ON THE METHOD OF GRINDING AND POLISHING OPTICAL LENSES AND SPECULA.
I originally intended to enter into particular details on this subject,
for the purpose of gratifying those mechanics and others who wish
to amuse themselves by constructing telescopes and other optical
instruments for their own use; but, having dwelt so long on the subject
of telescopes, in the preceding pages, I am constrained to confine
myself to a very general sketch.
1. _To grind and polish lenses for eye-glasses, microscopes, &c._
First provide an upright spindle, at the bottom of which a pulley is
fixed, which must be turned by a wheel by means of a cord and handle.
At the top of the spindle make a screw the same as a lathe-spindle, on
which you may screw chocks of different sizes, to which the brass tool
in which the lens is to be ground, may be fixed. Having fixed upon the
breadth and focal length of the lens, and whether it is to be a plano,
or a double convex--take a piece of tin-plate or sheet copper, and,
with a pair of compasses, draw an arch upon its surface, near one of
its extremities, with a radius equal to the focal distance of the lens,
if intended to be double convex, or with half that distance, if it is
to be plano-convex. Remove with a file that part of the copper which
is without the circular arch, and then a _convex_ gage is formed. With
the same radius strike another arch, and having removed that part of
the copper which is _within_ it, a _concave_ gage will be obtained. The
brass tool, in which the glass is to be ground, is then to be fixed
upon a turning-lathe, and turned into a portion of a concave sphere,
so as to correspond to the convex gage. In order to obtain an accurate
figure to the concave tool, a convex tool of exactly the same radius
is generally formed, and they are ground one upon another with flour
emery; and when they exactly coincide, they are fit for use. The convex
tool will serve for grinding _concave_ glasses of the same radius--and
it should be occasionally ground in the concave tool to prevent it from
altering its figure.
The next thing to be attended to is, to prepare the piece of glass
which is to be ground, by chipping it in a circular shape, by means
of a large pair of scissors, and removing the roughness from its
edges by a common grind-stone. The faces of the glass near the edges
should likewise be ground on the grind-stone, till they nearly fit
the concave gage, by which the labour of grinding in the tool will be
considerably saved. The next thing required is to prepare the emery for
grinding, which is done in the following manner. Provide four or five
clean earthen vessels; fill one of them with water, and put into it a
pound or half a pound of fine emery, and stir it about with a stick;
after which let it stand 3 or 4 seconds, and then pour it into another
vessel, which may stand about 10 seconds; then pour it off again into
the several vessels till the water is quite clear; and by this means,
emery of different degrees of fineness is obtained, which must be kept
separate from each other, and worked in their proper order, beginning
at the first, and working off all the marks of the grind-stone; then
take of the second, next of the third, &c.,--holding the glass upon
the pan or tool with a light hand, when it comes to be nearly fit
for polishing. The glass in this operation should be cemented to a
wooden handle, by means of pitch or other strong cement. After the
finest emery has been used, the roughness which remains may be taken
away, and a slight polish given by grinding the glass with pounded
pumice-stone. Before proceeding to the polishing, the glass should be
ground as smooth as possible, and all the scratches erased, otherwise
the polishing will become a tedious process. The polishing is performed
as follows: Tie a piece of linen rag or of fine cloth about the tool,
and with fine putty, (calcined tin), or colcothar of vitriol (a very
fine powder, sometimes called the red oxide of iron) moistened with
water, continue the grinding motion, and in a short time there will be
an excellent polish.
In order to grind lenses very accurately for the finest optical
purposes, particularly object-glasses for telescopes--the concave tool
is firmly fixed to a table or bench, and the glass wrought upon it by
the hand with circular strokes so that its centre may never go beyond
the edges of the tool. For every 6 or 7 circular strokes, the glass
should receive 2 or 3 cross ones along the diameter of the tool, and in
different directions; and while the operation is going on, the convex
tool should, at the end of five minutes, be wrought upon the concave
one for a few seconds, in order to preserve the same curvature to the
tools and to the glass. The finest polish is generally given in the
following way. Cover the concave tool with a layer of pitch hardened
by the addition of a little rosin, to the thickness of 1/15th of an
inch. Then, having taken a piece of thin writing paper, press it upon
the surface of the pitch with the convex tool, and pull the paper
quickly from the pitch before it has adhered to it; and if the surface
of the pitch is marked every where with the lines of the paper, it
will be truly spherical. If any paper remains on the surface of the
pitch, it may be rubbed off by soap and water, and if the marks of
the paper should not appear on any part of it, the operation must be
repeated, till the polisher or bed of pitch is accurately spherical.
The glass is then to be wrought on the polisher by circular and cross
strokes with the putty or colcothar, till it has received a complete
polish. When one side is finished, the glass must be separated from its
handle, by inserting the point of a knife between it and the pitch,
and giving it a gentle stroke. The pitch which remains upon the glass
may be removed by rubbing it with a little oil or spirits of wine. The
operation of polishing on cloth is slower, and the polish less perfect
than on pitch; but it is a mode best fitted for those who have little
experience, and who would be apt, in the first instance, to injure the
figure of the lens by polishing it on a bed of pitch.
2. _On the method of casting and grinding the Specula of Reflecting
Telescopes._
The first thing to be considered in the formation of reflecting
telescopes, is the _composition_ of the metal of which the specula
are made. The qualities required are--a sound uniform metal, free
from all microscopic pores--not liable to tarnish by absorption of
moisture from the atmosphere--not so hard as to be incapable of taking
a good figure and polish--nor so soft as to be easily scratched, and
possessing a high reflecting power. Various compositions have been
used for this purpose, of which the following are specimens:--Take
good Swedish copper 32 ounces, and when melted, add 14-1/2 ounces of
grain tin to it; then, having taken off the scoria, cast it into an
ingot. This metal must be a second time melted to cast a speculum; but
it will fuse in this compound state with a small heat, and therefore
will not calcine the tin to putty. It should be poured off as soon as
it is melted, giving it no more heat than is absolutely necessary. The
best method for giving the melted metal a good surface is this: the
moment before it is poured off, throw into the crucible a spoonful of
charcoal-dust; immediately after which the metal must be stirred with
a wooden spatula and poured into the moulds.--The following is another
composition somewhat similar. Take 2 parts copper as pure as it is
possible to procure; this must be melted in a crucible by itself. Then
put, in another crucible, 1 part of pure grain tin. When they are both
melted, mix and stir them with a wooden spatula, keeping a good flux
on the melted surface to prevent oxidation, and then pour the metal
quickly into the moulds, which may be made of founder’s loam.
The composition suggested, more than half a century ago, by the Rev.
Mr. Edwards, has often been referred to with peculiar approbation. This
gentleman took a great deal of pains to discover the best composition,
and to give his metals a fine polish and the true parabolical figure.
His telescopes were tried by Dr. Maskelyne, the Astronomer Royal, who
found them greatly to excel in brightness, and to equal in other
respects those made by the best artists. They showed a white object
perfectly white, and all objects of their proper colour. He found,
after trying various combinations, the following to be the best: namely
32 ounces of copper, with 15 or 16 ounces of grain tin, (according to
the purity of the copper) with the addition of one ounce of brass,
one of silver, and one ounce of arsenic. This, he affirms, will form
a metal capable, when polished in a proper manner, of reflecting more
light than any other metal yet made public.
The Rev. J. Little, in his observations on this subject in the ‘Irish
Transactions,’ proposes the following composition, which he found to
answer the purpose better than any he had tried, namely--32 parts
of best bar copper, previously fluxed with the black flux, of two
parts tartar and one of nitre, 4 parts brass, 16 parts tin, and 1-1/4
arsenic. If the metal be granulated, by pouring it, when first melted,
into water, and then fused a second time, it will be less porous than
at first. In this process, the chief object is, to hit on the exact
point of the saturation of the copper, &c., by the tin. For, if the
latter be added in too great quantity, the metal will be dull coloured
and soft; if too little, it will not attain the most perfect whiteness,
and will certainly tarnish.[35]
When the metal is cast, and prepared by the common grind-stone for
receiving its proper figure--the gages and grinding-tools are to be
formed in the same manner as formerly described for lenses, with this
difference, that the radius of the gages must always be _double_
the focal length of the speculum, as the focus of parallel rays by
reflection is at one half the radius of concavity. In addition to the
concave and convex tools--which should be only a little broader than
the metal itself--a convex elliptical tool of lead and tin should
be formed with the same radius, so that its transverse should be to
its conjugate diameter as 10 to 9, the latter being exactly equal to
the diameter of the metal. The grinding of the speculum is then to
be commenced, on this tool, with coarse emery powder and water, when
the roughness is taken off, by moving the speculum across the tool,
in different directions, walking round the post on which the tool
is fixed, holding the speculum by the wooden handle to which it is
cemented. It is then to be wrought with great care on the convex brass
tool, with circular and cross strokes, and with emery of different
degrees--the concave tool being sometimes ground upon the convex one,
to keep them all of the same radius, and when every scratch is removed
from its surface, it will be fit for receiving the final polish.
When the metal is ready for polishing, the elliptical tool is to
be covered with black pitch about 1/20th of an inch thick, and the
polisher formed in the same way as in the case of lenses, either with
the concave brass tool or with the metal itself. The colcothar of
vitriol should then be triturated between two surfaces of glass, and
a considerable quantity of it applied at first to the surface of the
polisher. The speculum is then to be wrought, in the usual way, upon
the polishing tool, till it has received a brilliant lustre, taking
care to use no more of the colcothar, if it can be avoided, and only a
small quantity of it, if it should be found necessary. When the metal
moves stiffly on the polisher, and the colcothar assumes a dark muddy
hue, the polish advances with great rapidity. The tool will then grow
warm, and would probably stick to the speculum, if its motion were
discontinued for a moment. At this stage of the process, therefore, we
must proceed with great caution, breathing continually on the polisher,
till the friction is so great, as to retard the motion of the speculum.
When this happens, the metal is to be slipped off the tool at one side,
cleaned with soft leather, and placed in a tube for the purpose of
trying its performance; and if the polishing has been conducted with
care, it will be found to have a true _parabolic_ figure.[36]
It was formerly the practice, before the speculum was brought to the
polisher, to smooth it on a _bed of hones_, or a convex tool made of
the best blue stone, such as clockmakers use in polishing their work,
which was made one fourth part larger than the metal which was to be
ground upon it, and turned as true as possible to a gage. But this tool
is not generally considered as absolutely necessary, except when silver
and brass enter into the composition of the metal, in order to remove
the roughness which remains after grinding with the emery.
_To try the figure of the metal._--In order to this, the speculum must
be placed in the tube of the telescope for which it is intended; and,
at about 20 or 30 yards distant, there should be put up a watch-paper,
or similar object, on which there are some very fine strokes of an
engraver. An annular kind of diagram should be made with card-paper,
so as to cover a circular portion of the middle part of the speculum,
between the hole and the circumference, equal in breadth to about
1/8 of its diameter. This paper ring should be fixed in the mouth
of the telescope, and remain so during the whole experiment. There
must likewise be two other circular pieces of card-paper cut out, of
such sizes, that one may cover the centre of the metal, by completely
filling the hole in the annular piece now described: and the other such
a round piece as shall exactly fill the tube, and so broad as that
the inner edge just touches the outward circumference of the middle
annular piece. All these pieces together will completely shut up the
mouth of the telescope. Let the round piece which covers the centre of
the metal be removed, and adjust the instrument so that the image may
be as sharp and distinct as possible. Then replace the central piece,
and remove the outside annular one, by which means the circumference
only of the speculum will be exposed; and the image now formed will be
from the rays reflected from the exterior side of the metal. If the two
images formed by these two portions of the metal be perfectly sharp and
equally distinct, the speculum is perfect and of the true parabolic
curve. If, on the contrary, the image from the outside of the metal
should not be distinct and that it should be necessary to bring the
little speculum _nearer_ by the screw, the metal is not yet brought to
the parabolic figure; but if, in order to procure distinctness, we be
obliged to move the small speculum farther off, then the figure of the
great speculum has been carried beyond the parabolic, and has assumed
the hyperbolic form.
_To adjust the eye-hole of Gregorian Reflectors._--If there is only
one eye-glass, then the distance of the small hole should be as nearly
as possible equal to its focal length. But in the compound Huygenian
eye-piece, the distance of the eye-hole may be thus found:--Multiply
the difference between the focal distance of the glass next to the
speculum, and the distance of the two eye-glasses, by the focal
distance of the glass nearest the eye; divide the product by the sum
of the focal distances of the two lenses, lessened by their distance,
and the quotient will be the compound focal distance required. Thus,
if the focal distance of the lens next the speculum be 3 inches, that
of the lens next the eye 1 inch, and their distance 2 inches, then the
compound focal distance from the eye-glass will be (3 - 2 × 1)/(3 × 1
- 2) = 1/2 inch.--The _diameter_ of the eye-hole is always equal to
the quotient obtained by dividing the diameter of the great speculum
by the magnifying power of the telescope. It is generally from 1/25th
to 1/50th of an inch in diameter. It is necessary, in many cases, to
obtain, _from direct experiment_, an accurate determination of the
place and size of the eye-hole, as on this circumstance depends, in a
certain degree, the accurate performance of the instrument.
_To center the two specula of Gregorian Reflectors._--Extend two fine
threads or wires across the aperture of the tube at right angles, so as
to intersect each other, exactly in the axis of the telescope. Before
the arm is finally fastened to the slider, place it in the tube, and
through the eye-piece (without glasses) the intersection of the cross
wires must be seen exactly in the centre of the hole of the arm. When
this exactness is obtained, let the arm be firmly riveted and soldered
to the slider.
_To centre lenses._--The centering of lenses is of great importance,
more especially for the object-glasses of achromatic instruments. The
following is reckoned a good method:--Let the lens to be centered be
cemented on a brass chuck, having the middle turned away so as not to
touch the lens, but near the edge, which will be hid when mounted. This
rim is very accurately turned flat where it is to touch the glass. When
the chuck and cement is warm it is made to revolve rapidly: while in
motion a lighted candle is brought before it, and its reflected image
attentively watched. If this image has any motion, the lens is not
flat or central; a piece of soft wood must therefore be applied to it
in the manner of a turning tool, till such time as the light becomes
stationary. When the whole has cooled, the edges of the lens must be
turned by a diamond, or ground with emery.
For more particular details in reference to grinding and polishing
specula and lenses, the reader is referred to Smith’s ‘Complete system
of Optics’--Imison’s ‘School of Arts’--_Huygenii Opera_--Brewster’s
Appendix to ‘Ferguson’s Lectures’--‘Irish Transactions,’ vol. X.,
or ‘Nicholson’s Journal,’ vol. XVI., Nos. 65, 66, for January and
February, 1807.
PART III.
ON VARIOUS ASTRONOMICAL INSTRUMENTS.
CHAPTER I.
ON MICROMETERS.
A micrometer is an instrument attached to a telescope, in order to
measure small spaces in the heavens, such as the spaces between two
stars, and the diameters of the sun, moon and planets--and by the
help of which the _apparent magnitude_ of all objects viewed through
telescopes may be measured with great exactness.
There are various descriptions of these instruments, constructed with
different substances, and in various forms, of which the following
constitute the principal variety. The _Wire_ micrometer--the _Spider’s
line_ micrometer--the Polymetric reticle--Divided _object glass_
micrometer--Divided _eye-glass_ micrometer--Ramsden’s _Catoptric_
micrometer--Rochon’s _crystal_ micrometer--Maskelyne’s _Prismatic_
micrometer--Brewster’s _micrometrical telescope_--Sir W. Herschel’s
_Lamp_ micrometer--Cavallo’s _Mother of Pearl_ micrometer, and several
others. But, instead of attempting even a general description of
these instruments, I shall confine myself merely to a very brief
description of _Cavallo’s Micrometer_, as its construction will be
easily understood by the general reader, as it is one of the most
simple of these instruments, and is so cheap as to be procured for
a few shillings; while some of the instruments now mentioned are so
expensive, as to cost nearly as much as a tolerably good telescope.[37]
This micrometer consists of a thin and narrow slip of mother of pearl
finely divided, which is placed in the focus of the eye-glass of a
telescope, just where the image of the object is formed; and it may be
applied either to a reflecting or a refracting telescope, provided the
eye-glass be a convex lens. It is about the 20th part of an inch broad,
and of the thickness of common writing paper, divided into equal parts
by parallel lines, every fifth and tenth of which is a little longer
than the rest. The simplest way of fixing it is to stick it upon the
diaphragm which generally stands within the tube, and in the focus of
the eye-glass. When thus fixed, if you look through the eye-glass, the
divisions of the micrometrical scale will appear very distinct, unless
the diaphragm is not exactly in the focus of the eye-glass, in which
case it must be moved to the proper place;--or, the micrometer may be
placed exactly in the focus of the eye-lens by the interposition of a
circular piece of paper, card, or by means of wax. If a person should
not like to see always the micrometer in the field of the telescope,
then the micrometrical scale, instead of being fixed to the diaphragm,
may be fitted to a circular perforated plate of brass, of wood, or even
of paper, which may be occasionally placed upon the said diaphragm. One
of these micrometers, in my possession, which contains 600 divisions in
an inch, is fitted up in a separate eye-tube, with a glass peculiar to
itself, which slides into the eye-piece of the telescope, when its own
proper glass is taken out.
_To ascertain the value of the divisions of this micrometer._--Direct
the telescope to the sun, and observe how many divisions of the
micrometer measure its diameter exactly. Then take out of the Nautical
Almanack the diameter of the sun for the day on which the observation
is made. Divide it by the above-mentioned number of divisions, and the
quotient is the value of one division of the micrometer. Thus, suppose
that 26-1/2 divisions of the micrometer measure the diameter of the
sun, and that the Nautical Almanack gives for the measure of the same
diameter 31´: 22´´, or 1882´´. Divide 1882 by 26.5, and the quotient is
71´´ or 1´: 11´´, which is the value of one division of the micrometer;
the double of which is the value of two divisions, and so on. The value
of the divisions may likewise be ascertained by the passage of an
equatorial star over a certain number of divisions in a certain time.
The stars best situated for this purpose are such as the following--δ
in the Whale, R. A. 37°: 3-1/3´, Dec. 37´: 50´´ S; δ in Orion, R. A.
80°: 11´: 42´´, Dec. 28´: 40´´ S; υ in the Lion, R. A. 171°: 25´: 21´´,
Dec. 23´: 22´´ N.; η in Virgo R. A. 182°: 10´, Dec. 33´: 27´´ N. But
the following is the most easy and accurate method of determining the
value of the divisions:--
Mark upon a wall or other place the length of _six inches_, which may
be done by making two dots or lines six inches asunder, or by fixing
a six inch ruler upon a stand. Then place the telescope before it,
so that the ruler or six-inch length may be at right angles with the
direction of the telescope, and just 57 feet 3-1/2 inches distant
from the object-glass of the telescope; this done, look through the
telescope at the ruler, or other extension of six inches, and observe
how many divisions of the micrometer are equal to it, and that same
number of divisions is equal to half a degree, or 30´; and this is all
that is necessary for the required determination. The reason of which
is, because an extension of six inches subtends an angle of 30´, at the
distance of 57 feet, 3-1/2 inches, as may be easily calculated from the
rules of plane Trigonometry.
[Illustration: _figure 85._]
Fig. 85, exhibits this micrometer scale, but shows it four times larger
than the real size of one which was adapted to a 3 feet achromatic
telescope magnifying 84 times. The divisions upon it are the 200ths of
an inch, which reach from one edge of the scale to about the middle of
it, excepting every fifth and tenth division, which are longer. Two
divisions of this scale are very nearly equal to one minute; and as a
quarter of one of these divisions may be distinguished by estimation,
therefore an angle of 1/8 of a minute, or of 7-1/2´´ may be measured
with it. When a telescope magnifies more, the divisions of the
micrometer must be more minute. When the focus of the eye-glass of the
telescope is shorter than half an inch, the micrometer may be divided
with the 500ths of an inch; by means of which, and the telescope
magnifying about 200 times, one may easily and accurately measure an
angle smaller than half a second. On the other hand, when the telescope
does not magnify above 30 times, the divisions need not be so minute.
In one of Dollond’s pocket telescopes, which, when drawn out for use
is only 14 inches long, a micrometer with the hundredths of an inch
is quite sufficient, and one of its divisions is equal to little less
than 3 minutes, so that an angle of a minute may be measured by it.
Supposing 11-1/2 of those divisions equal to 30´ or 23 to a degree--any
other angle measured by any other number of divisions, is determined
by proportion. Thus, suppose the diameter of the sun, seen through the
same telescope, be found equal to 12 divisions, say As 11-1/2 divisions
: are to 30 minutes :: so are 12 divisions : to ((12 × 30)/11.5) 31.3,
which is the required diameter of the sun.
_Practical uses of this Micrometer._--This micrometer may be applied
to the following purposes:--1. For measuring the apparent diameters of
the sun, moon, and planets. 2. For measuring the apparent distances of
the satellites from their primaries. 3. For measuring the cusps of the
moon in eclipses. 4. For measuring the apparent distances between two
contiguous stars--between a star and a planet--between a star and the
moon--or between a comet and the contiguous stars, so as to determine
its path. 5. For finding the difference of declination of contiguous
stars, when they have nearly the same R. Ascension. 6. For measuring
the small elevations or depressions of objects above and below the
horizon. 7. For measuring the proportional parts of buildings, and
other objects in perspective drawing. 8. For ascertaining whether a
ship at sea, or any moving object is coming nearer or going farther
off; for if the angle subtended by the object appears to increase,
it shows that the object is coming nearer, and if the angle appears
to decrease, it indicates that the object is receding from us. 9.
For ascertaining the real distances of objects of known extension,
and hence to measure heights, depths, and horizontal distances. 10.
For measuring the real extensions of objects when their distances
are known. 11. For measuring the distance and size of an object when
neither of them is known.
When the micrometer is adapted to those telescopes which have four
glasses in the eye-tube--and _when the eye-tube only is used_, it
may be applied to the following purposes:--1. For measuring the
real or lineal dimensions of small objects, instead of the angles.
For if the tube be unscrewed from the rest of the telescope, and
applied to small objects, it will serve for a microscope, having a
considerable magnifying power, as we have already shown, (p. 348);
and the micrometer, in that case, will measure the lineal dimensions
of the object, as the diameter of a hair, the length of a flea, or
the limbs of an insect. In order to find the value of the divisions
for this purpose, we need only apply a ruler, divided into tenths
of an inch, to the end of the tube, and, looking through the tube,
observe how many divisions of the micrometer measure one tenth of an
inch on the ruler, which will give the required value. Thus, if 30
divisions are equal to 1/10th of an inch, 300 of them must be equal
to 1 inch, and one division is equal to the 300dth part of an inch.
2. For measuring the magnifying power of other telescopes. This is
done by measuring the diameter of the pencil of light at the eye-end
of the telescope in question. For, if we divide the diameter of the
object lens by the diameter of this pencil of light, the quotient will
express how many times that telescope magnifies in diameter. Thus,
suppose that 300 divisions of the micrometer are equal to the apparent
extension of 1 inch--that the pencil of light is measured by 4 of these
divisions--and that the diameter of the object lens measures 1 inch
and 2 tenths:--Multiply 1.2 by 300, and the product 360, divided by 4,
gives 90 for the magnifying power of the telescope.
_Problems which may be solved by this micrometer._ I. The angle--not
exceeding one degree--which is subtended by an extension of 1 foot,
being given, to find its distance from the place of observation:--Rule
1. If the angle be expressed in minutes, say, as the given angle :
is to 60 :: so is 687.55 : to a fourth proportional, which gives the
answer in inches. 2. If the angle be expressed in seconds, say, As the
given angle : is to 3600 :: so is 687.55 to a fourth proportional,
which expresses the answer in inches. 3. If the angle be expressed in
minutes and seconds, turn it all into seconds, and proceed as above.
Example, at what distance is a globe of 1 foot in diameter, when it
subtends an angle of 2 seconds? 2 : 3600 :: 687.55 : (3600 × 687.55)/2
= 1237596 inches, or 103132-1/2 feet = the answer required. II. The
angle which is subtended by any known extension being given, to find
its distance from the place of observation. Rule, Proceed as if the
extension were of one foot, by Problem I, and call the answer B; then
if the extension in question be expressed in inches, say, as 12 inches
: are to that extension :: so is B : to a fourth proportional, which
is the answer in inches. But if the extension in question be expressed
in feet, then we need only multiply it by B, and the product is the
answer in inches.--Example, At what distance is a man 6 feet high, when
he appears to subtend an angle of 30´´? By Problem I, if the man were
1 foot high, the distance would be 82506 inches; but as he is 6 feet
high, therefore multiply 82506 by 6, and the product is the required
distance, namely 495036 inches, or 41253 feet.
For greater conveniency, especially in travelling, when one has not
the opportunity of making such calculations, the following two tables
have been calculated; the first of which shows the distance answering
to any angle from one minute to one degree, which is subtended by a
man whose height is considered an extension of 6 feet, because at a
mean, such is the height of a man when dressed with hat and shoes on.
These tables may be transcribed on a card, and may be kept always ready
with a pocket telescope furnished with a micrometer. Their use is to
ascertain distances without any calculations; and they are calculated
only to minutes, because with a pocket telescope and micrometer, it
is not possible to measure an angle more accurately than to a minute.
Thus, if we want to measure the extension of a street, let a foot ruler
be placed at the end of the street; measure the angular appearance of
it, which suppose to be 36´, and in the table we have the required
distance against 36´, which is 95-1/2 feet. Thus also a man who appears
to be 49´ high, is at the distance of 421 feet. Again, Suppose the
trunk of a tree which is known to be 3 feet in diameter be observed to
subtend an angle of 9´-1/2. Take the number answering to 9´ out of the
table, namely 382, and subtract from it a proportional part for the
half minute, namely 19.1, which subtracted from 382, leaves 362.9. This
multiplied by 3, the diameter of the tree, produces 1087.7 feet = the
distance from the object end of the telescope.
+-----------------------------------++-----------------------------------+
| Angles subtended by an || Angles subtended by an |
| extension of _one foot_ at || extension of _six feet_ at |
| different distances. || different distances. |
+-------+---------+-------+---------++-------+---------+-------+---------+
|Angles |Distances|Angles |Distances||Angles |Distances|Angles |Distances|
|Minutes|in feet. |Minutes|in feet. ||Minutes|in feet. |Minutes|in feet. |
+-------+---------+-------+---------++-------+---------+-------+---------+
| 1 | 3438 | 31 | 110.9 || 1 | 20626.8 | 31 | 665.4 |
| 2 | 1719 | 32 | 107.4 || 2 | 10313. | 32 | 644.5 |
| 3 | 1146 | 33 | 104.2 || 3 | 6875.4 | 33 | 625. |
| 4 | 859.4 | 34 | 101.1 || 4 | 5156.5 | 34 | 606.6 |
| 5 | 687.5 | 35 | 98.2 || 5 | 4125.2 | 35 | 589.3 |
| 6 | 572.9 | 36 | 95.5 || 6 | 3437.7 | 36 | 572.9 |
| 7 | 491.1 | 37 | 92.9 || 7 | 2946.6 | 37 | 557.5 |
| 8 | 429.7 | 38 | 90.4 || 8 | 2578.2 | 38 | 542.8 |
| 9 | 382 | 39 | 88.1 || 9 | 2291.8 | 39 | 528.9 |
| 10 | 343.7 | 40 | 85.9 || 10 | 2062.6 | 40 | 515.6 |
| 11 | 312.5 | 41 | 83.8 || 11 | 1875.2 | 41 | 503.1 |
| 12 | 286.5 | 42 | 81.8 || 12 | 1718.8 | 42 | 491.1 |
| 13 | 264.4 | 43 | 79.9 || 13 | 1586.7 | 43 | 479.7 |
| 14 | 245.5 | 44 | 78.1 || 14 | 1473.3 | 44 | 468.8 |
| 15 | 229.2 | 45 | 76.4 || 15 | 1375. | 45 | 458.4 |
| 16 | 214.8 | 46 | 74.7 || 16 | 1298.1 | 46 | 448.4 |
| 17 | 202.2 | 47 | 73.1 || 17 | 1213.3 | 47 | 438.9 |
| 18 | 191 | 48 | 71.6 || 18 | 1145.9 | 48 | 429.7 |
| 19 | 181 | 49 | 70.1 || 19 | 1085.6 | 49 | 421. |
| 20 | 171.8 | 50 | 68.7 || 20 | 1031.4 | 50 | 412.5 |
| 21 | 162.7 | 51 | 67.4 || 21 | 982.2 | 51 | 404.4 |
| 22 | 156.2 | 52 | 66.1 || 22 | 937.6 | 52 | 396.7 |
| 23 | 149.4 | 53 | 64.8 || 23 | 896.8 | 53 | 389.2 |
| 24 | 143.2 | 54 | 63.6 || 24 | 859.4 | 54 | 381.9 |
| 25 | 137.5 | 55 | 62.5 || 25 | 825. | 55 | 375. |
| 26 | 132.2 | 56 | 61.4 || 26 | 793.3 | 56 | 368.3 |
| 27 | 127.3 | 57 | 60.3 || 27 | 763.9 | 57 | 361.9 |
| 28 | 122.7 | 58 | 59.1 || 28 | 736.6 | 58 | 355.6 |
| 29 | 118.5 | 59 | 58.2 || 29 | 711.3 | 59 | 349.6 |
| 30 | 114.6 | 60 | 57.3 || 30 | 687.5 | 60 | 343.7 |
+-------+---------+-------+---------++-------+---------+-------+---------+
In this way the distance of a considerably remote object, as a town
or building at 10 or 12 miles distant, may be very nearly determined;
provided we have the lineal dimensions of a house or other object that
stands at right angles to the line of vision. The breadth of a river,
of an arm of the sea, or the distance of a light house, whose elevation
above the sea or any other point, is known, may likewise in this manner
be easily determined.
CHAPTER II.
ON THE EQUATORIAL TELESCOPE, OR PORTABLE OBSERVATORY.
The equatorial instrument is intended to answer a number of useful
purposes in Practical Astronomy, independently of any particular
observatory. Besides answering the general purpose of a Quadrant, a
Transit instrument, a Theodolite, and an Azimuth instrument--it is
almost the only instrument adapted for viewing the stars and planets
_in the day-time_, and for following them in their apparent diurnal
motions. It may be made use of in any steady room or place, and
performs most of the useful problems in astronomical science.
The basis of all equatorial instruments is a revolving axis, placed
parallel to the axis of the earth, by which an attached telescope is
made to follow a star or other celestial body in the arc of its diurnal
revolution, without the trouble of repeated adjustments for changes of
elevation, which quadrants and circles with vertical and horizontal
axes require. Such an instrument is not only convenient for many useful
and interesting purposes in celestial observations, but is essentially
requisite in certain cases, particularly in examining and measuring the
relative positions of two contiguous bodies, or in determining the
diameters of the planets, when the spider’s-line micrometer is used.
Christopher Scheiner is supposed to have been the first astronomer who,
in the year 1620, made use of a polar axis, but without any appendage
of graduated circles. It was not, however, till the middle of the
last century, that any instruments of this description, worthy of the
name, were attempted to be constructed. In 1741, Mr. Henry Hindley, a
clock-maker in York, added to the polar axis, an equatorial plate, a
quadrant of altitude, and declination semicircle; but when this piece
of mechanism was sent to London for sale in 1748, it remained unsold
for the space of 13 years. Mr. Short, the optician, published in the
Philosophical Transactions, for 1750, a ‘description of an equatorial
telescope,’ which was of the reflecting kind, and was mounted over a
combination of circles and semicircles, which were strong enough to
support a tube, and a speculum of the Gregorian construction 18 inches
in focal length. This instrument consisted of a somewhat cumbersome
and expensive piece of machinery--a representation of which may be
seen in volume III of Martin’s ‘_Philosophia Britannica_, or system of
the Newtonian philosophy.’ Various modifications of this instrument
have since been made by Nairne, Dollond, Ramsden, Troughton, and
other artists; but even at the present period, it has never come into
very general use, though it is one of the most pleasant and useful
instruments connected with astronomical observations.
As many of these instruments are somewhat complicated, and very
expensive, I shall direct the attention of the reader solely to
one which I consider as the most simple--which may be purchased
at a moderate expence, and is sufficiently accurate for _general_
observations.
[Illustration: _figure 86._]
This instrument consists of the following parts: A _horizontal circle_
EF (fig. 86.) divided into four quadrants of 90 degrees each. There is
a fixed nonius at N; and the circle is capable of being turned round
on an axis. In the centre of the horizontal circle is fixed a strong
upright pillar, which supports the centre of a vertical semicircle
AB, divided into two quadrants of 90 degrees each. This is called the
_semicircle of altitude_, and may, at any time, serve the purpose of
a quadrant in measuring either altitudes or depressions. It has a
nonius plate at K. At right angles to the plane of this semicircle, the
_equatorial circle_ MN is firmly fixed. It represents the equator, and
is divided into twice 12 hours, every hour being divided into 12 parts
of 5 minutes each. Upon the equatorial circle moves another circle,
with a chamfered edge, carrying a nonius by which the divisions on
the equatorial may be read off to single minutes; and at right angles
to this moveable circle is fixed the _semicircle of declination_ D,
divided into two quadrants of 90 degrees each. The telescope PO, is
surmounted above this circle, and is fixed to an index moveable on the
semicircle of declination, and carries a nonius opposite to Q. The
telescope is furnished with 2 or 3 Huygenian eye-pieces, and likewise
with a diagonal eye-piece for viewing objects near the zenith. Lastly,
there are 2 spirit levels fixed on the horizontal circle, at right
angles to each other, by means of which this circle is made perfectly
level when observations are to be made.
_To adjust the equatorial for observation._ Set the instrument
on a firm support. Then _to adjust the levels and the horizontal
circle_:--Turn the horizontal circle till the beginning O of the
divisions coincides with the middle stroke of the nonius, or near it.
In this situation one of the levels will be found to lie either in a
right line joining the 2 foot screws which are nearest the nonius, or
else parallel to such a right line. By means of the 2 last screws,
cause the bubble in the level to become stationary in the middle of
the glass; then turn the horizontal circle half round, by bringing
the other O to the nonius; and if the bubble remains in the middle,
as before, the level is well-adjusted; if it does not, correct the
position of the level, by turning one or both of the screws which
pass through its ends, till the bubble has moved half the distance it
ought to come to reach the middle, and cause it to move the other half
by turning the foot-screws already mentioned. Return the horizontal
circle to its first position, and if the adjustments have been well
made, the bubble will remain in the middle: if otherwise, the process
must be repeated till it bears this proof of its accuracy. Then turn
the horizontal circle till 90° stands opposite to the nonius; and by
the foot-screw,immediately opposite the other 90°, cause the bubble of
the same level to stand in the middle of the glass. Lastly, by its own
proper screws set the other level so that its bubble may occupy the
middle of its glass.
_To adjust the line of sight._ Set the nonius on the _declination_
semicircle at O, the nonius on the horary circle at VI, and the nonius
on the semicircle of altitude at 90. Look through the telescope towards
some part of the horizon, where there is a diversity of remote objects.
Level the horizontal circle, and then observe what object appears in
the centre of the cross-wires, or in the centre of the field of view,
if there be no wires. Reverse the semicircle of altitude, so that the
other 90° may apply to the nonius; taking care, at the same time, that
the other three noniuses continue at the same parts of their respective
graduations as before. If the remote object continues to be seen on the
centre of the cross-wires, the line of sight is truly adjusted.
_To find the correction to be applied to observations by the
semicircle of altitude._ Set the nonius on the declination-semicircle
to 0, and the nonius on the horary circle to XII; direct the telescope
to any fixed and distant object, by moving the horizontal circle and
semicircle of altitude, and nothing else; note the degree and minute
of altitude or depression; reverse the declination-semicircle, by
directing the nonius on the horary circle to the opposite XII; direct
the telescope again to the same object, by means of the horizontal
circle and semicircle of altitude, as before. If its altitude or
depression be the same as was observed in the other position, no
correction will be required; but, if otherwise, half the difference of
the two angles is the correction to be added to all observations made
with that quadrant, or half of the semicircle which shows the least
angle, or to be subtracted from all the observations made with the
other quadrant, or half of the semicircle. When the levels and other
adjustments are once truly made, they will be preserved in order for a
length of time, if not deranged by violence; and the correction to be
applied to the semicircle of altitude is a constant quantity.
_Description of the nonius._ The nonius--sometimes called the
_vernier_--is a name given to a device for subdividing the arcs of
quadrants and other astronomical instruments. It depends on the
simple circumstance, that if any line be divided into equal parts,
the length of each part will be greater, the fewer the divisions; and
contrariwise, it will be less in proportion as those divisions are
more numerous. Thus, in the equatorial now described, the distance
between the two extreme strokes on the nonius is exactly equal to 11
degrees on the limb, but that it is divided into 12 equal parts. Each
of these last parts will therefore be shorter than the _degree_ on the
limb in the proportion of 11 to 12, that is to say, it will be 1/12th
part, or 5 minutes shorter. Consequently, if the middle stroke be set
precisely opposite to any degree, the relative positions of the nonius
and the limb must be altered 5 minutes of a degree, before either of
the two adjacent strokes next the middle on the nonius, can be brought
to coincide with the nearest stroke of a degree; and so likewise the
second stroke on the nonius will require a change of 10 minutes, the
third of 15, and so on to 30, when the middle line of the nonius will
be seen to be equi-distant between 2 of the strokes on the limb; after
which the lines on the opposite side of the nonius will coincide in
succession with the strokes on the limb. It is clear from this, that
whenever the middle stroke of the nonius does not stand precisely
opposite to any degree, the odd minutes--or distance between it and
the degree immediately preceding--may be known by the _number_ of the
stroke marked on the nonius, which coincides with any of the strokes on
the limb.[38] In some instruments the nonius-plate has its divisions
fewer than the number of parts on the limb to which it is equal; but
when once a clear idea of the principle of any nonius is obtained, it
will be easy to transfer it to any other mode in which this instrument
is contrived.
_To find by this equatorial the_ MERIDIAN LINE, and the time,
FROM ONE OBSERVATION OF THE SUN. In order to this it is
requisite that the sun’s declination, and the latitude of the place
be known. The declination of the sun may be found, for every day,
in the Nautical Almanack, or any other astronomical Ephemeris; and
the latitude of the place may be found by means of the semicircle of
altitude, when the telescope is directed to the sun or a known fixed
star. It is likewise requisite to make the observation when the azimuth
and altitude of the sun alter quickly; and this is generally the case,
the farther that luminary is from the meridian:--Therefore, at the
distance of 3 or 4 hours, either before or after noon, (in summer)
adjust the horizontal circle; set the semicircle of altitude, so that
its nonius may stand at the co-latitude of the place; lay the plane
of the last-mentioned semicircle in the meridian, by estimation, its
0 being directed towards the depressed pole; place the nonius of the
declination semicircle to the declination, whether north or south. Then
direct the telescope towards the sun, partly by moving the declination
semicircle on the axis of the equatorial circle, and partly by moving
the horizontal circle on its own axis. There is but one position of
these which will admit of the sun being seen exactly in the middle
of the field of view. When this position is obtained, the nonius on
the equatorial circle shows _the apparent time_, and _the circle of
altitude is in the plane of the meridian_. When this position is
ascertained, the meridian may be settled by a land-mark at a distance.
With an equatorial instrument, nearly similar to that now described, I
formerly made a series of ‘_day observations_ on the celestial bodies,’
which were originally published in vol. 36 of ‘Nicholson’s Journal of
Natural Philosophy,’ and which occupy twenty pages of that journal.
Some of these observations I shall lay before the reader, after having
explained the manner in which they are made.
The instrument was made by Messrs. W. and S. Jones, opticians,
Holborn, London. The telescope which originally accompanied the
instrument was an achromatic refractor, its object-glass being 8-1/2
inches focal distance, and one inch diameter. This telescope, not
admitting sufficiently high magnifying powers for the observations
intended, was afterwards thrown aside for another telescope, having an
object-glass 20 inches focal length, and 1-3/4 inch diameter, which was
attached to the equatorial machinery in place of the small telescope.
It was furnished with magnifying powers of 15, 30, 45, 60, and 100
times. The instrument was placed on a firm pedestal about three feet
high. The feet of this pedestal had short iron pikes, which slipped
into corresponding holes in the floor of the apartment adjacent to a
south window, so that when the direction of the meridian was found, and
the circles properly adjusted, the instrument was in no danger of being
shifted from this position. Though this instrument generally stood
fronting the southern part of the heavens, yet the equatorial part,
along with the telescope, could occasionally be removed to another
position fronting the north and north-west, for observing the stars in
those quarters.
_Manner of observing stars and planets in the day-time by the
equatorial._ Before such observations can be made, the semicircle of
altitude must be placed in the meridian, and the degree and minute
pointed out by the nonius on the horizontal circle, when in this
position, noted down in a book, so that it may be placed again in the
same position, should any derangement afterwards happen. The semicircle
of altitude must be set to the co-latitude of the place; that is, to
what the latitude wants of 90°. Suppose the latitude of the place
of observation be 52° 30´ north, this latitude subtracted from 90°,
leaves 37° 30´ for the co-latitude; and therefore, the semicircle of
altitude--on which the equatorial circle is fixed--must be elevated to
37° 30´, and then the equatorial circle on the instrument coincides
with the equator in the heavens. Lastly, the telescope must be adjusted
on the declination semicircle, so as exactly to correspond with the
declination of the heavenly body to be viewed. If the body is in the
equator, the telescope is set by the index at 0 on the semicircle of
declination, or at the middle point between the two quadrants, and
then when the telescope, along with the semicircle of declination, is
moved from right to left, or the contrary, it describes an arc of the
equator. If the declination of the body be north, the telescope is
elevated to the northern division of the semicircle; if south, to the
southern part of it.
These adjustments being made, take the difference between the Right
Ascension of the sun and the body to be observed; and if the Right
Ascension of the body be greater than that of the sun, subtract the
difference from the time of observation; if not, add to the time of
observation.[39] The remainder in one case, or the sum in the other,
will be the hour and minute to which the nonius on the equatorial
circle is to be set; which being done, the telescope will point to the
star or planet to whose declination the instrument is adjusted. When
the heavenly body is thus found, it may be followed, in its diurnal
course, for hours, or as long as it remains above the horizon. For as
the diurnal motion of a star is parallel to the equator, the motion of
the telescope on the equatorial circle, will always be in the star’s
diurnal arc; and should it have left the field of the telescope for any
considerable time, it may be again recovered, by moving the telescope
onward according to the time which elapsed since it was visible in the
field of view. We may illustrate what has been now stated by an example
or two. Suppose on the 30th April, 1841, at 1 o’clock, P.M. we
wished to see the star _Aldebaran_. The Right Ascension of this star
is 4^h 27^m; and the sun’s Right Ascension for that day at noon, as
found in ‘White’s Ephemeris,’ or the ‘Nautical Almanack,’ is 2^h 30^m.
Subtract this last number from 4^h 27^m, and the remainder 1^h 57^m,
shows that the star comes to the meridian on that day at 57 minutes
past 1 o’clock, P.M. And as the time of observation is 1
P.M., the nonius which moves on the equatorial circle must be
set to 3 minutes past XI, as the star is at that hour 57 minutes from
the meridian. The declination of Aldebaran is 16° 11´ north, to which
point on the semicircle of declination, the telescope must be adjusted,
and then the star will be visible in the field of view. Again, suppose
we wished to observe the planet Venus on the 1st January, 1842, at
12 o’clock noon. The sun’s Right Ascension on that day is 18^h 46^m,
and that of Venus 17^h 41^m, from which the sun’s Right Ascension
being subtracted, the remainder is 22^h 55^m, or 55 minutes past 10,
A.M. Here, as the Right Ascension of Venus is too small to
have the sun’s Right Ascension taken from it, we borrow 24 hours, and
reckon the remainder from XII at noon. As the planet at 12 noon, is 1
hour 5 minutes past the meridian, the nonius on the equatorial circle
must be set to that point, and the telescope adjusted to 23° 6´ of
south declination, which is the declination of Venus for that day, when
this planet will appear in the field of view.
_Observations on the fixed stars and planets, made in the day-time by
the Equatorial._
For the purpose of illustrating the descriptions now given, and for
affording some information respecting celestial day observations,
I shall select a few of the observations above alluded to, which I
formerly published in Nicholson’s Journal, along with a few others
which have been since made. These observations were made with a view to
determine the following particulars:--1. What stars and planets may be
conveniently seen in the day-time, when the sun is above the horizon?
2. What degrees of magnifying power are requisite for distinguishing
them? 3. How near their conjunction with the sun they may be seen?
and 4. Whether the diminution of the aperture of the object-glass of
the telescope, or the increase of magnifying power, conduces most to
render a star or a planet visible in day-light. Having never seen such
observations recorded in books of astronomy or in scientific journals,
I was induced to continue them, almost every clear day for nearly a
year, in order to determine the points now specified. Some of the
results are stated in the following pages.
_Observations on fixed stars of the first magnitude._ April 23, 1813,
at 10^h 15^m, A.M., the sun being 5-1/2 hours above the
horizon. Saw the star _Vega_, or α Lyræ, very distinctly with a power
of 30 times. Having contracted the aperture of the object-glass to
9/10 of an inch, saw it on a darker ground, but not more plainly than
before. Having contracted the aperture still farther, to half an inch,
I perceived the star, but not so distinctly as before. The sky being
very clear, and the star in a quarter of the heavens nearly opposite
to the sun, I diminished the magnifying power to 15, and could still
perceive the star, but indistinctly; it was just perceptible. August
23, at 0^h 12^m, P.M., saw the star _Capella_, or α _Aurigæ_,
with a power of 60, and immediately afterwards with a power of 30;
the aperture undiminished. With this last power it appeared extremely
distinct, but not so brilliant and splendid as with the former power.
Having diminished the aperture to 9/10 of an inch, it appeared on a
darker ground, though in the former case, it was equally perceptible.
A few minutes afterwards, could distinguish it with a power of 15, the
aperture being contracted to half an inch. It appeared very small;
it was with difficulty the eye could fix upon it in the field of the
telescope; but when it was once perceived, its motion across the field
of view could be readily followed. It could not be perceived, when the
diminished aperture was removed. The sun was then shining in meridian
splendour.
August 10th, 9^h 30^m, A.M. Saw the star Sirius with a power
of 60, the aperture contracted to 9/10 inch. Saw it likewise when
the aperture was diminished to half an inch, but not so distinctly
as through the aperture of inch. Having put on a power of 30, could
distinguish it distinctly enough through each of the former apertures,
and likewise when they were removed; but somewhat more distinctly
with the apertures of nine-tenths and half an inch than without them.
At this time the star was 2^h 42^m in time of Right Ascension west
of the sun, having an elevation above the horizon of about 17° 10’;
the sun shining bright, and the sky very much enlightened in that
quarter of the heavens where the star appeared. There was also a
considerable undulation of the air, which is generally the case in
the hot mornings of summer--which renders a star more difficult to
be perceived than in the afternoon, especially when it is viewed at
a low altitude. June 4th, 1^h 30^m, P.M., saw Sirius with a
power of 30 with great distinctness, the aperture not contracted. The
star was then within 1^h 50^m, in time of Right Ascension east from
the sun. August 24th, 9^h 5^m, A.M., saw the star _Procyon_,
or α _Canis-Minoris_ distinctly with a power of 60, the aperture not
contracted. When diminished to 9/10 inch, it appeared rather more
distinct, as the ground on which it was seen was darker. With a power
of 30, and the aperture contracted to 9/10 inch, could perceive it, but
somewhat indistinctly. When the equatorial motion was performed, in
order to keep it in the field of view, it was sometime before the eye
could again fix upon it. When the aperture was diminished to half an
inch, it could not be perceived. Saw it when both the apertures were
removed, but rather more distinctly with the aperture of 9/10 inch. The
difference in the result of this observation, from that of Capella,
above stated, was owing to the star’s proximity to the sun, and the
consequent illumination of the sky in that quarter where it appeared.
Its difference in Right Ascension from that of the sun was then about
2^h 5^m of time, and its difference of declination about 4° 50´.[40]
This star may be considered as one of those which rank between the
first and second magnitudes.
Similar observations to the above were made and frequently repeated
on the stars Rigel, Aldebaran, Betelguese Cor-Leonis and other stars
of the first magnitude, which gave nearly the same results. The stars
Altares and Fomalhaut are not so easily distinguished, on account of
their great southern declination, and consequent low elevation above
the horizon. The following observation on _Arcturus_ may be added.
June 3rd, observed Arcturus very distinctly, a little before 7 in the
evening, the sun being about 1^h 40^m above the horizon, and shining
bright--with a power of 15; the aperture not contracted. It appeared
very small but distinct. This star is easily distinguishable at any
time of the day with a power of 30.
_Observations on stars of the second magnitude._ May 5, 1813, at 6^h,
P.M.; the sun being an hour and three quarters above the
horizon. Saw _Alphard_, or α Hydræ, a star of the second magnitude,
with a power of 60; the aperture diminished to 9/10 inch. A few minutes
afterwards could perceive it, but indistinctly, with a power of 30,
the aperture contracted as above. It could not be seen very distinctly
with this power, till about half an hour before sun-set. It was then
seen rather more distinctly when the aperture was contracted than
without the contraction. May 7th. Saw the star _Deneb_, or β _Leonis_,
distinctly with a power of 60, about an hour and a half before sun-set.
August 20th. Saw Ras Alkague, or α _Ophiuchi_, at 4^h 40^m, _P.M._,
with a power of 100, the sun being nearly 3 hours above the horizon,
and shining bright. Perceived it about an hour afterwards, with a
power of 60--with the aperture contracted to 9/10 inch, and also when
this contraction was removed. The star was seen nearly as distinctly
in the last case as in the first. August 27, 5^h, _P.M._, the same
star appeared quite distinct with a power of 60, the aperture not
contracted. It did not appear more distinct when the aperture was
contracted to 9/10 inch. The sun was then more than 2 hours above the
horizon. August 28th. Saw the star _Pollux_, or β _Gemini_, 2 hours
after sun-rise with a power of 60, aperture undiminished. November
12th, 1_{h} 30´, _P.M._ Saw the star _Altair_, or α _Aquilæ_, with an
8-1/2 inch telescope, 1 inch aperture, carrying a power of 45, the
aperture not contracted. Having contracted the aperture a little, it
appeared somewhat less distinct. This star is reckoned by some to
belong to the class of stars of the first magnitude; but in White’s
‘Ephemeris’ and other Almanacks, it is generally marked as being of the
second magnitude. It forms a kind of medium between stars of the 1st
and of the 2nd magnitude.
Similar observations, giving the same results, were made on the stars
Bellatrix, Orion’s Girdle, α Andromedæ, α Pegasi, Alioth, Benetnasch,
North Crown, or α Coronæ Borealis, and various other stars of the same
magnitude.
From the above and several hundreds of similar observations, _the
following conclusions_ are deduced.
1. That a magnifying power of 30 times is sufficient for distinguishing
a fixed star of the first magnitude, even at noon-day, at any season
of the year; provided it have a moderate degree of elevation above the
horizon, and be not within 30° or 40° of the sun’s body. Also, that, by
a magnifying power of 15, a star of this class may be distinguished,
when the sun is not above an hour and a half above the horizon. But,
in every case, higher powers are to be preferred. Powers of 45 or 60,
particularly the last, were found to answer best in most cases, as with
such powers the eye could fix on the star with ease, as soon as it
entered the field of the telescope.
2. That most of the stars of the 2nd magnitude may be seen with a power
of 60, when the sun is not much more than 2 hours above the horizon;
and, at any time of the day, the brightest stars of this class may be
seen with a power of 100, when the sky is serene, and the star not too
near the quarter in which the sun appears.
3. That, in every instance, an increase of magnifying power has
the principal effect in rendering a star easily perceptible. That
diminution of aperture, in most cases, produces a very slight effect;
in some cases, none at all; and, when the aperture is contracted beyond
a certain limit, it produces a hurtful effect. The cases in which a
moderate contraction is useful, are the two following:--1. When the
star appears in a bright part of the sky, not far from that quarter in
which the sun appears. 2. When an object-glass of a large aperture, and
a small degree of magnifying power, is used. In almost every instance
the contraction of the object-glass of the 8-1/2-inch telescope with
a power of 45, had a hurtful effect. But when the 20-inch telescope
carried a power of only 15, the contraction served to render the object
more perceptible.
_Observations on the Planets made in the day-time._
Some of the planets are not so easily distinguished in the day-time as
the fixed stars of the first magnitude. The one which is most easily
distinguished at all times, is the planet Venus.
1. _Observations on Venus._ My observations on this planet commenced
about the end of August, 1812, about three or four weeks after its
inferior conjunction. About that period, between ten and eleven in the
forenoon, with a power of 45, it appeared as a beautiful crescent,
quite distinct and well-defined, with a lustre similar to that of the
moon about sun-set, but of a whiter colour. The view of its surface and
phase was fully more distinct and satisfactory than what is obtained
in the evening after sun-set; for, being at a high elevation, the
undulation near the horizon did not affect the distinctness of vision.
The planet was then very distinctly seen with a power of 7 times, when
it appeared like a star of the first or second magnitude. I traced the
variation of its phases, almost every clear day, till the month of May,
1813. As at that time, it was not far from its superior conjunction
with the sun, I wished to ascertain how near its conjunction with that
luminary it might be seen; and particularly whether it might not be
possible, in certain cases, to see it at the moment of its conjunction.
The expressions of all astronomical writers previous to this period,
when describing the phases of Venus, either directly assert, or,
at least imply, that it is _impossible_ to see that planet, in any
instance, at the time of its superior conjunction. This is the language
of Dr. Long, Dr. Gregory, Dr. Brewster, Ferguson, Adams, B. Martin, and
most other writers on the science of astronomy. How far such language
is correct will appear from the following observations and remarks.
April 24, 1813, 10^h 50´ A.M. Observed Venus with a power of
30, the aperture not contracted. She was then about 31 minutes, in
time, of right ascension, distant from the sun. Their difference of
declination 3° 59´. She appeared distinct and well-defined. With a
power of 100, could distinguish her gibbous phase. May 1st, 10^h 20^m,
A.M. Viewed this planet with a power of 60; the aperture not
contracted. It appeared distinct. Saw it about the same time with
a power of 15, the aperture being contracted to 9/10 inch. Having
contracted the aperture to 1/2 inch, saw it more distinctly. When the
contracted apertures were removed, the planet could with difficulty be
distinguished, on account of the direct rays of the sun striking on
the inside of the tube of the telescope. The sun was shining bright,
and the planet about 25´ of time in R.A. west of his centre, their
difference of declination being 3° 7´. May 7th, 10^h, A.M.
Saw Venus distinctly with a power of 60, the sun shining bright. It
was then about 19´ in time of R.A. and 4° 27´ in longitude west of the
sun; their difference of declination being 2° 18´. I found a diminution
of aperture particularly useful when viewing the planet at this time,
even when the higher powers were applied. This was the last observation
I had an opportunity of making prior to the conjunction of Venus with
the sun, which happened on May 25th, at 9^h 30^m, A.M. Its
geocentric latitude at that time being about 16´ south, the planet must
have passed almost close by the sun’s southern limb. Cloudy weather for
nearly a month after the last observation, prevented any further views
of the planet, when it was in that part of the heavens which was within
the range of the instrument. The first day that proved favourable after
it had passed the superior conjunction, was June 5th. The following is
the memorandum of the observation then taken.
June 5th, 9^h, A.M. Adjusted the Equatorial Telescope for
viewing the planet Venus, but it could not be perceived, on account
of the direct rays of the sun entering the tube of the telescope.
I contrived an apparatus for screening his rays, but could not get
it conveniently to move along with the telescope; and therefore
determined to wait till past eleven, when the top of the window of the
place of observation would intercept the solar rays. At 11^h 20^m,
A.M., just as the sun had passed the line of sight from the
eye to the top of the window, and his body was eclipsed by it, I was
gratified with a tolerably distinct view of the planet, with a power
of 60. The aperture being contracted to 9/10 inch. The distinctness
increased as the sun retired, till, in two or three minutes, the planet
appeared perfectly well-defined. Saw it immediately afterwards, with
a power of 30, the aperture contracted as before. Saw it also quite
distinctly with a power of 15; but it could not be distinguished with
this power, when the contracted aperture was removed. At this time
Venus was just 3° in longitude, or about 13´ in time of R.A. east of
the sun’s centre, and of course only about 2-3/4 degrees from his
eastern limb; the difference of their declination being 27´, and the
planet’s latitude 11´ north.
Several years afterwards, I obtained views of this planet, when
considerably nearer the sun’s margin than as stated in the above
observation, particularly on the 16th October, 1819, when Venus was
seen when only 6 days and 19 hours past the time of the superior
conjunction. At that time its distance from the sun’s eastern limb
was only 1° 28´ 42´´. A subsequent observation proved that Venus can
be seen when only 1° 27´, from the sun’s margin--which I consider as
approximating to the nearest distance from the sun at which this
planet is distinctly visible.--I shall only state farther the two or
three following observations.
June 7th, 1813, 10^h, A.M. Saw Venus with a power of 60, the
aperture being contracted to 9/10 inch--the direct rays of the sun
_not being intercepted by the top of the window_. The aperture having
being further contracted to 1/2 inch, could perceive her, but not quite
so distinctly. When the contractions were removed, she could scarcely
be seen. She was then 3° 33´ in longitude, and nearly 15 minutes in
time of R.A. distant from the sun’s centre. Some fleeces of clouds
having moved across the field of view, she was seen remarkably distinct
in the interstices--the sun at the same time, being partly obscured
by them.--August 19th, 1^h 10´, P.M. Viewed Venus with a
magnifying power of 100. Could perceive her surface and gibbous phase
almost as distinctly as when the sun is below the horizon. She appeared
bright, steady in her light, and well defined, without that glare and
tremulous appearance she exhibits in the evening when near the horizon.
She was then nearly on the meridian. On the whole, such a view of this
planet is as satisfactory, if not preferable, to those views we obtain
with an ordinary telescope in the evening, when it is visible to the
naked eye.
All the particulars above stated have been confirmed by many subsequent
observations continued throughout a series of years. I shall state only
two recent observations which show that Venus may be seen somewhat
nearer the sun than what is deduced from the preceding observations,
and at the point of its superior conjunction. March 10th, 1842,
observed the planet Venus, then very near the sun, at 19 minutes past
11, A.M. It had passed the point of its superior conjunction
with the sun, on the 5th March, at 1^h 19^m, P.M. The
difference of right ascension between the sun and the planet was then
about 6-1/2 minutes of time, or about 1° 37-1/2´, and it was only about
1° 21´ distant from the sun’s eastern limb. It appeared quite distinct
and well-defined, and might perhaps have been seen on the preceding
day, had the observation been then made.--The following observation
shows that Venus may be seen still nearer the sun than in the preceding
observations, and even _at the moment of its superior_ conjunction. On
the 2nd of October, 1843, this planet passed the point of its superior
conjunction with the sun, at 4^h 15^m, P.M. At two o’clock,
P.M.--only two hours before the conjunction, I perceived the
planet distinctly, and kept it in view for nearly ten minutes, till
some dense clouds intercepted the view. It appeared tolerably distinct
and well-defined, though not brilliant, and with a round full face,
and its apparent path was distinctly traced several times across the
field of view of the telescope. I perceived it afterwards, about half
past four, P.M., only a few minutes after it had passed the
point of conjunction, on which occasion it appeared less distinct than
in the preceding observation, owing to the low altitude of the planet,
being then only a few degrees above the horizon. The observations,
in this instance, were made not with an equatorial instrument, which
I generally use in such observations, but with a good achromatic
telescope 44-1/2 inches focal distance, mounted on a common tripod,
with a terrestrial power of 95 times. A conical tube about ten inches
long was fixed on the object-end of the telescope, at the extremity of
which an aperture, 1-1/2 inch diameter was placed, so as to intercept,
as much as possible, the direct ingress of the solar rays. The top of
the upper sash of the window of the place of observation was likewise
so adjusted as to intercept the greater part of the sun’s rays from
entering the tube of the telescope. The sun’s declination at that time
was 3° 26´ south, and that of Venus 2° 12´ south; consequently, the
difference of declination was 1° 14´ = the distance of Venus from the
sun’s centre; and as the sun’s diameter was about 16´, Venus was then
only 58´ from the sun’s northern limb, or 6´ less than two diameters of
the sun.
This is the nearest approximation to the sun at which I have ever
beheld this planet, and it demonstrates that Venus may be seen even
when within a degree of the sun’s margin; and it is perhaps the nearest
position to that luminary in which this planet can be distinctly
perceived. It shows that the light reflected from the surface of Venus
is far more brilliant than that reflected from the surface of our moon;
for no trace of this nocturnal luminary can be perceived, even when at
a much greater distance from the sun, nor is there any other celestial
body that can be seen within the limit now stated. This is the first
observation, so far as my information extends, of Venus having been
seen at the time of her superior conjunction.[41]
The practical conclusion from this observation is, that, at the
superior conjunction of this planet, when its distance from the sun’s
margin is not less than 58´, _its polar and equatorial diameter may be
measured_ by a micrometer, when it will be determined whether or not
Venus be of a _spheroidal_ figure. The Earth, Mars, Jupiter and Saturn
are found to be not spheres but _spheroids_, having their polar shorter
than their equatorial diameters. But the true figure of Venus has never
yet been ascertained, because it is only at the superior conjunction
that she presents a full enlightened hemisphere, and when both
diameters can be measured, except at the time when she transits the
sun’s disk, which happens only twice in the course of 120 years.[42]
The following conclusions are deduced from the observations made on
Venus.
1. That this planet may be seen distinctly, with a moderate degree of
magnifying power, _at the moment of its superior conjunction with the
sun_, when its geocentric latitude, either north or south, at the
time of conjunction, is not less than 1° 14´, or, when the planet is
about 58´ from the sun’s limb. This conclusion is deduced from the
observation of Oct. 2, 1843,[45] stated above.
2. Another conclusion is--that during the space of 583 days, or about
19 months--the time this planet takes in moving from one conjunction
with the sun to a like conjunction again--when its latitude at the
time of its superior conjunction exceeds 1° 14´, it may be seen
with an equatorial telescope every clear day without interruption,
except about the period of its _inferior_ conjunction, when its dark
hemisphere is turned towards the earth, and a short time before and
after it. When its geocentric latitude is less than 1° 14´, it will be
hid only about four days before, and the same time after its superior
conjunction. During the same period it will be invisible to the naked
eye, and consequently no observations can be made upon it with a common
telescope, for nearly six months, and sometimes more, according as its
declination is north or south, namely about two or three months before,
and the same time after its superior conjunction, except where there
is a very free and unconfined horizon. In regard to the time in which
this planet can be hid about the period of its _inferior_ conjunction,
I have ascertained from observation, that it can never be hid longer
than during a space of 2 days 22 hours; having seen Venus, about noon,
like a fine slender crescent, only 35 hours after she had passed the
point of her inferior conjunction; and in a late instance she was seen
when little more than a day from the period of conjunction. The longest
time, therefore, that this planet can be hid from view during a period
of 583 days, is only about 10 days; and when its latitude at the time
of the superior conjunction, equals or exceeds 1° 14´, it can be hid
little more than two days. This is a circumstance which cannot be
affirmed of any other celestial body, the sun only excepted.
3. That every variation of the phases of this planet--from a slender
crescent to a full enlightened hemisphere--may, on every clear day,
be conveniently exhibited by means of the equatorial telescope.
This circumstance renders this instrument peculiarly useful in the
instruction of the young in the principles of astronomy. For, if the
phase which Venus should exhibit at any particular time be known, the
equatorial telescope may be directed to the planet, and its actual
phase in the heavens be immediately exhibited to the astronomical pupil.
4. Since it is only at the period of the superior conjunction that
this planet presents a full enlightened hemisphere, and since it is
only when this phase is presented that both its diameters can be
measured--it is of some importance that observations be made on it at
the moment of conjunction, by means of powerful telescopes furnished
with micrometers, so as to determine the difference (if any) between
its polar and equatorial diameters.
5. Another conclusion from the observations on Venus, is, that a
moderate diminution of the aperture of the object-glass of the
telescope is useful, and even necessary in viewing this planet when
near the sun. Its effect is owing in part to the direct solar rays
being thereby more effectually excluded; for when these rays enter
directly into the tube of the telescope, it is very difficult, and
almost impossible to perceive this planet, or any other celestial body
when in the vicinity of the sun.
_Observations on Jupiter and other planets._
This planet is very easily distinguished in the day-time with a very
moderate magnifying power, when it is not within 30° or 35° of the sun.
The following extract from my memorandums may serve as a specimen. May
12, 1813, 1^h 40^m, P.M. Saw Jupiter with a power of 15 times,
the aperture not contracted. The planet appeared so distinct with this
power, that I have reason to believe, it would have been perceived with
a power of 6 or 7 times. When the aperture was contracted 9/10 inch,
and afterwards to half an inch, there was little perceptible difference
in its appearance. It was then about 58° in longitude, east of the sun.
Though Jupiter when at a considerable distance from the sun, and near
his opposition, appears to the naked eye with a brilliancy nearly equal
to that of Venus, yet there is a very striking difference between them,
in respect of lustre, when viewed in day-light. Jupiter, when viewed
with a high magnifying power, in the day-time, always exhibits a very
dull cloudy appearance; whereas Venus appears with a moderate degree of
splendour. About the end of June 1813, between 5 and 6 in the evening,
having viewed the planet Venus, then within 20° of the sun, and which
appeared with a moderate degree of lustre, I directed the telescope to
Jupiter, at that time more than 32° from the sun, when the contrast
between the two planets was very striking, Jupiter appearing so faint
as to be just discernible, though his apparent magnitude was nearly
double that of Venus. In this observation a power of 65 was used.
In his approach towards the sun, about the end of July, I could not
perceive him when he was within 16° or 17° of his conjunction with that
luminary.--_These circumstances furnish a sensible and popular proof_,
independently of astronomical calculations, _that the planet Jupiter
is placed at a much greater distance from the sun than Venus_; since
its light is so faint as to be scarcely perceptible when more than 20
degrees from the sun, while that of Venus is distinctly seen amidst
the full splendour of the solar rays, when only about a degree from
the margin of that luminary. With a power of 65 I have been enabled
to distinguish the _belts_ of Jupiter before sun-set, but could never
perceive any of his satellites till the sun was below the horizon.
There are no observations which so sensibly and strikingly indicate
the different degrees of light emitted by the different planets as
those which are made in the day-time. To a common observer, during
night, Jupiter and Venus appear, in a clear sky, nearly with equal
brilliancy, and even Mars, when about the point of his _opposition_ to
the sun, appears with a lustre somewhat similar, though tinged with a
ruddy hue; but when seen in day-light their aspect is very dissimilar.
This circumstance evidently indicates, 1. that these planets are
placed at different distances from the sun, and consequently are
furnished with different degrees of light proportional to the square
of their distances from that luminary;--and 2. that there are certain
circumstances connected with the surfaces and atmospheres of the
planetary bodies, which render the light they emit more or less
intense, independently of their different distances from the central
luminary. For Mars, though much nearer to the sun than Jupiter, is not
so easily distinguished in the day-time, and, even in the night-time,
appears with a less degree of lustre.
My observations on _Saturn_ in day-light, have not been so frequent as
those on Jupiter. I have been enabled to distinguish his ring several
times before sun-set, with a power of 65; but his great southern
declination, and consequent low altitude, at the periods when these
observations were made, were unfavourable for determining the degree
of his visibility in day-light; for a planet or a star is always more
distinctly perceptible in a _high_ than in a low altitude, on account
of the superior purity of the atmosphere through which a celestial
object is seen when at a high elevation above the horizon. This planet,
however, is not nearly so distinctly visible in day-light as Jupiter,
and I have chiefly seen it, when the sun was not more than an hour or
two above the horizon, but never at noon-day; although it is probable
that with powerful instruments it may be seen even at that period
of the day. The planet _Mars_ is seldom distinctly visible in the
day-time, except when at no great distance from its opposition to the
sun. The following is a memorandum of an observation on Mars, when in a
favourable position. October 24, 1836. Saw the planet Mars distinctly
with a power of about 60, at 40 minutes past 9 A.M., the
sun having been above the horizon nearly three hours. It appeared
tolerably distinct, but scarcely so brilliant as a fixed star of the
first magnitude, but with apparently as much light as Jupiter generally
exhibits when viewed in day-light. It could not be traced longer at the
time, so as to ascertain if it could be seen at mid-day; on account
of the interposition of the western side of the window of the place
of observation. The ruddy aspect of this planet--doubtless caused by
a dense atmosphere with which it is environed--is one of the causes
which prevents its appearing with brilliancy in the day-time. With
respect to the planet _Mercury_, I have had opportunities of observing
it several times after sun-rise, and before sun-set, about 10 or 12
days before and after its greatest elongation from the sun, with a
power of 45. I have several times searched for this planet about noon,
but could not perceive it. The air, however, at the times alluded to,
was not very clear, and I was not certain that it was within the field
of the telescope; and therefore, I am not convinced but that, with a
moderately high power, it may be seen even at noon-day.
Such are some specimens of the observations I have made on the heavenly
bodies in the day-time, and the conclusions which may be deduced from
them. I have been induced to communicate them, from the consideration,
that the most minute facts, in relation to any science, are worthy of
being known, and may possibly be useful. They may at least gratify the
astronomical tyro with some information which he will not find in the
common treatises on astronomy, and may perhaps excite him to prosecute
a train of similar observations for confirming or correcting those
which have been noted above.
Besides the deductions already stated, the following general
conclusions may be noted.--1. That a celestial body may be as easily
distinguished at noon-day, as at any time between the hours of nine in
the morning and three in the afternoon, except during the short days
in winter. 2. They are more easily distinguished at a high than at
a low altitude--in the afternoon than in the morning, especially if
their altitudes be low--and in the northern region of the heavens than
in the southern. The difficulty of perceiving them at a low altitude
is obviously owing to the thick vapours near the horizon. Their being
less easily distinguished in the morning than in the afternoon is owing
to the undulations of the atmosphere, which are generally greater in
the morning than in the afternoon. This may be evidently perceived
by looking at distant land-objects at those times, in a hot day,
through a telescope which magnifies about 40 or 50 times, when they
will be found to appear tremulous and distorted in consequence of these
undulations, especially if the sun be shining bright. In consequence
of this circumstance, we can seldom use a high terrestrial power with
effect on land objects, except early in the morning, and a short
time before sun-set. Their being more easily distinguished in the
northern region of the heavens is owing to that part of the sky being
of a deeper azure, on account of its being less enlightened than the
southern with the splendour of the solar rays.
_Utility of Celestial Day Observations._
The observations on the heavenly bodies in the day-time, to which I
have now directed the attention of the reader, are not to be considered
as merely gratifications of a rational curiosity, but may be rendered
subservient to the promotion of astronomical science. As to the planet
Venus--when I consider the degree of brilliancy it exhibits, even in
day-light, I am convinced that useful observations might frequently
be made on its surface in the day-time, to determine some of its
physical peculiarities and phenomena. Such observations might set
at rest any disputes which may still exist respecting the period of
rotation of this planet. Cassini, from observations on a bright spot,
which advanced 20° in 24^h 34^m determined the time of its rotation to
be 23 hours, 20 minutes. On the other hand, Bianchini, from similar
observations, concluded that its diurnal period was 24 days and 8
hours. The difficulty of deciding between these two opinions, arises
from the short time in which observations can be made on this planet,
either before sun-rise, or after sun-set, which prevents us from
tracing, with accuracy, the progressive motion of its spots for a
sufficient length of time. And, although an observer should mark the
motion of the spots at the same hour, on two succeeding evenings, and
find they had moved forward about 15° in 24 hours, he would still be
at a loss to determine, whether they had moved only 15°, in all, since
the preceding observation, or had finished a revolution and 15° more.
If, therefore, any spots could be perceived on the surface of Venus
in the day-time, their motion might be traced, when she is in north
declination, for 12 hours or more, which would completely settle the
period of rotation. That it is not improbable that spots, fitted for
this purpose, may be discovered on her disk in the day-time, appears
from some of the observations of Cassini, who saw one of her spots when
the sun was more than eight degrees above the horizon.[46] The most
distinct and satisfactory views I have ever had of this planet were
those which I obtained in the day-time, in summer, when it was viewed
at a high altitude, with a 44-1/2 inch achromatic telescope, carrying a
power of 150. I have at such times distinctly perceived the distinction
between the shade and colour of its margin, and the superior lustre of
its central parts, and some spots have occasionally been seen, though
not so distinctly marked as to determine its rotation. Such distinct
views are seldom to be obtained in the evening after sun-set, on
account of the undulations of the atmosphere, and the dense mass of
vapours through which the celestial bodies are viewed when near the
horizon.
Nor do I consider it altogether improbable that its _satellite_ (if
it have one, as some have supposed) may be detected in the day time,
when this planet is in a favourable position for such an observation;
particularly when a pretty large portion of its enlightened surface
is turned towards the earth, and when its satellite, of course, must
present a similar phase. About the period of its greatest elongation
from the sun, and soon after it assumes a crescent phase, in its
approach to the inferior conjunction, may be considered as the most
eligible times for prosecuting such observations. If this supposed
satellite be about one third or one fourth of the diameter of its
Primary, as Cassini, Short, Baudouin, Montbarron, Montaigne, and other
astronomers supposed, it must be nearly as large as Mercury, which has
been frequently seen in day-light. If such a satellite have a real
existence, and yet undistinguishable in day-light, its surface must be
of a very different quality for reflecting the rays of light from that
of its primary; for it is obvious to every one who has seen Venus with
a high power, in the day-time, that a body of equal brilliancy--though
four times less in diameter--would be quite perceptible, and exhibit a
visible disk. Such observations, however, would be made, with a much
greater effect in Italy and other Southern countries, and particularly
in Tropical climates, such as the southern parts of Asia and America,
and in the West India Islands, where the sky is more clear and serene,
and where the planet may be viewed at higher altitudes, and for a
greater length of time, without the interruption of clouds, than in our
island.
Again, the apparent magnitudes of the fixed stars--the quantity of
light they respectively emit--and the precise class of magnitude which
should be assigned to them--might be more accurately determined by
day observations, than by their appearance in the nocturnal sky. All
the stars which are reckoned to belong to the _first magnitude_ are
not equally distinguishable in day-light. For example, the stars
_Aldebaran_ and _Procyon_ are not so easily distinguished, nor do they
appear with the same degree of lustre by day, as the stars α _Lyræ_
and _Capella_. In like manner the stars _Altair_, _Alphard_, _Deneb
Ras Alkague_, considered as belonging to the _second_ magnitude,
are not equally distinguishable by the same aperture and magnifying
power--which seems to indicate, that a different quantity of light
is emitted by these stars, arising from a difference either in their
magnitude, their distance, or the quality of the light with which they
are irradiated.
The following are likewise practical purposes to which celestial day
observations may be applied. In accurately adjusting Circular and
Transit instruments, it is useful, and even necessary, for determining
the exact position of the meridian, to take observations of certain
stars, which differ greatly in zenith distance, and which transit the
meridian nearly at the same time. But as the stars best situated for
this purpose, cannot, at every season, be seen in the evenings, we
must, in certain cases, wait for several months till such observations
can be made, unless we make them in the day-time, which can very easily
be done, if the instrument have a telescope adapted to it, furnished
with such powers as those above stated, or higher powers if required. I
have likewise made use of observations on the stars in the day time for
adjusting a clock or watch to meantime, when the sun was in a situation
beyond the range of the instrument, or obscured by clouds, and when
I did not choose to wait till the evening. This may, at first view,
appear to some as paradoxical; since the finding of a star in day-light
depends on our knowing its right Ascension from the sun, and this last
circumstance depends, in some measure, on our knowing the true time.
But if a watch or clock is known not to have varied above seven or
eight minutes from the time, a star of the first magnitude may easily
be found, by moving the telescope a little backwards or forwards, till
the star appear; and when it is once found, the exact variation of the
movement is then ascertained, by comparing the calculations which were
previously necessary, with the time pointed out by the nonius on the
Equatorial circle--or, in other words, by ascertaining the difference
between the time assumed, and the time indicated by the instrument,
when the star appears in the centre of the field of view. All this may
be accomplished in five or six minutes.
Besides the practical purposes now stated, the Equatorial telescope is
perhaps the best instrument for instructing a learner in the various
operations of practical astronomy, and particularly for enabling him
to distinguish the names and positions of the principal stars. For,
when the right Ascension and Declination of any star is known, from
astronomical tables, the telescope may be immediately adjusted to
point to it, which will infallibly prevent his mistaking one star for
another. In this way, likewise, the precise position of the planet
_Mercury_, _Uranus_, _Vesta_, _Juno_, _Ceres_, _Pallas_--a small
comet, a nebula, a double star, or any other celestial body not easily
distinguishable by the naked eye, may be readily pointed out, when its
right Ascension and Declination are known to a near approximation.
In conclusion, I cannot but express my surprise, that the Equatorial
telescope is so little known, even by many of the lovers of
astronomical science. In several respectable academies in this part of
Britain, and, if I am not misinformed, in most of our universities,
this instrument is entirely unknown. This is the more unaccountable,
as a small equatorial may be purchased for a moderate sum; and as
there is no single instrument so well adapted for illustrating all the
operations of Practical Astronomy. Where very great accuracy is not
required, it may occasionally be made to serve the general purposes
of a _transit instrument_ for observing the passages of the sun and
stars across the meridian. It may likewise be made to serve as a
_theodolite_ for surveying land and taking horizontal angles--as a
_Quadrant_ for taking angles of altitude--as a _level_--as an _equal
altitude instrument_--an _azimuth instrument_ for ascertaining the
sun’s distance from the north or south points of the horizon--and
as an accurate Universal Sun Dial, for finding the exact _mean_ or
_true_ time, on any occasion when the sun is visible. The manner of
applying it to these different purposes will be obvious to every one
who is in the least acquainted with the nature and construction of this
instrument.
The price of a small Equatorial instrument, such as that described
p. 454, is about 16 guineas, exclusive of some of the eye-pieces,
which were afterwards added for the purpose of making particular
observations. Instruments of a larger size, and with more complicated
machinery, sell from 50 to 100 guineas and upwards. Messrs. W. and S.
Jones, Holborn, London, construct such instruments.
ON THE QUADRANT.
[Illustration: _figure 87._]
Every circle being supposed to be divided into 360 equal parts, or
degrees,--it is evident, that 90 degrees, or the fourth part of a
circle, will be sufficient to measure all angles, between the horizon
of any place and the line perpendicular to it which goes up to the
zenith. Thus, in fig. 87, the line CB represents the plane of the
horizon. ACBH, the quadrant, AC the perpendicular to the horizon,
and A the zenith point. If the lines BC and CA represent a pair of
compasses with the legs standing perpendicular to each other, and
the curved lines AB, DE and FG, the quarter of as many circles of
different sizes--it is evident that although each of these differs
from the others in size, yet that each contains the same portion of a
circle, namely a quadrant or fourth part; and thus it would be from the
smallest to the largest quadrant that could be formed,--they would all
contain exactly 90 degrees each. By the application of this principle
the comparative measure of angles may be extended to an indefinite
distance. By means of an instrument constructed in the form of a
quadrant of a circle, with its curved edge divided into 90 equal parts,
the altitude of any object in the heavens can at any time be determined.
There are various constructions of this instrument, some of them
extremely simple, and others considerably complex and expensive,
according to the degree of accuracy which the observations require. The
following is a description of the _Pillar Quadrant_, as it was made by
Mr. Bird, for the observatory of Greenwich, and several continental
observatories.
This instrument consists of a quadrant E E H G L (fig. 88.) mounted on
a pillar B, which is supported by a tripod AA, resting on three foot
screws. The quadrant, the pillar, and the horizontal circle all revolve
round a vertical axis. A telescope H is placed on the horizontal
radius, and is directed to a meridian mark previously made on some
distant object for placing the plane of the instrument in the meridian,
and also for setting the zero, or beginning of the scale truly
horizontal. This is sometimes done by a level instead of a telescope,
and sometimes by a plumb-line G, suspended from near the centre, and
brought to bisect a fine dot made on the limb, where a microscope is
placed to examine the bisection. The weight or plummet at the end of
the plumb-line is suspended in the cistern of water _b_, which keeps it
from being agitated by the air. A similar dot is made for the upper end
of the plumb-line upon a piece of brass, adjustable by a screw _d_, in
order that the line may be exactly at right angles to the telescope,
when it is placed at O. The quadrant is screwed by the centre
of its frame, against a piece of brass _e_ with three screws, and this
piece is screwed to the top of the pillar B with other three screws.
By means of the first three screws, the plane of the quadrant can be
placed exactly parallel to the vertical axis, and by the other screws
the telescope H can be placed exactly perpendicular to it. The nut of
the delicate screw L is attached to the end of the telescope F, by a
universal joint. The collar for the other end is jointed in the same
manner to a clamp which can be fastened to any part of the limb.
A similar clamp-screw and slow motion is seen at _n_ for the lower
circle, which is intended to hold the circle fast, and adjust its
motion. The divisions of the lower, or horizontal circle, are read by
verniers, or noniuses, fixed to the arms of the tripod at _l_ and _m_,
and, in some cases three are used to obtain greater accuracy.
[Illustration: _figure 88._]
In using this quadrant, the axis of the telescope H is adjusted to a
horizontal line, and the plane of the quadrant to a vertical line, by
the means already stated. The screw of the champ L is then loosened,
and the telescope directed to the star, or other object, whose altitude
is required. The clamp screw being fixed, the observer looks through
the telescope, and with the nut of the screw L he brings the telescope
into a position where the star is bisected by the intersection of the
wires in the field of the telescope. The divisions are then to be read
off upon the vernier, and the altitude of the star will be obtained.
By means of the horizontal circle D, all angles in the plane of the
horizon may be accurately measured--such as the amplitudes and azimuths
of the celestial bodies.
Quadrants of a more simple construction than the above, may be
occasionally used, such as Gunter’s, Cole’s, Sutton’s and others; but
none of these are furnished with telescopes, or telescopic sights, and
therefore an altitude cannot be obtained by them with the same degree
of accuracy as with that which has been now described.
By means of the Quadrant, not only the altitudes of the heavenly bodies
may be determined, but also the distances of objects on the earth by
observations made at two stations--the altitude of fireballs and other
meteors in the atmosphere--the height of a cloud, by observation on
its altitude and velocity--and numerous other problems, the solution of
which depends upon angular measurements. A _Mural Quadrant_ is the name
given to this instrument when it is fixed upon a wall of stone, and in
the plane of the meridian, such as the quadrant which was erected by
Flamstead in the Observatory at Greenwich. Although the quadrant was
formerly much used in astronomical observations, yet it may be proper
to state, that its use has now been almost completely superseded by
the recent introduction of _Astronomical Circles_, of which we shall
now give the reader a very short description, chiefly taken from
Troughton’s account of the instrument he constructed, as found in Sir
D. Brewster’s Supplement to Ferguson’s Astronomy.
THE ASTRONOMICAL CIRCLE.
[Illustration: _figure 89._]
An astronomical circle is a _complete circle_ substituted in place
of the quadrant, and differs from it only in the superior accuracy
with which it enables the astronomer to make his observations. The
large vertical or declination circle CC (fig. 89.) is composed of two
complete circles strengthened by an edge bar on their inside, and
firmly united at their extreme borders by a number of short braces or
bars which stand perpendicular between them, and which keep them at
such a distance as to admit the achromatic telescope TT. This double
circle is supported by 16 conical bars, firmly united along with the
telescope, to a horizontal axis. The exterior limb of each circle is
divided into degrees and parts of a degree, and these divisions are
divided into seconds by means of the micrometer microscopes _mm_,
which read off the angle on opposite sides of each circle. The cross
wires in each microscope may be moved over the limb till they coincide
with the nearest division of the limb, by means of the micrometer
screws _cc_, and the space moved through is ascertained by the
divisions on the graduated head above _c_, assisted by a scale within
the microscope. The microscopes are supported by two arms proceeding
from a small circle concentric with the horizontal axis, and fixed
to the vertical columns. This circle is the centre upon which they
can turn round nearly a quadrant for the purpose of employing a new
portion of the divisions of the circle, when it is reckoned prudent to
repeat any delicate observations upon any part of the limb. At _h_ is
represented a level for placing the axis in a true horizontal line, and
at _k_ is fixed another level parallel to the telescope, for bringing
the zero of the divisions to a horizontal position. The horizontal axis
to which the vertical circle and the telescope are fixed, is equal in
length to the distance between the vertical pillars, and its pivots are
supported by semicircular bearings, placed at the top of each pillar.
These two vertical pillars are firmly united at their bases to a cross
bar _f_. To this cross bar is also fixed a vertical axis about three
feet long, the lower end of which terminating in an obtuse point, rests
in a brass conical socket firmly fastened at the bottom of the hollow
in the stone pedestal D, which receives the vertical axis. This socket
supports the whole weight of the moveable part of the instrument. The
upper part of the vertical axis is supported by two pieces of brass,
one of which is seen at _e_, screwed to the ring _i_, and containing
a right angle, or Y. At each side of the ring, opposite to the points
of contact, is placed a tube containing a heliacal spring, which, by
a constant pressure on the axis, keeps it against its bearings, and
permits it to turn, in these four points of contact, with an easy and
steady motion. The two bearings are fixed upon two rings capable of
a lateral adjustment; the lower one by the screw _d_ to incline the
axis to the east or west, while the screw _b_ gives the upper one _i_
a motion in the plane of the meridian. By this means the axis may be
adjusted to a perpendicular position as exactly as by the usual method
of the tripod with feet screws. These rings are attached to the centre
piece _s_, which is firmly connected with the upper surface of the
stone by six conical Tubes A, A, A, &c., and brass standards at every
angle of the pedestal. Below this frame lies the azimuth circle EE
consisting of a circular limb, strengthened by ten hollow cones firmly
united with the vertical axis, and consequently turning freely along
with it. The azimuth circle EE is divided and read off in the same
manner as the vertical circle. The arms of the microscopes BB project
from the ring _i_, and the microscopes themselves are adjustable by
screws, to bring them to zero and to the diameter of the circle. A
little above the ring _i_ is fixed an arm L which embraces and holds
fast the vertical axis with the aid of a champ screw. The arm L is
connected at the extremity with one of the arms A, by means of the
screw _a_, so that by turning this screw, a slow motion is communicated
to the vertical axis and the azimuth circle.
In order to place the instrument in a true vertical position, a
plumb-line, made of fine silver wire, is suspended from a small hook
at the top of the vertical tube _n_, connected by braces with one of
the large pillars. The plumb-line passes through an angle in which it
rests, and by means of a screw may be brought into the axis of the
tube. The plummet at the lower end of the line is immersed in a cistern
of water _t_, in order to check its oscillations, and is supported on
a shelf proceeding from one of the pillars. At the lower end of the
tube _n_ are fixed two microscopes _o_ and _p_, at right angles to
one another, and opposite to each is placed a small tube containing a
lucid point. The plumb-line is then brought into such a position by
the screws _d_, _b_, and by altering the suspension of the plumb-line
itself, that the image of the luminous point, like the disk of a
planet, is formed on the plumb-line, and accurately bisected by it. The
vertical axis is then turned round, and the plumb-line examined in some
other position. If it still bisects the luminous point, the instrument
is truly vertical; but if it does not, one half of the deviation must
be corrected by the screws _d_ _b_, and the other half by altering the
suspension of the line till the bisection of the circular image is
perfect in every position of the instrument.
It is not many years since Circular Repeating instruments came into
general use. The principle on which the construction of a repeating
circle is founded appears to have been first suggested by Professor
Mayer of Gottingen, in 1758; but the first person who applied this
principle to measure round the limb of a divided instrument, was Borda,
who about the year 1789, caused a repeating circle to be constructed
that would measure with equal facility horizontal and vertical angles.
Afterwards, Mr. Troughton greatly improved the construction of Borda’s
instrument by the introduction of several contrivances which ensure,
at the same time, its superior accuracy and convenience in use; and
his instruments have been introduced into numerous observatories.
Circular instruments, on a large scale, have been placed in the Royal
Observatory of Greenwich, and in most of the principal observatories
on the continent of Europe. Although it is agreed on all hands that
greater accuracy may be obtained by a repeating circle, than by any
other having the same radius, yet there are some objections to its use
which do not apply to the altitude and azimuth circle. The following
are the principal objections, as stated in Vol. I., of the ‘Memoirs of
the Astronomical Society of London.’ 1. The origin of the repeating
circle is due to _bad dividing_, which ought not to be tolerated in any
instrument in the present state of the art. 2. There are three sources
of fixed error which cannot be exterminated, as they depend more on the
materials than on the workmanship; first, the zero of the level changes
with variations of temperature; secondly, the resistance of the centre
work to the action of the tangent screws; and thirdly, the imperfection
of the screws in producing motion, and in securing permanent positions.
3. The instrument is applied with most advantage to slowly moving or
circumpolar stars; but in low altitudes these stars are seen near the
horizon, where refraction interferes. 4. Much time and labour are
expended, first in making the observations, and again in reducing them.
5. When any one step in a series of observations is bad, the whole time
and labour are absolutely lost. 6. When the instrument has a telescope
of small power, the observations are charged with errors of vision,
which the repeating circle will not cure. 7. This instrument cannot be
used as a transit instrument, nor for finding the exact meridian of a
place.
A great variety of directions is necessary in order to enable the
student of practical astronomy thoroughly to understand and to apply
this instrument to practice, which the limited nature of the present
work prevents us from detailing.--As this instrument consists of a
variety of complicated pieces of machinery, it is necessarily somewhat
expensive. A six inch brass astronomical circle for altitudes, zenith
or polar distances, azimuths, with achromatic telescope, &c., is marked
in Messrs. W. and S. Jones’ catalogue of astronomical instruments, at
£27 6s. A circle 12 inches diameter, from £36 15s. to £68 5s. An 18
inch ditto, of the best construction, £105. The larger astronomical
circles for public observatories, from 100 to a 1000 guineas and
upwards, according to their size, and the peculiarity of their
construction.
THE TRANSIT INSTRUMENT.
A Transit instrument is intended for observing celestial objects as
they pass across the meridian. It consists of a telescope fixed at
right angles to a horizontal axis--which axis must be so supported that
what is called _the line of collimation_, or the line of sight of the
telescope, may move in the plane of the meridian. This instrument was
first invented by Romer in the year 1689, but has since received great
improvements by Troughton, Jones and other modern artists. Transit
instruments may be divided into two classes, _Portable_, and _Fixed_.
The portable instrument, when placed truly in the meridian, and well
adjusted, may be advantageously used as a stationary instrument in an
observatory, if its dimensions be such as to admit of a telescope of
3-1/2 feet focal length; but when the main tube is only from 20 to
30 inches long, with a proportional aperture, it is more suited for
a travelling instrument to give the exact time; and, when carried on
board a ship in a voyage of discovery, may be taken on shore at any
convenient place, for determining the solar time of that place, and for
correcting the daily rate of the Chronometer giving the time at the
first meridian, so that the longitude of the place of observation may
be obtained from the difference of the observed and indicated times,
after the proper corrections have been made.
[Illustration: _figure 90._]
The following is a brief description of one of Mr. Troughton’s Portable
Transit Instruments. In fig. 90. PP is an achromatic telescope firmly
fixed, by the middle to a double conical and horizontal axis HH, the
pivots of which rest on angular bearings called Ys, at the top of
the standards B, B, rendered steady by oblique braces DD, fastened
to the central part of the circle, AA. In large fixed instruments,
the pivots and angular bearings are supported on two massive stone
pillars, sunk several feet into the ground, and are sometimes supported
by mason-work, to secure perfect stability. The axis HH has two
adjustments, one for making it exactly level, and the other for placing
the telescope in the meridian. A graduated circle L is fixed to the
extremity of the pivot which extends beyond one of the Ys, and the two
radii that carry the verniers _aa_, are fitted to the extremities of
the pivot in such a way as to turn round independent of the axis. The
double verniers have a small level attached to them, and a third arm
_b_, which is connected with the standard B by means of a screw _s_.
If the verniers are placed by means of the level, in a true horizontal
position, when the axis of the telescope is horizontal, and the arm _b_
screwed by the screw _s_ to the standard B, the verniers will always
read off the inclination of the telescope, and will enable the observer
to point it to any star, by means of its meridian altitude. The whole
instrument rests on three foot screws entered into the circle AA. In
the field of view of the telescope, there are several parallel vertical
wires, crossed at right angles with a horizontal one, and the telescope
is sometimes furnished with a diagonal eye-piece, for observing stars
near the zenith. A level likewise generally accompanies the instrument,
in order to place it horizontal, by being applied to the pivots of the
axis.
In order to fix the transit instrument exactly in the meridian, a good
clock regulated to sidereal time is necessary. This regulation may be
effected by taking equal altitudes of the sun or a star before and
after they pass the meridian, which may be done by small quadrants,
or by a good sextant. The axis H of the instrument is then to be
placed horizontal by a spirit level, which accompanies the transit,
and the greatest care must be taken that the axis of vision describes
in the heavens a great circle of the sphere. To ascertain whether the
telescope be in the plane of the meridian, observe by the clock when
a circumpolar star seen through the telescope transits both above and
below the pole; and if the times of describing the eastern and western
parts of its circuit be equal, the telescope is then in the plane of
the meridian; otherwise, certain adjustments must be made. When the
telescope is at length perfectly adjusted, a land-mark must be fixed
upon, at a considerable distance--the greater the better. This mark
must be in the horizontal direction of the intersection of the cross
wires, and in a place where it can be illuminated, if possible, in the
night time, by a lantern hanging near it; which mark being on a fixed
object, will serve at all times afterwards for examining the position
of the telescope.
Various observations and adjustments are requisite in order to fixing a
transit instrument exactly in the plane of the meridian. There is the
adjustment of the _level_--the horizontal adjustment of the axis of
the telescope--the placing of the parallel lines in the focus of the
eye-glass, so as to be truly vertical, and to determine the equatorial
value of their intervals--the collimation in _azimuth_, so that a
line passing from the middle vertical line to the optical centre of
the object-glass, is at right angles with the axis of the telescope’s
motion--the collimation in _altitude_, so that the horizontal line
should cross the parallel vertical lines, not only at right angles, but
also in the optical centre of the field of view--with various other
particulars; but of which our limited space will not permit us to enter
into details. Those who wish to enter into all the minute details in
reference to the construction and practical application of this and the
other instruments above described, as well as all the other instruments
used by the Practical Astronomer, will find ample satisfaction in
perusing the Rev. Dr. Pearson’s Introduction to Practical Astronomy,
4to., Vol. II.
A portable Transit instrument, with a cast-iron stand, the axis 12
inches in length, and the achromatic telescope about 20 inches, packed
in a case, sells at about 16 guineas: with a brass-framed stand and
other additions, at about 20 guineas. Transit instruments of larger
dimensions are higher in proportion to their size, &c.
CHAPTER III.
ON OBSERVATORIES.
In order to make observations, with convenience and effect, on the
heavenly bodies, it is expedient that an _observatory_, or place for
making the requisite observations, be erected in a proper situation.
The following are some of the leading features of a spot adapted for
making celestial observations: 1. It should command an extensive
visible horizon all around, particularly towards the south and the
north. 2. It should be a little elevated above surrounding objects.
3. It should be, if possible, at a considerable distance from
manufactories, and other objects which emit much smoke or vapour,
and even from chimney-tops where no sensible smoke is emitted, as
the heated air from the top of funnels causes undulations in the
atmosphere. 4. It should be at a distance from swampy ground or valleys
that are liable to be covered with fogs and exhalations. 5. It should
not, if possible, be too near public roads, particularly if paved with
stones, and frequented by heavy carriages, as in such situations,
undulations and tremulous motions may be produced, injurious to the
making of accurate observations with graduated instruments. 6. It is
expedient that the astronomical observer should have access to some
distant field within a mile of the observatory, on which a meridian
mark may be fixed, after his graduated instruments are properly
adjusted. The distance at which a meridian mark should be erected will
depend in part on the focal length of the telescope generally used
for making observations on the Right Ascensions and declinations of
the stars. It should be fixed at such a distance that the mark may
be distinctly seen without altering the focus of the telescope when
adjusted to the sun or stars, which, in most cases, will require to be
at least half a mile from the place of observation, and more if it can
be obtained.