Richard A. Proctor - Half hours with the Telescope
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Richard A. Proctor >> Half hours with the Telescope
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The peculiarities to be noted are the _curvature_, _indistinctness_, and
_false colouring_ of the image.
The curvature of the image is the least important of the three defects
named--a fortunate circumstance, since this defect admits neither of
remedy nor modification. The image of a distant object, instead of lying
in a plane, that is, forming what is technically called a _flat field_,
forms part of a spherical surface whose centre is at the centre of the
object-glass. Hence the centre of the field of view is somewhat nearer
to the eye than are the outer parts of the field. The amount of
curvature clearly depends on the extent of the field of view, and
therefore is not great in powerful telescopes. Thus, if we suppose that
the angular extent of the field is about half a degree (a large or
low-power field), the centre is nearer than the boundary of the field by
about 1-320th part only of the field's diameter.
The indistinctness of the image is partly due to the obliquity of the
pencils which form parts of the image, and partly to what is termed
_spherical aberration_. The first cause cannot be modified by the
optician's skill, and is not important when the field of view is small.
Spherical aberration causes those parts of a pencil which fall near the
boundary of a convex lens to converge to a nearer (_i.e._ shorter) focus
than those which fall near the centre. This may be corrected by a proper
selection of the forms of the two lenses which replace, in all modern
telescopes, the single lens hitherto considered.
The false colouring of the image is due to _chromatic aberration_. The
pencil of light proceeding from a point, converges, not to one point,
but to a short line of varying colour. Thus a series of coloured images
is formed, at different distances from the object-glass. So that, if a
screen were placed to receive the mean image _in focus_, a coloured
fringe due to the other images (_out of focus, and therefore too large_)
would surround the mean image.
Newton supposed that it was impossible to get rid of this defect, and
therefore turned his attention to the construction of reflectors. But
the discovery that the _dispersive_ powers of different glasses are not
proportional to their reflective powers, supplied opticians with the
means of remedying the defect. Let us clearly understand what is the
discovery referred to. If with a glass prism of a certain form we
produce a spectrum of the sun, this spectrum will be thrown a certain
distance away from the point on which the sun's rays would fall if not
interfered with. This distance depends on the _refractive_ power of the
glass. The spectrum will have a certain length, depending on the
_dispersive_ power of the glass. Now, if we change our prism for another
of exactly the same shape, but made of a different kind of glass, we
shall find the spectrum thrown to a different spot. If it appeared that
the length of the new spectrum was increased or diminished in exactly
the same proportion as its distance from the line of the sun's direct
light, it would have been hopeless to attempt to remedy chromatic
aberration. Newton took it for granted that this was so. But the
experiments of Hall and the Dollonds showed that there is no such strict
proportionality between the dispersive and refractive powers of
different kinds of glass. It accordingly becomes possible to correct the
chromatic aberration of one glass by superadding that of another.
[Illustration: _Fig. 4._]
This is effected by combining, as shown in fig. 4, a convex lens of
_crown_ glass with a concave lens of _flint_ glass, the convex lens
being placed nearest to the object. A little colour still remains, but
not enough to interfere seriously with the distinctness of the image.
But even if the image formed by the object-glass were perfect, yet this
image, viewed through a single convex lens of short focus placed as in
fig. 1, would appear curved, indistinct, coloured, and also _distorted_,
because viewed by pencils of light which do not pass through the centre
of the eye-glass. These effects can be diminished (but not entirely
removed _together_) by using an _eye-piece_ consisting of two lenses
instead of a single eye-glass. The two forms of eye-piece most commonly
employed are exhibited in figs. 5 and 6. Fig. 5 is Huyghens' eye-piece,
called also the _negative_ eye-piece, because a real image is formed
_behind_ the _field-glass_ (the lens which lies nearest to the
object-glass). Fig. 6 represents Ramsden's eye-piece, called also the
_positive_ eye-piece, because the real image formed by the object-glass
lies _in front of_ the field-glass.
[Illustration: _Fig. 5._]
[Illustration: _Fig. 6._]
The course of a slightly oblique pencil through either eye-piece is
exhibited in the figures. The lenses are usually plano-convex, the
convexities being turned towards the object-glass in the negative
eye-piece, and towards each other in the positive eye-piece. Coddington
has shown, however, that the best forms for the lenses of the negative
eye-piece are those shown in fig. 5.
The negative eye-piece, being achromatic, is commonly employed in all
observations requiring distinct vision only. But as it is clearly unfit
for observations requiring micrometrical measurement, or reference to
fixed lines at the focus of the object-glass, the positive eye-piece is
used for these purposes.
For observing objects at great elevations the diagonal eye-tube is
often convenient. Its construction is shown in fig. 7. ABC is a totally
reflecting prism of glass. The rays from the object-glass fall on the
face AB, are totally reflected on the face BC, and emerge through the
face AC. In using this eye-piece, it must be remembered that it
lengthens the sliding eye-tube, which must therefore be thrust further
in, or the object will not be seen in focus. There is an arrangement by
which the change of direction is made to take place between the two
glasses of the eye-piece. With this arrangement (known as the _diagonal
eye-piece_) no adjustment of the eye-tube is required. However, for
amateurs' telescopes the more convenient arrangement is the diagonal
eye-tube, since it enables the observer to apply any eye-piece he
chooses, just as with the simple sliding eye-tube.
[Illustration: _Fig. 7._]
We come next to the important question of the _mounting_ of our
telescope.
The best known, and, in some respects, the simplest method of
mounting a telescope for general observation is that known as the
_altitude-and-azimuth_ mounting. In this method the telescope is
pointed towards an object by two motions,--one giving the tube the
required _altitude_ (or elevation), the other giving it the required
_azimuth_ (or direction as respects the compass points).
For small alt-azimuths the ordinary pillar-and-claw stand is
sufficiently steady. For larger instruments other arrangements are
needed, both to give the telescope steadiness, and to supply slow
movements in altitude and azimuth. The student will find no difficulty
in understanding the arrangement of sliding-tubes and rack-work commonly
adopted. This arrangement seems to me to be in many respects defective,
however. The slow movement in altitude is not uniform, but varies in
effect according to the elevation of the object observed. It is also
limited in range; and quite a little series of operations has to be gone
through when it is required to direct the telescope towards a new
quarter of the heavens. However expert the observer may become by
practice in effecting these operations, they necessarily take up some
time (performed as they must be in the dark, or by the light of a small
lantern), and during this time it often happens that a favourable
opportunity for observation is lost.
These disadvantages are obviated when the telescope is mounted in such a
manner as is exhibited in fig. 8, which represents a telescope of my own
construction. The slow movement in altitude is given by rotating the rod
_he_, the endless screw in which turns the small wheel at _b_, whose
axle in turn bears a pinion-wheel working in the teeth of the quadrant
_a_. The slow movement in azimuth is given in like manner by rotating
the rod _h'e'_, the lantern-wheel at the end of which turns a
crown-wheel on whose axle is a pinion-wheel working in the teeth of the
circle _c_. The casings at _e_ and _e'_, in which the rods _he_ and
_h'e'_ respectively work, are so fastened by elastic cords that an
upward pressure on the handle _h_, or a downward pressure on the handle
_h'_, at once releases the endless screw or the crown-wheel
respectively, so that the telescope can be swept at once through any
desired angle in altitude or azimuth. This method of mounting has other
advantages; the handles are conveniently situated and constant in
position; also, as they do not work directly on the telescope, they can
be turned without setting the tube in vibration.
[Illustration: _Fig. 8._]
I do not recommend the mounting to be exactly as shown in fig. 8. That
method is much too expensive for an alt-azimuth. But a simple
arrangement of belted wheels in place of the toothed wheels _a_ and _c_
might very readily be prepared by the ingenious amateur telescopist; and
I feel certain that the comfort and convenience of the arrangement would
amply repay him for the labour it would cost him. My own
telescope--though the large toothed-wheel and the quadrant were made
inconveniently heavy (through a mistake of the workman who constructed
the instrument)--worked as easily and almost as conveniently as an
equatorial.
Still, it is well for the observer who wishes systematically to survey
the heavens--and who can afford the expense--to obtain a well-mounted
_equatorial_. In this method of mounting, the main axis is directed to
the pole of the heavens; the other axis, at right angles to the first,
carries the telescope-tube. One of the many methods adopted for mounting
equatorials is that exhibited--with the omission of some minor
details--in fig. 9. _a_ is the polar axis, _b_ is the axis (called the
declination axis) which bears the telescope. The circles _c_ and _d_
serve to indicate, by means of verniers revolving with the axes, the
motion of the telescope in right ascension and declination,
respectively. The weight _w_ serves to counterpoise the telescope, and
the screws _s_, _s_, _s_, _s_, serve to adjust the instrument so that
the polar axis shall be in its proper position. The advantage gained by
the equatorial method of mounting is that only one motion is required to
follow a star. Owing to the diurnal rotation of the earth, the stars
appear to move uniformly in circles parallel to the celestial equator;
and it is clear that a star so moving will be kept in the field of
view, if the telescope, once directed to the star, be made to revolve
uniformly and at a proper rate round the polar axis.
[Illustration: _Fig. 9._]
The equatorial can be directed by means of the circles _c_ and _d_ to
any celestial object whose right ascension and declination are known. On
the other hand, to bring an object into the field of view of an
alt-azimuth, it is necessary, either that the object itself should be
visible to the naked eye, or else that the position of the object should
be pretty accurately learned from star-maps, so that it may be picked up
by the alt-azimuth after a little searching. A small telescope called a
_finder_ is usually attached to all powerful telescopes intended for
general observation. The finder has a large field of view, and is
adjusted so as to have its axis parallel to that of the large telescope.
Thus a star brought to the centre of the large field of the finder
(indicated by the intersection of two lines placed at the focus of the
eye-glass) is at, or very near, the centre of the small field of the
large telescope.
If a telescope has no finder, it will be easy for the student to
construct one for himself, and will be a useful exercise in optics. Two
convex lenses not very different in size from those shown in fig. 1, and
placed as there shown--the distance between them being the sum of the
focal lengths of the two glasses--in a small tube of card, wood, or tin,
will serve the purpose of a finder for a small telescope. It can be
attached by wires to the telescope-tube, and adjusted each night before
commencing observation. The adjustment is thus managed:--a low power
being applied to the telescope, the tube is turned towards a bright
star; this is easily effected with a low power; then the finder is to be
fixed, by means of its wires, in such a position that the star shall be
in the centre of the field of the finder when also in the centre of the
telescope's field. When this has been done, the finder will greatly help
the observations of the evening; since with high powers much time would
be wasted in bringing an object into the field of view of the telescope
without the aid of a finder. Yet more time would be wasted in the case
of an object not visible to the naked eye, but whose position with
reference to several visible stars is known; since, while it is easy to
bring the point required to the centre of the _finder's_ field, in which
the guiding stars are visible, it is very difficult to direct the
_telescope's_ tube on a point of this sort. A card tube with wire
fastenings, such as we have described, may appear a very insignificant
contrivance to the regular observer, with his well-mounted equatorial
and carefully-adjusted finder. But to the first attempts of the amateur
observer it affords no insignificant assistance, as I can aver from my
own experience. Without it--a superior finder being wanting--our
"half-hours" would soon be wasted away in that most wearisome and
annoying of all employments, trying to "pick up" celestial objects.
It behoves me at this point to speak of star-maps. Such maps are of many
different kinds. There are the Observatory maps, in which the places of
thousands of stars are recorded with an amazing accuracy. Our beginner
is not likely to make use of, or to want, such maps as these. Then there
are maps merely intended to give a good general idea of the appearance
of the heavens at different hours and seasons. Plate I. presents four
maps of this sort; but a more complete series of eight maps has been
published by Messrs. Walton and Maberly in an octavo work; and my own
'Constellation-Seasons' give, at the same price, twelve quarto maps (of
four of which those in Plate I. are miniatures), showing the appearance
of the sky at any hour from month to month, or on any night, at
successive intervals of two hours. But maps intermediate in character to
these and to Observatory maps are required by the amateur observer.
Such are the Society's six gnomonic maps, the set of six gnomonic maps
in Johnstone's 'Atlas of Astronomy,' and my own set of twelve gnomonic
maps. The Society's maps are a remarkably good set, containing on the
scale of a ten-inch globe all the stars in the Catalogue of the
Astronomical Society (down to the fifth magnitude). The distortion,
however, is necessarily enormous when the celestial sphere is presented
in only six gnomonic maps. In my maps all the stars of the British
Association Catalogue down to the fifth magnitude are included on the
scale of a six-inch globe. The distortion is scarcely a fourth of that
in the Society's maps. The maps are so arranged that the relative
positions of all the stars in each hemisphere can be readily gathered
from a single view; and black duplicate-maps serve to show the
appearance of the constellations.
It is often convenient to make small maps of a part of the heavens we
may wish to study closely. My 'Handbook of the Stars' has been prepared
to aid the student in the construction of such maps.
In selecting maps it is well to be able to recognise the amount of
distortion and scale-variation. This may be done by examining the spaces
included between successive parallels and meridians, near the edges and
angles of the maps, and comparing these either with those in the centre
of the map, or with the known figures and dimensions of the
corresponding spaces on a globe.
We may now proceed to discuss the different tests which the intending
purchaser of a telescope should apply to the instrument.
The excellence of an object-glass can be satisfactorily determined only
by testing the performance of the telescope in the manner presently to
be described. But it is well to examine the quality of the glass as
respects transparency and uniformity of texture. Bubbles, scratches, and
other such defects, are not very important, since they do not affect the
distinctness of the field as they would in a Galilean Telescope,--a
little light is lost, and that is all. The same remark applies to dust
upon the glass. The glass should be kept as free as possible from dirt,
damp, or dust, but it is not advisable to remove every speck which,
despite such precaution, may accidentally fall upon the object-glass.
When it becomes necessary to clean the glass, it is to be noted that the
substance used should be soft, perfectly dry, and free from dust. Silk
is often recommended, but some silk is exceedingly objectionable in
texture,--old silk, perfectly soft to the touch, is perhaps as good as
anything. If the dust which has fallen on the glass is at all gritty,
the glass will suffer by the method of cleaning commonly adopted, in
which the dust is _gathered up_ by pressure. The proper method is to
clean a small space near the edge of the glass, and to _sweep_ from that
space as centre. In this way the dust is _pushed before_ the silk or
wash-leather, and does not cut the glass. It is well always to suspect
the presence of gritty dust, and adopt this cautious method of cleaning.
The two glasses should on no account be separated.
In examining an eye-piece, the quality of the glass should be noted, and
care taken that both glasses (but especially the field-glass) are free
from the least speck, scratch, or blemish of any kind, for these defects
will be exhibited in a magnified state in the field of view. Hence the
eye-pieces require to be as carefully preserved from damp and dust as
the object-glass, and to be more frequently cleaned.
The tube of the telescope should be light, but strong, and free from
vibration. Its quality in the last respect can be tested by lightly
striking it when mounted; the sound given out should be dead or
non-resonant. The inside of the tube must absorb extraneous light, and
should therefore be coloured a dull black; and stops of varying radius
should be placed along its length with the same object. Sliding tubes,
rack-work, etc., should work closely, yet easily.
The telescope should be well balanced for vision with the small
astronomical eye-pieces. But as there is often occasion to use
appliances which disturb the balance, it is well to have the means of at
once restoring equilibrium. A cord ring running round the tube (pretty
tightly, so as to rest still when the tube is inclined), and bearing a
small weight, will be all that is required for this purpose; it must be
slipped along the tube until the tube is found to be perfectly balanced.
Nothing is more annoying than, after getting a star well in the field,
to see the tube shift its position through defective balance, and thus
to have to search again for the star. Even with such an arrangement as
is shown in fig. 8, though the tube cannot readily shift its position,
it is better to have it well balanced.
The quality of the stand has a very important influence on the
performance of a telescope. In fact, a moderately good telescope,
mounted on a steady stand, working easily and conveniently, will not
only enable the observer to pass his time much more pleasantly, but will
absolutely exhibit more difficult objects than a finer instrument on a
rickety, ill-arranged stand. A good observing-chair is also a matter of
some importance, the least constraint or awkwardness of position
detracting considerably from the power of distinct vision. Such, at
least, is my own experience.
But the mere examination of the glasses, tube, mounting, &c., is only
the first step in the series of tests which should be applied to a
telescope, since the excellence of the instrument depends, not on its
size, the beauty of its mounting, or any extraneous circumstances, but
on its performance.
The observer should first determine whether the chromatic aberration is
corrected. To ascertain this the telescope should be directed to the
moon, or (better) to Jupiter, and accurately focussed for distinct
vision. If, then, on moving the eye-piece towards the object-glass, a
ring of purple appears round the margin of the object, and on moving the
eye-glass in the contrary direction a ring of green, the chromatic
aberration is corrected, since these are the colours of the secondary
spectrum.
To determine whether the spherical aberration is corrected, the
telescope should be directed towards a star of the third or fourth
magnitude, and focussed for distinct vision. A cap with an aperture of
about one-half its diameter should then be placed over the object-glass.
If no new adjustment is required for distinct vision, the spherical
aberration is corrected, since the mean focal length and the focal
length of the central rays are equal. If, when the cap is on, the
eye-piece has to be pulled out for distinct vision, the spherical
aberration has not been fully corrected; if the eye-piece has to be
pushed in, the aberration has been over-corrected. As a further test, we
may cut off the central rays, by means of a circular card covering the
middle of the object-glass, and compare the focal length for distinct
vision with the focal length when the cap is applied. The extent of the
spherical aberration may be thus determined; but if the first experiment
gives a satisfactory result, no other is required.
A star of the first magnitude should next be brought into the field of
view. If an irradiation from one side is perceived, part of the
object-glass has not the same refractive power as the rest; and the
part which is defective can be determined by applying in different
positions a cap which hides half the object-glass. If the irradiation is
double, it will probably be found that the object-glass has been too
tightly screwed, and the defect will disappear when the glass is freed
from such undue pressure.
If the object-glass is not quite at right angles to the axis of the
tube, or if the eye-tube is at all inclined, a like irradiation will
appear when a bright star is in the field. The former defect is not
easily detected or remedied; nor is it commonly met with in the work of
a careful optician. The latter defect may be detected by cutting out
three circular cards of suitable size with a small aperture at the
centre of each, and inserting one at each end of the eye-tube, and one
over the object-glass. If the tube is rightly placed the apertures will
of course lie in a right line, so that it will be possible to look
through all three at once. If not, it will be easy to determine towards
what part of the object-glass the eye-tube is directed, and to correct
the position of the tube accordingly.
The best tests for determining the defining power of a telescope are
close double or multiple stars, the components of which are not very
unequal. The illuminating power should be tested by directing the
telescope towards double or multiple stars having one or more minute
components. Many of the nebulae serve as tests both for illumination and
defining power. As we proceed we shall meet with proper objects for
testing different telescopes. For the present, let the following list
suffice. It is selected from Admiral Smyth's tests, obtained by
diminishing the aperture of a 6-in. telescope having a focal length of
8-1/2 feet:
A two-inch aperture, with powers of from 60 to 100, should exhibit
[alpha] Piscium (3".5). | [delta] Cassiopeiae (9".5),
| mag. (4 and 7-1/2)
[gamma] Leonis (3".2). | Polaris (18".6), mag. (2-1/2
| and 9-1/2)
A four-inch, powers 80 to 120, should exhibit
[xi] Ursae Majoris (2".4). | [sigma] Cassiopeiae (3".1),
| mag. (6 and 8).
[gamma] Ceti (2".6). | [delta] Geminorum (7".1),
| mag. (4 and 9).
The tests in the first column are for definition, those in the second
for illumination. It will be noticed that, though in the case of Polaris
the smaller aperture may be expected to show the small star of less than
the 9th magnitude, a larger aperture is required to show the 8th
magnitude component of [sigma] Cassiopeiae, on account of the greater
closeness of this double.
In favourable weather the following is a good general test of the
performance of a telescope:--A star of the 3rd or 4th magnitude at a
considerable elevation above the horizon should exhibit a small well
defined disc, surrounded by two or three fine rings of light.
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