SEEING AND MAGNIFICATION
Few things are more generally disappointing than one’s first glimpse
of the Heavens through a telescope. The novice is fed up with maps of
Mars as a great disc full of intricate markings, and he generally sees
a little wriggling ball of light with no more visible detail than an
egg. It is almost impossible to believe that, at a fair opposition,
Mars under the power of even the smallest astronomical telescope really
looks as big as the full moon. Again, one looks at a double star
to see not two brilliant little discs resplendent in color, but an
indeterminate flicker void of shape and hue.
The fact is, that most of the time over most of the world seeing
conditions are bad, so that the telescope does not have a fair chance,
and on the whole the bigger the telescope the worse the chance. One
famous English astronomer, possessed of a fine refractor that would be
reckoned large even now-a-days, averred that he had seen but one first
class night in fifteen years past.
The case is really much less bad than this implies, for even in rather
unfavorable climates many a night, at some o’clock or other, will
furnish an hour or two of pretty good seeing, while now and then,
without any apparent connection with the previous state of the weather,
a night will turn up when the pictures in the popular astronomies come
true, the stars shrink to steady points set in clean cut rings, and no
available power seems too high.
One can get a good idea of the true inwardness of bad seeing by trying
to read a newspaper through an opera glass across a hot stove. If the
actual movements in the atmosphere could be made visible they would
present a strange scene of turbulence—rushing currents taking devious
courses up and around obstacles, slowly moving whirlpools, upward
slants such as gulls hug on the quarter of a liner, great downward
rushes dreaded by the aviator, and over it all incessant ripples in
every direction.
And movements of air are usually associated with changes of
temperature, as over the stove, varying the refraction and contorting
the rays that come from a distant star until the image is quite ruined.
The condition for excellence of definition is that the atmosphere
through which we see shall be homogeneous, whatever its temperature,
humidity, or general trend of movement. Irregular refraction is
the thing to be feared, particularly if the variations are sudden
and frequent. Hence the common troubles near the ground and about
buildings, especially where there are roofs and chimneys to radiate
heat—even in and about an observatory dome.
Professor W. H. Pickering, who has had a varied experience in
climatic idiosyncrasies, gives the Northern Atlantic seaboard the bad
preëminence of having the worst observing conditions of any region
within his knowledge. The author cheerfully concurs, yet now and
then, quite often after midnight, the air steadies and, if the other
conditions are good, definition becomes fairly respectable, sometimes
even excellent.
Temperature and humidity as such, seem to make little difference, and a
steady breeze unless it shakes the instrument is relatively harmless.
Hence we find the most admirable definition in situations as widely
different as the Harvard station at Mandeville, Jamaica; Flagstaff,
Arizona 7000 feet up and snow bound in winter; Italy, and Egypt. The
first named is warm and with very heavy rainfall and dew, the second
dry with rather large seasonal variation of temperature, and the others
temperate and hot respectively.
Perhaps the most striking evidence of the importance of uniformity
was noted by Evershed at an Indian station where good conditions
immediately followed the flooding of the rice fields with its tendency
to stabilize the temperature. Mountain stations may be good as at
Flagstaff, Mt. Hamilton, or Mt. Wilson, or very bad as Pike’s Peak
proved to be, probably owing to local conditions.
In fact much of the trouble comes from nearby sources, atmospheric
waves and ripples rather than large movements, ripples indeed often
small compared with the aperture of the telescope and sometimes in or
not far outside of the tube itself.
Aside from these difficulties, there are still others which have to do
with the transparency of the atmosphere with respect to its suspended
matter. This does not affect the definition as such, but it cuts down
the light to a degree that may interfere seriously with the observation
of faint stars and nebulæ. The smoke near a city aggravates the
situation, but in particular it depends on general weather conditions
which may be persistent or merely temporary.
Often seeing conditions may be admirable save for this lack of
transparency in the atmosphere, so that study of the moon, of planetary
markings and even of double stars, not too faint, may go on quite
unimpeded. The actual loss of light may reach however a magnitude or
more, while the sky is quite cloudless and without a trace of fog or
noticeable haziness by day.
There have been a good many nights the past year (1921) when Alcor
(80 Ursæ Majoris) the tiny neighbor of Mizar, very nearly of the 4th
magnitude, has been barely or not at all visible while the seeing
otherwise was respectably good. Ordinarily stars of 6^_m_ should be
visible in a really clear night, and in a brilliant winter sky in the
temperate zones, or in the clear air of the tropics, a good many eyes
will do better than this, reaching 6^_m_.5 or even 7^_m_, occasionally
a bit more.
The relation of air waves and such like irregularities to telescopic
vision was rather thoroughly investigated by Douglass more than twenty
years ago (Pop. Ast. =6=, 193) with very interesting results. In
substance, from careful observation with telescopes from 4 inches up
to 24 inches aperture, he found that the real trouble came from what
one may call ripples, disturbances from say 4 inches wave length down
to ¾ inch or less. Long waves are rare and relatively unimportant
since their general effect is to cause shifting of the image as a whole
rather than the destruction of detail which accompanies the shorter
waves.
This rippling of the air is probably associated with the contact
displacements in air currents such as on a big scale become visible
in cloud forms. Clearly ripples, marked as they are by difference
of refraction, located in front of a telescope objective, produce
different focal lengths for different parts of the objective and render
a clean and stable image quite out of the question.
In rough terms Douglass found that waves of greater length than half
the aperture did not materially deteriorate the image, although they
did shift it as a whole, while waves of length less than one third the
aperture did serious mischief to the definition, the greater as the
ripples were shorter, and the image itself more minute in dimension or
detail.
Hence there are times when decreasing the aperture of an objective by
a stop improves the seeing considerably by increasing the relative
length of the air waves. Such is in fact found to be the case in
practical observing, especially when the seeing with a large aperture
is decidedly poor. In other words one may often gain more by increased
steadiness than he loses by lessened “resolving power,” the result
depending somewhat on the class of observation which chances to be
under way.
And this brings us, willy-nilly, to the somewhat abstruse matter of
resolving power, depending fundamentally upon the theory of diffraction
of light, and practically upon a good many other things that modify the
character of the diffraction pattern, or the actual visibility of its
elements.
When light shines through a hole or a slit the light waves are bent at
the margins and the several sets, eventually overlapping, interfere
with each other so as to produce a pattern of bright and dark elements
depending on the size and shape of the aperture, and distributed about
a central bright image of that aperture. One gets the effect well in
looking through an open umbrella at a distant street light. The outer
images of the pattern are fainter and fainter as they get away from the
central image.
Without burdening the reader for the moment with details to be
considered presently, the effect in telescopic vision is that a star
of real angular diameter quite negligible, perhaps 0.″001 of arc, is
represented by an image under perfect conditions like Fig. 154, of
quite perceptible diameter, surrounded by a system of rings, faint but
clear-cut, diminishing in intensity outwards. When the seeing is bad no
rings are visible and the central disc is a mere bright blur several
times larger than it ought to be.
The varying appearance of the star image is a very good index of the
quality of the seeing, so that, having a clear indication of this
appearance, two astronomers in different parts of the world can gain a
definite idea of each other’s relative seeing conditions. To this end
a standard scale of seeing, due largely to the efforts of Prof. W. H.
Pickering, has come into rather common use. (H. A. =61= 29). It is as
follows, based on observations with a 5 inch telescope.
STANDARD SCALE OF SEEING
1. Image usually about twice the diameter of the third ring.
2. Image occasionally twice the diameter of the third ring.
3. Image of about the same diameter as the third ring, and brighter at
the centre.
4. Disc often visible, arcs (of rings) sometimes seen on brighter stars.
5. Disc always visible, arcs frequently seen on brighter stars.
6. Disc always visible, short arcs constantly seen.
7. Disc sometimes sharply defined, (_a_) long arcs. (_b_) Rings
complete.
8. Disc always sharply defined, (_a_) long arcs. (_b_) Rings complete
all in motion.
9. Rings, (_a_) Inner ring stationary, (_b_) Outer rings momentarily
stationary.
10. Rings all stationary, (_a_) Detail between the rings sometimes
moving. (_b_) No detail between the rings.
The first three scale numbers indicate very bad seeing; the next two,
poor; the next two, good; and the last three, excellent. One can
get some idea of the extreme badness of scale divisions 1, 2, 3, in
realizing that the third bright diffraction ring is nearly 4 times the
diameter of the proper star-disc.
It must be noted that for a given condition of atmosphere the seeing
with a large instrument ranks lower on the scale than with a small one,
since as already explained the usual air ripples are of dimensions that
might affect a 5 inch aperture imperceptibly and a 15 inch aperture
very seriously.
Douglass (loc. cit.) made a careful comparison of seeing conditions for
apertures up to 24 inches and found a systematic difference of 2 or 3
scale numbers between 4 or 6 inches aperture, and 18 or 24 inches. With
the smallest aperture the image showed merely bodily motion due to air
waves that produced serious injury to the image in the large apertures,
as might be expected.
There is likewise a great difference in the average quality of seeing
as between stars near the zenith and those toward the horizon, due
again to the greater opportunity for atmospheric disturbances in the
latter case. Pickering’s experiments (loc. cit.) show a difference
of nearly 3 scale divisions between say 20° and 70° elevation. This
difference, which is important, is well shown in Fig. 182, taken from
his report.
The three lower curves were from Cambridge observations, the others
obtained at various Jamaica stations. They clearly show the systematic
regional differences, as well as the rapid falling off in definition
below altitude 40°, which points the importance of making provision for
comfortable observing above this altitude.
[Illustration: FIG. 182.—Variation of Seeing with Altitude.]
[Illustration: FIG. 183.—Airy’s Diffraction Pattern.]
The relation of the diffraction pattern as disclosed in the moments
of best seeing to its theoretical form is a very interesting one. The
diffraction through a theoretically perfect objective was worked out
many years ago by Sir George Airy who calculated the exact distribution
of the light in the central disc and the surrounding rings.
This is shown from the centre outwards in Fig. 183, in which the
ordinates of the curve represent relative intensities while the
abscissæ represent to an arbitrary scale the distances from the axis.
It will be at once noticed that the star image, brilliant at its
centre, sinks, first rapidly and then more slowly, to a minimum and
then very gradually rises to the maximum of the first bright ring, then
as slowly sinks again to increase for the second ring and so on.
[Illustration: FIG. 184.—Diffraction Solid for a Star.]
For unity brightness in the centre of the star disc the maximum
brightness of the first ring is 0.017, of the second 0.004 and the
third 0.0016. The rings are equidistant and the star disc has a radius
substantially equal to the distance between rings. One’s vision does
not follow down to zero the intensities of the rings or of the margin
of the disc, so that the latter has an apparent diameter materially
less than the diameter to the first diffraction minimum, and the rings
themselves look sharper and thinner than the figure would show, even
were the horizontal scale much diminished. The eye does not descend in
the presence of bright areas to its final threshold of perception.
One gains a somewhat vivid idea of the situation by passing to three
dimensions as in Fig. 184, the “diffraction solid” for a star, a
conception due to M. André (Mem. de l’Acad. de Lyon =30=, 49). Here
the solid represents in volume the whole light received and the height
taken at any point, the intensity at that point.
A cross section at any point shows the apparent diameter of the disc,
its distance to the apex the remaining intensity, and the volume above
the section the remaining total light. Substantially 85% of the total
light belongs to the central cone, for the theoretical distribution.
Granting that the eye can distinguish from the background of the sky,
in presence of a bright point, only light above a certain intensity,
one readily sees why the discs of faint stars look small, and why shade
glasses are sometimes useful in wiping out the marginal intensities
of the solid. There are physiological factors that alter profoundly
the appearance of the actual star image, despite the fact that the
theoretical diffraction image for the aperture is independent of the
star’s magnitude.
Practically the general reduction of illumination in the fainter stars
cuts down the apparent diameters of their discs, and reduces the number
of rings visible against the background of the sky.
The scale of the diffraction system determines the resolving power of
the telescope. This scale is given in Airy’s original paper (Cambr.
Phil. Trans. =1834= p. 283), from which the angle α to any maximum or
minimum in the ring system is defined by
sin α = _n_λ/_R_
in which λ is numerically the wave length of any light considered and
_R_ is the radius of the objective.
We therefore see that the ring system varies in dimension inversely
with the aperture of the objective and directly with the wave length
considered. Hence the bigger the objective the smaller the disc and
its surrounding ring system; and the greater the wave length, i.e. the
redder the light, the bigger the diffraction system. Evidently there
should be color in the rings but it very seldom shows on account of the
faintness of the illumination.
Now the factor _n_= is for the first dark ring 0.61, and for the
first bright ring 0.81, as computed from Airy’s general theory, and
therefore if we reckon that two stars will be seen as separate when
the central disc of one falls on the first dark ring of the other the
angular distance will be
Sinα = 0.61 λ/_R_′
and, taking λ at the brightest part of the spectrum i.e., about 560
μμ, in the yellow green, with α taken for sin α, we can compute this
assumed separating power for any aperture. Thus 560 μμ being very
nearly 1/45,500 inch, and assuming a 5 inch telescope, the instrument
should on this basis show as double two stars whose centres are
separated by 1.″1 of arc.
In actual fact one can do somewhat better than this, showing that
the visible diameter of the central disc is in effect less than the
diameter indicated by the diffraction pattern, owing to the reasons
already stated. Evidently the brightness of the star is a factor in the
situation since if very bright the disc gains apparent size, and when
very faint there is sufficient difficulty in seeing one star, let alone
a pair.
The most thorough investigation of this matter of resolving power was
made by the Rev. W. R. Dawes many years ago (Mem. R.A.S. =35=, 158).
His study included years of observation with telescopes of different
sizes, and his final result was to establish what has since been known
as “Dawes’ Limit.”
To sum up Dawes’ results he established the fact that on the average a
one inch aperture would enable one to separate two 6th magnitude stars
the centers of which were separated by 4.56″. Or, to generalize from
this basis, the separating power of any telescope is for very nearly
equal stars, moderately bright, 4″.56/_A_ where _A_ is the aperture of
the telescope in inches.
Many years of experience have emphasized the usefulness of this
approximate rule, but that it is only approximate must be candidly
admitted. It is a limit decidedly under that just assigned on the basis
of the theory of diffraction for the central bright wave-lengths of
the spectrum. Attempts have been made to square the two figures by
assuming in the diffraction theory a wave length of 1/55,000 inch, but
this figure corresponds to a point well up into the blue, of so low
luminosity that it is of no importance whatever in the visual use of a
telescope.
The fact is that the visibility of two neighboring bright points as
distinct, depends on a complex of physical and physiological factors,
the exact relations of which have never been unravelled. To start with
we have the principles of diffraction as just explained, which define
the relation of the stellar disc to the center of the first dark ring,
but we know that under no circumstances can one see the disc out to
this limit, since vision fails to take cognizance of the faint rim of
the image. The apparent diameter of the diffraction solid therefore
corresponds to a section taken some distance above the base, the exact
point depending on the sensitiveness of the particular observer’s eye,
the actual brilliancy of the center of the disc, and the corresponding
factors for the neighboring star.
[Illustration: FIG. 185.—Diffraction Solid for a Disc.]
Under favorable circumstances one would not go far amiss in taking the
visible diameter of the disc at about half that reckoned to the center
of the first dark ring. This figure in fact corresponds to what has
been shown to be within the grasp of a good observer under favorable
conditions, as we shall presently see.
On the other hand, if the stars are decidedly bright there is increase
of apparent diameter of the disc due to the phenomenon known as
irradiation, the spreading of light about its true image on the retina
which corresponds quite closely to the halation produced by a bright
spot on a photographic plate.
If, on the contrary, the stars are very faint the total amount of
light available is not sufficient to make contrast over and above the
background sufficient to disclose the two points as separate, while if
the pair is very unequal the brighter one will produce sufficient glare
to quite over-power the light from the smaller one so that the eye
misses it entirely.
A striking case of this is found in the companion to Sirius, an
extremely difficult object for ordinary telescopes although the
distance to the companion is about 10.6″ and its magnitude is 8.4,
making a superlatively easy double for the very smallest telescope
save for the overpowering effect of the light of the large star.
Another notoriously difficult object for small telescopes is δ Cygni, a
beautiful double of which the smaller component falls unpleasantly near
the first diffraction maximum of the primary in which it is apt to be
lost.
“Dawes’ Limit” is therefore subject to many qualifying factors. Lewis,
in the papers already referred to (Obs. =37=, 378) did an admirable
piece of investigation in going through the double star work of about
two score trained observers working with telescopes all the way from 4
inches to 36 inches aperture.
From this accumulation of data several striking facts stand out. First
there is great difference between individual observers working with
telescopes of similar aperture as respects their agreement with “Dawes’
Limit,” showing the effect of variation in the physiological factors as
well as instrumental ones.
Second, there is also a very large difference between the facility of
observing equal bright pairs and equal faint pairs, or unequal pairs of
any kind, again emphasizing the physiological as well as the physical
factors.
Finally, there is most unmistakable difference between small and large
apertures in their capacity to work up to or past the standard of
“Dawes’Limit.” The smaller telescopes are clearly the more efficient
as would be anticipated from the facts just pointed out regarding the
different effect of the ordinary and inescapable atmospheric waves on
small and large instruments.
The big telescopes are unquestionably as good optically speaking as
the small ones but under the ordinary working conditions, even as good
as those a double star observer seeks, the smaller aperture by reason
of less disturbance from atmospheric factors does relatively much the
better work, however good the big instrument may be under exceptional
conditions.
This is admirably shown by the discussion of the beautiful work of the
late Mr. Burnham, than whom probably no better observer of doubles has
been known to astronomy. His records of discovery with telescopes of
6, 9.4, 12, 18½ and 36 inches show the relative ease of working to
the theoretical limit with instruments not seriously upset by ordinary
atmospheric waves.
With the 6 inch aperture Burnham reached in the average 0.53 of Dawes’
limit, quite near the rough figure just suggested, and he also fell
well inside Dawes’ limit with the 9.4 inch instrument. With none
of the others did he reach it and in fact fell short of it by 15 to
60%. All observations being by the same notably skilled observer
and representing discoveries of doubles, so that no aid could have
been gained by familiarity, the issue becomes exceedingly plain
that size with all its advantages in resolving power brings serious
countervailing limitations due to atmosphere.
But a large aperture has besides its possible separating power one
advantage that can not be discounted in “light grasp,” the power of
discerning faint objects. This is the thing in which a small telescope
necessarily fails. The “light grasp” of the telescope obviously depends
chiefly on the area of the objective, and visually only in very minor
degree on the absorption of the thicker glass in the case of a large
lens.
According to the conventional scale of star magnitudes as now in
universal use, stars are classified in magnitudes which differ from
each other by a light ratio of 2.512. a number the logarithm of which
is 0.4, a relation suggested by Pogson some forty years ago. A second
magnitude star therefore gives only about 40% of the light of a first
magnitude star, while a third magnitude star gives again a little less
than 40% of the light of a second magnitude star and so on.
But doubling the aperture of a telescope increases the available area
of the objective four times and so on, the “light grasp” being in
proportion to the square of the aperture. Thus a 10 inch objective will
take in and deliver nearly 100 times as much light as would a 1 inch
aperture. If one follows Pogson’s scale down the line he will find that
this corresponds exactly to 5 stellar magnitudes, so that if a 1 inch
aperture discloses, as it readily does, a 9th magnitude star, a 10 inch
aperture should disclose a 14th magnitude star.
Such is substantially in fact the case, and one can therefore readily
tabulate the minimum visible for an aperture just as he can tabulate
the approximate resolving power by reference to Dawes’ limit. Fig. 186
shows in graphic form both these relations for ready reference, the
variation of resolving power with aperture, and that of “light grasp,”
reckoned in stellar magnitudes.
It is hardly necessary to state that considerable individual and
observational differences will be found in each of these cases, in the
latter amounting to not less than 0.5 to 1.0 magnitude either way.
The scale is based on the 9th magnitude star just being visible with
1 inch aperture, whereas in fact under varying conditions and with
various observers the range may be from the 8th to 10th magnitude. All
these things, however convenient, must be taken merely at their true
value as good working approximations.
Even the diffraction theory can be taken only as an approximation since
no optical surface is absolutely perfect and in the ordinary refracting
telescope there is a necessary residual chromatic aberration beside
whatever may remain of spherical errors.
[Illustration: FIG. 186.—Light-grasp and Resolving Power.]
It is a fact therefore, as has been shown by Conrady (M.N. =79=
575) following up a distinguished investigation by Lord Rayleigh
(Sci. Papers =1= 415), that a certain small amount of aberration can
be tolerated without material effect on the definition, which is
very fortunate considering that the secondary spectrum represents
aberrations of about 1/2,000 of the focal length, as we have already
seen.
The chief effect of this, as of very slight spherical aberration,
is merely to reduce the maximum intensity of the central disc of
the diffraction pattern and to produce a faint haze about it which
slightly illuminates the diffraction minima. The visible diameter
of the disc and the relative distribution of intensity in it is not
however materially changed so that the main effect is a little loss and
scattering of light.
With larger aberrations these effects are more serious but where the
change in length of optical path between the ray proceeding through the
center of the objective and that from the margin does not exceed ¼λ
the injury to the definition is substantially negligible and virtually
disappears when the image is focussed for the best definition, the loss
of maximum intensity in the star disc amounting to less than 20%.
Even twice this error is not a very serious matter and can be for
the most part compensated by a minute change of focus as is very
beautifully shown in a paper by Buxton(M. N. =81=, 547), which should
be consulted for detail of the variations to be effected.
Conrady finds a given change _dp_ in the difference in lengths of the
optical paths, related to the equivalent linear change of focus, _df_,
as follows:—
_df_ = 8_dp_(_f_/_A_)²
A being the aperture and f the focal length, which indicates for
telescopes of ordinary focal ratio a tolerance of the order of ±0.01
inch before getting outside the limit λ for variation of path.
For instruments of greater relative aperture the precision of focus
and in general the requirements for lessened aberration are far more
severe, proportional in fact to the square of this aperture. Hence
the severe demands on a reflector for exact figure. An instrument
working at F/5 or F/6 is extremely sensitive to focus and demands great
precision of figure to fall within permissible values, say ¼λ to ½λ,
for _dp_.
Further, with a given value of _dp_ and the relation established by
the chromatic aberration, _i.e._, about _f_/2000, a relation is also
determined between _f_ and _A_, required to bring the aberration within
limits. The equation thus found is
_f_ = 2.8_A_²
This practically amounts to the common F/15 ratio for an aperture of
approximately 5 inches. For smaller apertures a greater ratio can be
well used, for larger, a relatively longer focus is indicated, the
penalty being light spread into a halo over the diffraction image and
reducing faint contrasts somewhat seriously.
This is one of the factors aside from atmosphere, interfering with
the full advantage of large apertures in refractors. While as already
noted small amounts of spherical aberration may be to a certain
extent focussed out, the sign of _df_ must change with the sign of
the residual aberration, and a quick and certain test of the presence
of spherical aberration is a variation in the appearance of the image
inside and outside focus.
To emphasize the importance of exact knowledge of existing aberrations
note Fig. 187, which shows the results of Hartmann tests on a typical
group of the world’s large objectives. All show traces of residual
zones, but differing greatly in magnitude and position as the attached
scales show. The most conspicuous aberrations are in the big Potsdam
photographic refractor, the least are in the 24 inch Lowell refractor.
The former has since been refigured by Schmidt and revised data are not
yet available; the latter received its final figure from the Lundins
after the last of the Clarks had passed on.
Now a glance at the curves shows that the bad zone of the Potsdam glass
was originally near the periphery, (I), hence both involved large area
and, from Conrady’s equation, seriously enlarged _df_ due to the large
relative aperture at the zone. An aberrant zone near the axis as in the
stage (III) of the Potsdam objective or in the Ottawa 15 inch objective
is much less harmful for corresponding reasons. Such differences have
a direct bearing on the use of stops, since these may do good in case
of peripheral aberration and harm when the faults are axial. Unless
the aberrations are known no general conclusions can be drawn as to
the effect of stops. Even in the Lowell telescope shown as a whole in
Fig. 188, the late Dr. Lowell found stops to be useful in keeping down
atmospheric troubles and reducing the illumination although they could
have had no effect in relation to figure. Fig. 188 shows at the head
of the tube a fitting for a big iris diaphragm, controlled from the
eye-end, the value of which was well demonstrated by numerous observers.
There are, too, cases in which a small instrument, despite intrinsic
lack of resolving power, may actually do better work than a big one.
Such are met in instances where extreme contrast of details is
sought, as has been well pointed out by Nutting (Ap. J. =40=, 33) and
the situation disclosed by him finds amplification in the extraordinary
work done by Barnard with a cheap lantern lens of 1½ inch diameter
and 5½ inches focus (Pop. Ast., =6=, 452).
[Illustration: FIG. 187.—Hartmann Tests of Telescopes [From Hartmann’s
Measures].]
The fact is that every task must seek its own proper instrument. And in
any case the interpretation of observed results is a matter that passes
far beyond the bounds of geometrical optics, and involves physiological
factors that are dominant in all visual problems.
With respect to the visibility of objects the general diffraction
theory again comes into play. For a bright line, for example, the
diffraction figure is no longer chiefly a cone like Fig. 183,
but a similar long wedge-shaped figure, with wave-like shoulders
corresponding to the diffraction rings. The visibility of such a line
depends not only on the distribution of intensity in the theoretical
wedge but on the sensitiveness of the eye and the nature of the
background and so forth, just as in the case of a star disc.
If the eye is from its nature or state of adaptation keen enough
on detail but not particularly sensitive to slight differences of
intensity, the line will very likely be seen as if a section were made
of the wedge near its thin edge. In other words the line will appear
thin and sharp as the diffraction rings about a star frequently do.
With an eye very sensitive to light and small differences of contrast
the appearance of absolutely the same thing may correspond to a section
through the wedge near its base, in other words to a broad strip
shading off somewhat indistinctly at the edges, influenced again by
irradiation and the character of the background.
If there be much detail simultaneously visible the diffraction patterns
may be mixed up in a most intricate fashion and one can readily see the
confusion which may exist in correlating the work of various observers
on things like planetary and lunar detail.
In the planetary case the total image is a complex of illuminated
areas of diffraction at the edges, which may be represented as the
diffraction solid of Fig. 185, in which the dotted lines show what may
correspond fairly to the real diameter of the planet, the edge shading
off in a way again complicated by irradiation.
[Illustration: FIG. 188.—The Lowell Refractor Fitted with Iris
Diaphragm.]
Fancy detail superimposed on a disc of this sort and one has a vivid
idea of the difficulty of interpreting observations.
It would be an exceedingly good thing if everyone who uses his
telescope had the advantage of at least a brief course in microscopy,
whereby he would gain very much in the practical understanding of
resolving power, seeing conditions, and the interpretation of the
image. The principles regarding these matters are in fact very much the
same with the two great instruments of research.
Aperture, linear in the case of the telescope and the so-called
numerical in the case of the microscope, bear precisely the same
relation to resolution, the minimum resolvable detail being in each
case directly proportional to aperture in the senses here employed.
Further, although the turbulence of intervening atmosphere does
not interfere with the visibility of microscopic detail, a similar
disturbing factor does enter in the form of irregular and misplaced
illumination. It is a perfectly easy matter to make beautifully
distinct detail quite vanish from a microscopic image merely by
mismanagement of the illumination, just as unsteady atmosphere will
produce substantially the same effect in the telescopic image.
In the matter of magnification the two cases run quite parallel, and
magnification pushed beyond what is justified by the resolving power
of the instrument does substantially little or no good. It neither
discloses new detail nor does it bring out more sharply detail which
can be seen at all with a lower power.
The microscopist early learns to shun high power oculars, both from
their being less comfortable to work with, and from their failing to
add to the efficiency of the instrument except in some rare cases
with objectives of very high resolving power. Furthermore in the
interpretation of detail the lessons to be learned from the two
instruments are quite the same, although one belongs to the infinitely
little and the other to the infinitely great.
Nothing is more instructive in grasping the relation between resolving
power, magnification, and the verity of detail, than the study under
the microscope of some well known objects. For example, in Fig. 189
is shown a rough sketch of a common diatom, _Navicula Lyra_. The
tiny siliceous valve appears thus under an objective of slightly
insufficient resolving power. The general form of the object is
clearly perceived, as well as the central markings, standing boldly out
in the form which suggests the specific name. No trace of any finer
detail appears and no amount of dexterity in arranging the illumination
or increase of magnifying power will show any more than here appears,
the drawing being one actually made with the camera lucida, using an
objective of numerical aperture just too small to resolve the details
of the diatoms on this particular slide.
Figure 189_a_ shows what happens when, with the same magnifying power,
an objective of slightly greater aperture is employed. Here the whole
surface of the valve is marked with fine striations, beautifully
sharp and distinct like the lines of a steel engraving. There is a
complete change of aspect wrought by an increase of about 20% in the
resolving power. Again nothing further can be made out by an increase
of magnification, the only effect being to make the outlines a little
hazier and the view therefore somewhat less satisfactory.
[Illustration: FIG. 189.—The Stages of Resolution.]
Finally in Fig. 189_b_ we have again the same valve under the same
magnifying power, but here obtained from an objective of numerical
aperture 60% above that used for the main figure. The sharp striæ now
show their true character. They had their origin in lines of very
clearly distinguished dots, which are perfectly distinct, and are due
to the resolving power at last being sufficient to show the detail
which previously merely formed a sharp linear diffraction pattern
entirely incapable of being resolved into anything else by the eye,
however much it might be magnified.
Here one has, set out in unmistakable terms, the same kind of
differences which appear in viewing celestial detail through telescopes
of various aperture. What cannot be seen at all with a low aperture
may be seen with higher ones under totally different aspects; while in
each case the apparent sharpness and clarity of the image is somewhat
extraordinary.
Further in Fig. 189_b_ in using the resolving power of the objective
of high numerical aperture, the image may be quite wrecked by a little
carelessness in focussing, or by mismanagement of light, so that one
would hardly know that the valve had markings other than those seen
with the objectives of lower aperture, and under these circumstances
added magnification would do more harm than good. In precisely the same
way mismanagement of the illumination in Fig. 189_a_ would cause the
striæ to vanish and with _Navicula Lyra_, as with many other diatoms,
the resolution into striæ is a thing which often depends entirely on
careful lighting, and the detail flashes into distinctness or vanishes
with a suddenness which is altogether surprising. For “lighting” read
“atmosphere,” and you have just the sort of conditions that exist in
telescope vision.
With respect to magnifying powers what has already been said is
sufficient to indicate that on the whole the lowest power which
discloses to the eye the detail within the reach of the resolving power
of the objective is the most satisfactory.
Every increase above this magnifies all the optical faults of the
telescope and the atmospheric difficulties as well, beside decreasing
the diameter of the emergent pencil which enters the eye, and thereby
causing serious loss of acuity. For the eye like any other optical
instrument loses resolving power with decrease of effective aperture,
and, besides, a very narrow beam entering it is subject to the
interference of entoptic defects, such as floating motes and the like,
to a serious extent.
Figure 190 shows from Cobb’s experiments (Am. Jour. of Physiol., =35=,
335) the effect of reduction of ocular aperture upon acuity. The curve
shows very plainly that for emergent pencils below a millimeter (1/25
inch) in diameter, visual acuity falls off almost in direct proportion
to the decreasing aperture. Below this figure there can be only
incidental gains, such as may be due to opening up double stars and
simultaneously so diminishing the general illumination as to render the
margins of the star discs a little less conspicuous.
An emergent pencil of this diameter is not quite sufficient for the
average eye to utilize fully the available resolving power and some
excess of magnification even though it actually diminishes visual
acuity materially, may be of some service.
[Illustration: FIG. 190.—Resolving Power of the Eye.]
Increased acuity will of course be gained for the same magnification
in using an objective of greater diameter, to say nothing of increased
resolving power, at the cost, of course, of relatively greater
atmospheric troubles.
To come down to figures as to the resolving power of the eye, often
repeated experiments have shown that two points offering strong
contrast with the background can be noted as separate by the normal eye
when at an angular separation of about 3′ of arc. People, as we have
seen, differ considerably in acuity so that now and then individuals
will considerably better this figure, while others, far less keen
sighted, may require a separation of 4′ or even 5′.
The pair of double stars ε_{1}, ε_{2}, Lyræ, separated by 3′ 27″
mags. nearly 4 and 5 respectively, can be seen as separate by those
of fairly keen vision, while Mizar and Alcor, 11′ apart, seem thrown
wide to nearly every one. On the other hand the writer has never known
anybody who could separate the two components of Asterope of the
Pleiades, distant a scant 2½ but of mags. 6.5 and 7.0 only, while
Pleione and Atlas, distance about 5¼′, mags. 6.5 and 4, are very
easy.
Assuming for liberality that the separation constant is in the
neighborhood of 5′ one can readily estimate the magnification that for
any telescope will take full advantage of its resolving power. As we
have already seen this resolving power is practically 4.″56/_A_ for
equal stars moderately bright. An objective of 4.56′ inches aperture
has a resolving constant of 1″ and to develop this should take a
magnification of say 300, about 65 to the inch of aperture, requiring a
focal length of ocular about 0.20 to 0.25 inch for telescopes of normal
relative aperture, and pushing the emergent pencil down to little more
than 0.02 inch,—rather further than is physiologically desirable.
Except for these extreme stunts of separation, half to two thirds this
power is preferable and conditions under which one can advantageously
go above this limit are very rare indeed.
A thoroughly good objective or mirror will stand quite 100
magnification to the inch without, as the microscopist would say,
“breaking down the image,” but in at least nine cases out of ten the
result will be decidedly unsatisfactory.
As the relative aperture of the instrument increases, other things
being equal, one is driven to oculars of shorter and shorter focus
to obtain the same magnification and soon gets into trouble. Very
few oculars below 0.20 inch in focus are made, and such are rarely
advisable, although occasionally in use down to 0.15 inch or
thereabouts. The usual F/15 aperture is a figure quite probably as much
due to the undesirability of extremely short focus oculars as to the
easier corrections of the objective.
In the actual practice of experienced observers the indications of
theory are well borne out. Data of the habits of many observers of
double stars are of record and the accomplished veteran editor of _The
Observatory_, Mr. T. Lewis, took the trouble in one of his admirable
papers on “Double Star Astronomy” (Obs. =36=, 426) to tabulate from the
original sources the practice of a large group of experts. The general
result was to show the habitual use with telescopes of moderate size
of powers around 50 per inch of aperture, now and then on special
occasions raised to the neighborhood of 70 per inch.
But the data showed unequivocally just what has been already indicated,
that large apertures, suffering severely as they generally do from
turbulence of the air, will not ordinarily stand their due proportion
of magnification. With the refractors of 24 inches aperture and
upwards the records show that even in this double star work, where, if
anywhere, high power counts, the general practice ran in the vicinity
of 30 per inch of aperture.
Analyzing the data more completely in this respect Mr. Lewis found that
the best practise of the skilled observers studied was approximately
represented by the empirical equation
_m_ = 140 √_A_
Of course the actual figures must vary with the conditions of location
and the general quality of the seeing, as well as the work in hand. For
other than double star work the tendency will be generally toward lower
powers. The details which depend on shade perception rather than visual
acuity are usually hurt rather than helped when magnified beyond the
point at which they are fairly resolved, quite as in the case of the
microscope.
Now and then they may be made more distinct by the judicious use of
shade glasses. Quite apart from the matter of the high powers which can
advantageously be used on a telescope, one must for certain purposes
consider the lowest powers which are fairly applicable. This question
really turns on the largest utilizable emergent pencil from the eye
piece. It used to be commonly stated that ⅛ inch for the emergent
pencil was about a working maximum, leading to a magnification of 8
per inch of aperture of the objective. This in view of our present
knowledge of the eye and its properties is too low an estimate of
pupillary aperture. It is a fact which has been well known for more
than a decade that in faint light, when the eye has become adapted to
its situation, the pupil opens up to two or three times this diameter
and there is no doubt that a fifth or a fourth of an inch aperture
can be well utilized, provided the eye is properly dark-adapted. For
scrutinizing faint objects, comet sweeping and the like, one should
therefore have one ocular of very wide field and magnifying power of 4
or 5 per inch of aperture, the main point being to secure a field as
wide is practicable. One may use for such purposes either a very wide
field Huyghenian, or, if cross wires are to be used, a Kellner form.
Fifty degrees of field is perfectly practicable with either. As regards
the rest of the eyepiece equipment the observer may well suit his own
convenience and resources. Usually one ocular of about half the maximum
power provided will be found extremely convenient and perhaps oftener
used than either the high or low power. Oculars of intermediate power
and adapted for various purposes will generally find their way into any
telescopic equipment. And as a last word do not expect to improve bad
conditions by magnifying. If the seeing is bad with a low power, cap
the telescope and await a better opportunity.
APPENDIX
WORK FOR THE TELESCOPE
To make at first hand the acquaintance of the celestial bodies is, in
and of itself, worth the while, as leading the mind to a new sense of
ultimate values. To tell the truth the modern man on the whole knows
the Heavens less intimately than did his ancestors. He glances at his
wrist-watch to learn the hour and at the almanac to identify the day.
The rising and setting of the constellations, the wandering of the
planets among the stars, the seasonal shifting of the sun’s path—all
these are a sealed book to him, and the intricate mysteries that lie in
the background are quite unsuspected.
The telescope is the lifter of the cosmic veil, and even for merely
disclosing the spectacular is a source of far-reaching enlightenment.
But for the serious student it offers opportunities for the genuine
advancement of human knowledge that are hard to underestimate. It is
true that the great modern observatories can gather information on
a scale that staggers the private investigator. But in this matter
fortune favors the pertinacious, and the observer who settles to a line
of deliberate investigation and patiently follows it is likely to find
his reward. There is so much within the reach of powerful instruments
only, that these are in the main turned to their own particular spheres
of usefulness.
For modest equipment there is still plenty of work to do. The study
of variable stars offers a vast field for exploration, most fruitful
perhaps with respect to the irregular and long-period changes of which
our own Sun offers an example. Even in solar study there are transient
phenomena of sudden eruptions and of swift changes that escape the eye
of the spectro-heliograph, and admirable work can be done, and has been
done, with small telescopes in studying the spectra of sun spots
Temporary stars visible to the naked eye or to the smallest instruments
turn up every few years and their discovery has usually fallen to the
lot of the somewhat rare astronomer, professional or amateur, who knows
the field of stars as he knows the alphabet. The last three important
novæ fell to the amateurs—two to the same man. Comets are to be had
for the seeking by the persistent observer with an instrument of fair
light-grasp and field; one distinguished amateur found a pair within a
few days, acting on the theory that small comets are really common and
should be looked for—most easily by one who knows his nebulæ, it should
be added.
And within our small planetary system lies labor sufficient for
generations. We know little even about the superficial characters of
the planets, still less about their real physical condition. We are not
even sure about the rotation periods of Venus and Neptune. The clue to
many of the mysteries requires eternal vigilance rather than powerful
equipment, for the appearance of temporary changes may tell the whole
story. The old generation of astronomers who believed in the complete
inviolability of celestial order has been for the most part gathered to
its fathers, and we now realize that change is the law of the universe.
Within the solar system there are planetary surfaces to be watched,
asteroids to be scanned for variability or change of it, meteor swarms
to be correlated with their sources, occultations to be minutely
examined, and when one runs short of these, our nearest neighbor the
Moon offers a wild and physically unknown country for exploration. It
is suspected with good reason of dynamic changes, to say nothing of the
possible last remnants of organic life.
Much of this work is well within the useful range of instruments of
three to six inches aperture. The strategy of successful investigation
is in turning attention upon those things which are within the scope of
one’s equipment, and selecting those which give promise of yielding to
a well directed attack. And to this end efforts correlated with those
of others are earnestly to be advised. It is hard to say too much of
the usefulness of directed energies like those of the Variable Star
Association and similar bodies. They not only organize activities to
an important common end, but strengthen the morale of the individual
observer.
INDEX
A
Abbé, roof prism, 162
Aberration, compensated by minute change of focus, 266
illuminates the diffraction minima, 265
relation determines of focus and aperture, 266
Achromatic long relief ocular, 146
objective, 77
Achromatism, condition for, 78
determination of, 78
imperfection of, 87
Adjustment where Polaris invisible, 235
Air waves, length of, 255
Alt-azimuth mount for reflector, 102
mounts, with slow motions, 102
setting up an, 228
Anastigmats, 84
Annealing, pattern of strain, 68
Astigmatism, 84, 209
of figure, 210
Astronomy, dawn of popular, 19
B
Bacon, Roger, alleged description of telescopes, 6
Barlow lens, 152
“Bent,” objective, 86
Binocular, 2
advantage of, exaggerated, 151
for strictly astronomical use, 152
telescopes for astronomical use, 163
C
Camouflage, in optical patents, 97
Cassegrain, design for reflecting telescope, 22
Cassegrain, sculptor and founder of statues, 22
Cell, taking off from a telescope, 202
Chromatic aberration, 11, 76
investigation of, 210
correction, differences in, 91
error of the eye, 90
Clairault’s condition, 81
two cemented forms for, 81
Clarks, portable equatorial mounting, 109
terrestrial prismatic eyepiece, 158
Clock, the cosmic, 233
Clock drive, 110, 174
Clock mechanism, regulating rate of motor, 179
Coddington lens, 137
Cœlostat constructions, 126
tower telescopes, 127
Color correction, commonly used, 211
examined by spectroscope, 211
of the great makers, 90
Coma-free, condition combined with Clairault’s, 83
Comet seeker, Caroline Herschel’s 118
seekers with triple objective, 119
Crowns distinguished from flints, 64
Curves, struggle for non-spherical, 18
D
Davon micro-telescope, 148
Dawes’ Limit, 261
in physiological factors, 263
Declination circle, 108
adjustment of, 239
Declination circle, adjustment by, 237
facilitates setting up instrument, 110
Definition condition for excellence of, 254
good in situations widely different, 254
DeRheita, 12
constructed binoculars, 13
terrestrial ocular, 13
Descartes’ dioptrics, publication of, 11
lens with elliptical curvature, 12
Dew cap, 219
Diaphragms, importance of, 43
Diffraction figure for bright line, 269
pattern, 256
solid, apparent diameter of, 262
solid of planet, 269
solid for a star, 260
spectra, 190
system, scale of, 260
varies inversely with aperture, 260
through objective, 258
Digges, account suggests camera obscura, 7
Dimensions, customary, telescope of, 24
Discs, inspection of glass, 66
roughing to form, 69
Distortion, 86
Dolland, John, 28
published his discovery of achromatism, 29
Peter, early triple objective, 29
Dome wholly of galvanized iron, 250
Domes, 246
Driving clock, a simple, 174
pendulum controlled, 177
clocks spring operated, 175
E
English equatorial, 110
mounts, mechanical stability of, 113
Equatorial, adjustments of, 230
Equatorial, coudé, 124
mount, different situations in using, 229
mount, first by Short, 104
mount, pier overhung, 115
mount in section, 107
two motions necessary in, 106
Equilibrating levers, devised by T. Grubb, 39
Evershed, direct vision solar spectroscope, 189
Eye lens, simple, preferred by Sir W. Herschel, 136
Eyepiece, compensating, 142
Huygenian, 139
Huygenian, achromatism of, 140
Huygenian, with cross wires, 140
Huygenian, field of, 141
Huygenian focal length of, 143
measuring focus of, 136
microscope form, 147, 148
monocentric, 139
a simple microscope, 134
Tolles solid, 141
F
Field, curvature of, 85
glass, arrangement of parts, 151
Galilean, 150
lens diameter possible, 150
Field lens, 139
Figuring locally, 73
process of, 73
Filar micrometer, 172
Finder, 108, 132
adjustment of, 230
Fine grinding, 69
Fixed eyepiece mounts, 118
Flints, highly refractive due to Guinand, 36
Foucault, 39
development of silver on glass reflector, 41
knife edge test, 212
Foucault, methods of working and testing, 41
Fraunhofer, 36
applied condition of absence of coma, 82
form of objectives, 37
long list of notable achievements, 38
“Front view” telescope, 32
mechanical difficulty of, 33
Furnaces, glass, classes of, 59
G
Galilean telescope, small field of, 9
Galileo, exhibited telescope to senators of Venice, 8
grasps the general principles, 7
produces instrument magnifying 32 times, 8
Gascoigne, William, first using genuine micrometer, 12
Gauss, Objective, 82
Gerrish, application of drive, 181
motor drive, 179
Ghosts, 137
Glass, dark, as sunshade, 166
forming and annealing, 62
inspection of raw, 61
losses by volatilization, 58
materials of, 59
origin of, 57
persistent bubbles in, 58
a solid solution, 57
Grating spectroscopes, 190
Gratings, spectroscope, 189
Gregory, James, described construction which bears his name, 19
failed of material success, 20
Grubb, Sir Howard, objectives, 74
Guinand, Pierre Louis, improvements in optical glass, 36
H
Hadley, disclosed test for true figure, 27
John, real inventor of reflector, 25
Hadley’s reflector, tested with satisfactory results, 26
Hall, Chester Moor, designed first achromatic telescope, 27
had telescopes made as early as 1733, 27
Hand telescope, magnifying power, 150
monocular, 151
Hartmann test, 213
on large objectives, 267
principle of, 214
Hartness, turret telescope, 130, 131
Heliometer, principle of, 171
Hensoldt, prism form, 163
Herschel’s discovery of Uranus, 32
forty foot telescope, 34
Sir John, 35
Sir John, proposed defining condition, 81
Sir William, 31
Herschel’s time, instruments of, 35
Hevelius, construction for objective of 150 feet, 17
directions for designing Galilean and Keplerian telescopes, 14
invention of first periscope, 15
Johannes, 13
mention of advantage of plano convex lens, 14
mentions telescope due to DeRheita, 14
Housing reflector of 36 inch aperture, 243
rolling on track, 242
simplest instrument for fixed, 241
Huygens, Christian, devised methods of grinding & polishing, 16
Huygens’ eyepiece, introduction of, 24
Huygens, sketch of Mars, 16
I
Image, correct extra focal, 208
critical examination of, 204
Image, curvature of, 87
seen without eyepiece, 134
showing unsymmetrical coloring, 208
Interference rings, eccentric, 205
Irradiation, 262
J
Jansen, Zacharius, 4
K
Kellner, ocular, 145
Kepler, astronomical telescope, 10
differences of from Galilean form, 10
Knife edge test of parabolic mirror, 212
L
Lacquer, endurance of coating, 223
Latitude scale, 232
Lenses, determinate forms for, 80
Lens, magnifying power of, 134
“crossed,” 24
polishing the fine ground, 70
power of, 78
triple cemented, a useful ocular, 138
simple achromatic, 137
single, has small field, 137
spotted, cleaning of, 217
Light grasp and resolving power, 265
small telescope fails in, 264
Light ratio of star magnitudes, 264
Light transmitted by glass, 53
Lippershey, Jan, 2
discovery, when made, 5
retainer to, 3
Lunette à Napoleon Troisiéme, 154, 155, 162
M
Magnifying power, directly as ratio of increase in tangent, 135
powers, increase of, 273
Marius, Simon, 5
used with glasses from spectacles, 5
Marius, picked up satellites of Jupiter, 5
Meridian photometer, 194
Metius, James, 4
Metius, tale of, 4
Micrometer, double image, 171
square bar, 171
Micrometers, 168
Micrometry, foundations of, 12
Mirror’s, aberrations of, 92
adjustment of, 206
concave spherical, 92
final burnishing of, 226
hyperboloidal, 96
lacquer coating for surface, 221
mounting, by Browning, 49
parabolic oblique, shows aberration, 95
surface, prevention of injury to, 220
Mittenzwey ocular, 141
Mountain stations, good or very bad, 254
Mounts, alt-azimuth and equatorial, 98
Myopia, glasses for, came slowly, 2
N
Navicula Lyra, stages of resolution of, 271
Newton, abandoned parabolic mirror, 21
blunder in experiment, 20
gave little information about material for mirrors, 23
Isaac, attempt at a reflector, 20
Normal spectra, 190
O
Objective, adjustable mount for, 44
adjusting screws of, 44
Clark’s form, 83
cleansing, 203
examination of, 202
Objective, four-part, 85
Fraunhofer flint-ahead, 83
how to clean, 216
spacers, to take out, 217
typical striæ in, 203
Objective prism, photographing with, 185, 187
Objectives, crown glass equiconvex, 80
over-achromatized, 90
rated on focal length for green 24
Observatories, cost of Romsey, 252
Observatory at small expense, 249
Romsey, description of, 249
with simple sliding roof, 245
Observing box, 229
Oblique fork alt-azimuth, 100
Ocular, apparent angular field of, 146
terrestrial, 147
Tolles terrestrial, 147
typical form, 45
Oculars, radius of curvature of image in, 146
undesirability of short focus, 275
Open fork mount, 115
well suited to big reflectors, 117
Optical axis, to adjust declination of, 238
Optical glass, classes of, 63
data and analysis of, 64
industry, due to single man, 36
production of, 60
Orthoscopic ocular, 145
P
Parallactic mount, 104
Petition for annulment of Dolland’s patent, 29
Photometer, artificial star Zöllner, 194
extinction, 198
photoelectric cell, 199
precision of astronomical, 199
selenium cell, 199
Zöllner, 197
Photometers, three classes in stellar, 193
“Photo-visual, objective,” 89
Pillar-and-claw stand, 98
Pillar mount, 240
Pitch, optician’s, 71
Placement for tripod legs, 236
Polar and coudé forms of reflector, 125
axis, adjustment of by level, 232
axis, alignment to meridian, 232
axis, setting with finder altitude of, 234
telescope, 119, 122
Polaris, hour angle of, 233
a variable star, 199
Polarizing photometer, 193
Pole, position, 234
Polishing machine, 70
surface of tool, 72
tool, 71
Porro’s second form, 157
work, original description of, 156
Porta, description unintelligible, 7
Portable equatorial, adjustment of, 230
telescopes, mounting of, 228
Porter polar reflector, 130
Position angle micrometer of Lowell Observatory, 173
Powers, lowest practicable, 276
Prismatic inversion, Porro’s first form, 155
Prismatic inverting system, the first, 154
Prisms, Dove’s, 154
Prism field glasses, stereoscopic effect of, 159
Prism glass, 152
loss of light in, 160
objectives of, 161
weak points of, 160
R
Resolving constant, magnification to develop, 275
power and verity of detail, 2
power of the eye, 274
Reticulated micrometer, 169
Reversion prism, 153
Right ascension circle, 108
Ring micrometer, 169
computation of results of, 170
Ring system faults due to strain, 205
“Romsey” observatory type, 248
Rack motion in altitude, 100
Ramsden, ocular, 144
Reflection, coefficient of, from silvered surface, 54
Reflector costs, 55
cover for, 242
development in England, 41
for astrophysical work, 56
light-grasp of, 53
relative aperture of, 50
section of Newtonian, 45
skeleton construction, 49
suffers from scattered light, 56
working field of, 55
Refractive index, 63
Refractors and reflectors, relative advantages of, 52
few made after advent of reflector, 27
in section, 43
light transmission of, 53
Refractors, relative equivalent apertures of, 54
tubes of, 42
S
Scheiner, Christopher, use of Kepler’s telescope, 11
devised parallactic mount, 11
Secondary spectrum, 87
new glasses reducing, 88
Seeing, 257
conditions, for difference of aperture, 257
conditions generally bad, 253
standard scale of, 256
true inwardness of bad, 253
Separating power, to compute, 261
Short, James, mastered art of figuring paraboloid, 27
took up Gregorian construction with success, 27
Shortened telescope, 152
Sights, on portable mount, 229
Silver films, condition of, 54
Silvering, Ludin’s process, 225
processes, 222
process, Dr. Brashear’s, 222
Sine condition, Abbé’s, 82
Slit, spectroscope, Abbé type, 184
Snow cœlostat telescope, 127
Solar diagonal, 166
eye piece diaphragms in, 168
early spectroscopes, 188
polarizing eyepiece, 167
spectroscope, 187
Spacers, 44, 218
Spectacle lenses, combination of, 2
Spectacles for presbyopia, 2
invention of, 1
Spectra, visibility of stellar, 183
Spectro-heliograph, principle of, 191
simple type of Hale’s, 191
Spectroscope, 182
construction of astronomical, 182
of Lowell refractor, 185
ocular, McClean form, 183
Specula, small, methods of support, 49
Speculum metal composition of, 24
Sphenoid prisms, 158, 163
Spherical aberration, 11
amount of, 80
annulling in both directions, 84
examination for, 207
quick test of, 267
remedy for, 79
concave mirror, errors of, 22
Star, appearance of, 204
artificial, 66, 203
diagonal, 165
disc, apparent diameter of, 259
image of reflector, 206
Steinheil, achromatic ocular, 144
Karl August, silvering specula, 39
Striæ, location of, 67
Surface, treatment of deterioration of, 218
T
Taylor, triplets with reduced secondary spectrum, 89
Telescopes, choice and purchase of, 201
Early in 1610 made in England, 6
first, 3
the first astronomical, 9
improvement of early, 11
lineage of, 1
name devised, 9
Telescopes, portable and fixed, 108
1609, for sale in Paris, 5
size and mounting of early, 14
Telescopic vision, discovery of, 2
Templets, designed curves of, 69
Tests for striæ and annealing, 68
Transparency, lack of in atmosphere, 255
Triplet, cemented, 85
Turret housing of reflector, 244
V
Variable stars, 192
W
Wedge calibrated by observation, 197
photographic, 197
photometer, 197
Wind, shelter from, 240
Z
Zeiss, binocular of extreme stereoscopic effect, 161
Zöllner, photometer modification of, 198
Zonal aberration, 209
* * * * *
Transcriber's Notes
Obvious typographical errors have been silently corrected. Variations
in hyphenation and accents have been standardised but all other
spelling and punctuation remains unchanged.
Italics are represented thus _italic_, bold thus =bold=, subscript thus
_{s} and underline thus underline=.
In caption of Fig. 49.—Spherical Aberration of Concave Lens. Concave
has been changed to Convex
In “An objective of 4.56′ inches aperture has a resolving constant of
1″ and to develop this should take a magnification of say 300,” 1″ has
been hand altered in the original and may be 1′.
The table “Characteristics of Optical Glasses″ has been divided to fit
within the width restriction.