.
Direct. Indirect. ½ Diff.
17 97 10
16 97 9·5
———————
9·75 mean.
Readings.
170·1
170·
169·5
169·8
—————
4) 679·4
—————
169·8
109·8
90·0
—————
19·8
169·8 Position = 150°
19·8
————— Distance = 1˝·828.
150
* * * * *
No. 2. _Feb. 5th, 1875·09._
DOUBLE STARS.
STRUVE 577.
R. A.—4h. 34m. 9s. DECL. 37° 17´
Magnitudes—7, 8.
POSITION.
Zero, 88·9.
[Illustration]
DISTANCE.
Direct. Indirect. ½ Diff.
12·5 99·5 6·5
12·6 99·2 6·7
———————
6·6 mean.
Readings.
79·5
81·5
81·2
—————
3) 242·2
—————
81·1 mean.
88·9
90·0
—————
-1·1
81·1
-1·1
—————
82·2 Position = 262°·2.
180·0
————— Distance = 1´·237.
262·2
The star having been found, the date and decimal of the year are entered
at the top, and a position taken by bringing the thick wires parallel to
the stars. A distance—say direct—is then taken, and the degrees of
position 170°·1, and divisions of the micrometer screw seventeen, read
off with the assistance of a lamp and entered in their proper columns.
The micrometer is then disarranged and a new measure of position and an
indirect distance taken, and so on. At the end of the readings, or at
any convenient time, the zero for position is found by turning the
micrometer until the wires are approximately horizontal, and then
allowing a star to traverse the field by its own motion, or rather that
of the earth, and bringing the thick wires parallel to its direction of
motion; this may be more conveniently done by means of the slow-motion
handle of the telescope in R. A., which gives one the power of
apparently making the star traverse backwards and forwards in the field.
The position of the wires is altered until the star runs along one of
them. The position is then read off and entered as the zero. In
describing the adjustments of the position circle we made the vernier
read 0° when the star runs along the wire, for that is practically the
only datum line attainable; since, however, the angles are reckoned from
the north, it is convenient to set the circle to read 90° when the star
runs along the wire, so that it reads 0° when the wires are north and
south.
Now as positions are measured from north 0° in a direction contrary to
that of the hands of a watch, and an astronomical telescope inverts, we
repeat the bottom of the field is 0°, the right 90°, and so on; now the
reading just taken for zero is the reading when the wires are E. and W.,
so that we must deduct 90° from this reading, giving 19°·8 as the
reading of the circle when the wires were north and south, or in the
position of the real zero of the field. Of course theoretically the
micrometer ought to read 0° when the wires are north and south, but in
screwing on the instrument from night to night it never comes exactly to
the same place, so that it is found easier to make the requisite
correction for index error rather than alter the eye end of the
telescope to adjustment every night. The readings of position must
therefore be corrected by the number of degrees noted when the wires are
at the real zero, which in the case in point is 19°·8, which may be
called the index error.
It is also obvious that the micrometer may be turned through 180° and
still have its wires parallel to any particular line. The position of
the stars also depends upon the star fixed on for the centre round which
our degrees are counted; for in the case of two stars just one over the
other in the field of view, if we take the upper one as centre, then the
position of the system is 0°, but if the lower one, then it is 180°; in
the case of two equal or nearly equal stars, it is difficult to say
which shall be considered as centre, and so the position given by two
different persons might differ by 180°. There are also generally two
verniers on the position circle, one on each side, and these of course
give readings 180° different from each other, so that 180° has often to
be added or subtracted from the calculated result to give the true
position. All that is really measured by the position micrometer is the
relative position of the line joining the stars with the N. and S. line.
In order, therefore, to find, whether 180° should be added or not, a
circle is printed on the form, with two bars across for a guide to the
eye, and the stars as seen are roughly dotted down in their apparent
position—in the case in point about 150°. Our readings being now made,
we first take a mean of those of position, which is 169°·8, nearly, and
the zero is 109°·8; deduct 90° from this to give the reading of the N.
and S. line 19°·8, then we deduct this from the mean of position, 169·8,
giving us 150° as the position angle of the stars.
It often happens that the observed zero is less than 90°, and then we
must add 360° to it before subtracting the 90°, or what is perhaps best,
subtract the observed zero from 90°, and treat the result as a minus
quantity, and therefore add it to the mean of position readings instead
of subtracting as usual. The observations of the second star give a case
in point: the zero is 88°·9, and subtracting this from 90°, we get 1°·1;
we put this down as -1°·1 to distinguish it from a result when 90° is
subtracted from the zero; it is then added to the mean of position
readings 81°·1, giving 82°·2, but on reference to the dots showing the
approximate position of the stars, it is seen that 180° must be added to
their result, giving 262°·2 as the position of the stars.
Now as to distance, take the case of the second star. Subtract the first
indirect reading from 100°, giving 0·5, and add this to the direct
reading, 12·5, making 13·0, which is the difference between the two
readings taken on either side of the fixed wire; the half of this, 6·5,
is placed in the next column, and the same process is repeated with the
next two readings: a mean of these is then taken, which is 6·6 for the
number of divisions corresponding to the distance of the stars. In the
micrometer used in this case, 5·3 divisions go to 1˝, so that 6·6 is
divided by 5·3, giving 1˝·237 as the distance. A table showing the value
in seconds of the divisions from one to twenty or more, saves much time
in making distance calculations; the following is the commencement of a
table of this kind where 5·3 divisions correspond to 1˝.
┌──────┬─────┬────┬────┬────┬────┬────┬────┬────┬────┬────┐
│Divi- │ 0 │ ·1 │ ·2 │ ·3 │ ·4 │ ·5 │ ·6 │ ·7 │ ·8 │ ·9 │
│sions │ │ │ │ │ │ │ │ │ │ │
│ of │ │ │ │ │ │ │ │ │ │ │
│micro-│ │ │ │ │ │ │ │ │ │ │
│meter.│ │ │ │ │ │ │ │ │ │ │
├──────┼─────┼────┼────┼────┼────┼────┼────┼────┼────┼────┤
│ 0 │0·000│·018│·037│·056│·075│·093│·112│·131│·150│·168│
├──────┼─────┼────┼────┼────┼────┼────┼────┼────┼────┼────┤
│ 1 │0·187│·205│·224│·243│·262│·280│·299│·318│·337│·356│
├──────┼─────┼────┼────┼────┼────┼────┼────┼────┼────┼────┤
│ 2 │0·375│·393│·412│·431│·450│·468│·487│·506│·525│·543│
└──────┴─────┴────┴────┴────┴────┴────┴────┴────┴────┴────┘
In the first column are the divisions, and in the top horizontal line
the parts of a division, and the number indicated by any two figures
consulted is the corresponding number of seconds of arc. In the case of
a half difference of 2·3 we look along the line commencing at 2 until we
get under 3, when we get 0˝·431 as the seconds corresponding to 2·3
divisions.
It is necessary to adjust the quantity of light from the lamp in the
field, so that the wires are sufficiently visible while the stars are
not put out by too much illumination; for the majority of stars a red
glass before the lamp is best. This gives a field of view which renders
the wires visible without masking the stars, but a green or blue light
is sometimes very serviceable. A shaded lamp should be used for reading
the circles on the micrometer, so as not to injure the sensitiveness of
the eye by diffused light in the observatory. A lamp fixed to the
telescope, having its light reflected on the circles, but otherwise
covered up, is a great advantage over the hand-lamp. In very faint
stars, which are masked by a light in the field sufficient to see the
wires, the wires can be illuminated in the same manner as in the
transit, but there is this disadvantage—the fine wires appear much
thickened by irradiation, so that distances, especially of close stars,
become difficult to take.
* * * * *
We come now to the differential observations made with the equatorial.
Let us explain what is meant. Suppose it is desired to determine with
the utmost accuracy the position of a new comet in the sky. If we take
an ordinary equatorial, or an extraordinary equatorial (excepting
probably the fine equatorial at Greenwich), and try to determine its
place by means of the circles, its distance from the meridian giving its
right ascension and its distance from the equator giving its
declination, we shall be several seconds out, on account of want of
rigidity of its parts; but if we do it by means of such an instrument as
the transit circle at Greenwich, we wait till the comet is exactly on
the meridian, and determine its position in the way already described.
As a matter of fact, however, the transit circle is not the instrument
usually used for this purpose, but the equatorial. We do not however
just bring the comet or other object into the middle of the field and
then read off the circles, but we differentiate from the positions of
known stars; so that all that has to be done in order to get as perfect
a place for the comet as can be got for it by waiting till it comes to
the meridian—which perhaps it will do in the day-time, when it will not
be visible at all—is to determine its distance in right ascension and
declination from a known star, by means of a micrometer. Of course one
will choose the brightest part of the comet and a well-known star, the
place of which has been determined either by its appearance in one of
the catalogues, or by special transit observations made in that behalf.
We then by the position micrometer determine its angle of position and
distance from the known star at a time carefully noted, or we measure
the difference in right ascension and the difference in declination.
[Illustration:
FIG. 163.—Ring Micrometer.
]
Continental astronomers have another way of doing this which we will
attempt to explain. Suppose we wish to find the difference in
declination of a star and Jupiter, we place the ring, A D, Fig. 163, in
the eyepiece of the telescope and watch the passage of Jupiter and the
star over this ring micrometer. It will be clear that, as the motion of
the heavens is perfectly uniform, it will take very much less time for
the star to travel over the ring from B to C than it will for Jupiter to
travel over the ring from _b_ to _c_, because the star is further from
the centre; and by taking the time of external and internal contact at
each side of the ring, the details of which we need not enter upon here,
the Continental astronomers are in the habit of making differential
observations of the minutest accuracy by means of this ring micrometer,
whilst we prefer to make them by the wire micrometer.
BOOK VI.
_ASTRONOMICAL PHYSICS._