in the direction of a star produced by the swing of the earth from one
side of its orbit to the other. But we have already remarked that our
solar system, with the earth as one of its bodies, has been journeying
straightforward through space during all historic times. It follows,
therefore, that we are continually changing the position from which we
view the stars, and that, if the latter were at rest, we could, by
measuring the apparent speed with which they are moving in the opposite
direction from that of the earth, determine their distance. But since
every star has its own motion, it is impossible, in any one case, to
determine how much of the apparent motion is due to the star itself,
and how much to the motion of the solar system through space. Yet, by
taking general averages among groups of stars, most of which are
probably near each other, it is possible to estimate the average
distance by this method. When an attempt is made to apply it, so as to
obtain a definite result, the astronomer finds that the data now
available for the purpose are very deficient. The proper motion of a
star can be determined only by comparing its observed position in the
heavens at two widely separate epochs. Observations of sufficient
precision for this purpose were commenced about 1750 at the Greenwich
Observatory, by Bradley, then Astronomer Royal of England. But out of
3000 stars which he determined, only a few are available for the
purpose. Even since his time, the determinations made by each
generation of astronomers have not been sufficiently complete and
systematic to furnish the material for anything like a precise
determination of the proper motions of stars. To determine a single
position of any one star involves a good deal of computation, and if we
reflect that, in order to attack the problem in question in a
satisfactory way, we should have observations of 1,000,000 of these
bodies made at intervals of at least a considerable fraction of a
century, we see what an enormous task the astronomers dealing with this
problem have before them, and how imperfect must be any determination
of the distance of the stars based on our motion through space. So far
as an estimate can be made, it seems to agree fairly well with the
results obtained by the other methods. Speaking roughly, we have
reason, from the data so far available, to believe that the stars of
the Milky Way are situated at a distance between 100,000,000 and
200,000,000 times the distance of the sun. At distances less than this
it seems likely that the stars are distributed through space with some
approach to uniformity. We may state as a general conclusion, indicated
by several methods of making the estimate, that nearly all the stars
which we can see with our telescopes are contained within a sphere not
likely to be much more than 200,000,000 times the distance of the sun.
The inquiring reader may here ask another question. Granting that all
the stars we can see are contained within this limit, may there not be
any number of stars outside the limit which are invisible only because
they are too far away to be seen?
This question may be answered quite definitely if we grant that light
from the most distant stars meets with no obstruction in reaching us.
The most conclusive answer is afforded by the measure of starlight. If
the stars extended out indefinitely, then the number of those of each
order of magnitude would be nearly four times that of the magnitude
next brighter. For example, we should have nearly four times as many
stars of the sixth magnitude as of the fifth; nearly four times as many
of the seventh as of the sixth, and so on indefinitely. Now, it is
actually found that while this ratio of increase is true for the
brighter stars, it is not so for the fainter ones, and that the
increase in the number of the latter rapidly falls off when we make
counts of the fainter telescopic stars. In fact, it has long been known
that, were the universe infinite in extent, and the stars equally
scattered through all space, the whole heavens would blaze with the
light of countless millions of distant stars separately invisible even
with the telescope.
The only way in which this conclusion can be invalidated is by the
possibility that the light of the stars is in some way extinguished or
obstructed in its passage through space. A theory to this effect was
propounded by Struve nearly a century ago, but it has since been found
that the facts as he set them forth do not justify the conclusion,
which was, in fact, rather hypothetical. The theories of modern science
converge towards the view that, in the pure ether of space, no single
ray of light can ever be lost, no matter how far it may travel. But
there is another possible cause for the extinction of light. During the
last few years discoveries of dark and therefore invisible stars have
been made by means of the spectroscope with a success which would have
been quite incredible a very few years ago, and which, even to-day,
must excite wonder and admiration. The general conclusion is that,
besides the shining stars which exist in space, there may be any number
of dark ones, forever invisible in our telescopes. May it not be that
these bodies are so numerous as to cut off the light which we would
otherwise receive from the more distant bodies of the universe? It is,
of course, impossible to answer this question in a positive way, but
the probable conclusion is a negative one. We may say with certainty
that dark stars are not so numerous as to cut off any important part of
the light from the stars of the Milky Way, because, if they did, the
latter would not be so clearly seen as it is. Since we have reason to
believe that the Milky Way comprises the more distant stars of our
system, we may feel fairly confident that not much light can be cut off
by dark bodies from the most distant region to which our telescopes can
penetrate. Up to this distance we see the stars just as they are. Even
within the limit of the universe as we understand it, it is likely that
more than one-half the stars which actually exist are too faint to be
seen by human vision, even when armed with the most powerful
telescopes. But their invisibility is due only to their distance and
the faintness of their intrinsic light, and not to any obstructing
agency.
The possibility of dark stars, therefore, does not invalidate the
general conclusions at which our survey of the subject points. The
universe, so far as we can see it, is a bounded whole. It is surrounded
by an immense girdle of stars, which, to our vision, appears as the
Milky Way. While we cannot set exact limits to its distance, we may yet
confidently say that it is bounded. It has uniformities running through
its vast extent. Could we fly out to distances equal to that of the
Milky Way, we should find comparatively few stars beyond the limits of
that girdle. It is true that we cannot set any definite limit and say
that beyond this nothing exists. What we can say is that the region
containing the visible stars has some approximation to a boundary. We
may fairly anticipate that each successive generation of astronomers,
through coming centuries, will obtain a little more light on the
subject--will be enabled to make more definite the boundaries of our
system of stars, and to draw more and more probable conclusions as to
the existence or non-existence of any object outside of it. The wise
investigator of to-day will leave to them the task of putting the
problem into a more positive shape.
V
MAKING AND USING A TELESCOPE
The impression is quite common that satisfactory views of the heavenly
bodies can be obtained only with very large telescopes, and that the
owner of a small one must stand at a great disadvantage alongside of
the fortunate possessor of a great one. This is not true to the extent
commonly supposed. Sir William Herschel would have been delighted to
view the moon through what we should now consider a very modest
instrument; and there are some objects, especially the moon, which
commonly present a more pleasing aspect through a small telescope than
through a large one. The numerous owners of small telescopes throughout
the country might find their instruments much more interesting than
they do if they only knew what objects were best suited to examination
with the means at their command. There are many others, not possessors
of telescopes, who would like to know how one can be acquired, and to
whom hints in this direction will be valuable. We shall therefore give
such information as we are able respecting the construction of a
telescope, and the more interesting celestial objects to which it may
be applied.
Whether the reader does or does not feel competent to undertake the
making of a telescope, it may be of interest to him to know how it is
done. First, as to the general principles involved, it is generally
known that the really vital parts of the telescope, which by their
combined action perform the office of magnifying the object looked at,
are two in number, the OBJECTIVE and the EYE-PIECE. The former brings
the rays of light which emanate from the object to the focus where the
image of the object is formed. The eye-piece enables the observer to
see this image to the best advantage.
The functions of the objective as well as those of the eye-piece may,
to a certain extent, each be performed by a single lens. Galileo and
his contemporaries made their telescopes in this way, because they knew
of no way in which two lenses could be made to do better than one. But
every one who has studied optics knows that white light passing through
a single lens is not all brought to the same focus, but that the blue
light will come to a focus nearer the objective than the red light.
There will, in fact, be a succession of images, blue, green, yellow,
and red, corresponding to the colors of the spectrum. It is impossible
to see these different images clearly at the same time, because each of
them will render all the others indistinct.
The achromatic object-glass, invented by Dollond, about 1750, obviates
this difficulty, and brings all the rays to nearly the same focus.
Nearly every one interested in the subject is aware that this
object-glass is composed of two lenses--a concave one of flint-glass
and a convex one of crown-glass, the latter being on the side towards
the object. This is the one vital part of the telescope, the
construction of which involves the greatest difficulty. Once in
possession of a perfect object-glass, the rest of the telescope is a
matter of little more than constructive skill which there is no
difficulty in commanding.
The construction of the object-glass requires two completely distinct
processes: the making of the rough glass, which is the work of the
glass-maker; and the grinding and polishing into shape, which is the
work of the optician. The ordinary glass of commerce will not answer
the purpose of the telescope at all, because it is not sufficiently
clear and homogeneous. OPTICAL GLASS, as it is called, must be made of
materials selected and purified with the greatest care, and worked in a
more elaborate manner than is necessary in any other kind of glass. In
the time of Dollond it was found scarcely possible to make good disks
of flint-glass more than three or four inches in diameter. Early in the
present century, Guinand, of Switzerland, invented a process by which
disks of much larger size could be produced. In conjunction with the
celebrated Fraunhofer he made disks of nine or ten inches in diameter,
which were employed by his colaborer in constructing the telescopes
which were so famous in their time. He was long supposed to be in
possession of some secret method of avoiding the difficulties which his
predecessors had met. It is now believed that this secret, if one it
was, consisted principally in the constant stirring of the molten glass
during the process of manufacture. However this may be, it is a curious
historical fact that the most successful makers of these great disks of
glass have either been of the family of Guinand, or successors, in the
management of the family firm. It was Feil, a son-in-law or near
relative, who made the glass from which Clark fabricated the lenses of
the great telescope of the Lick Observatory. His successor, Mantois, of
Paris, carried the art to a point of perfection never before
approached. The transparency and uniformity of his disks as well as the
great size to which he was able to carry them would suggest that he and
his successors have out-distanced all competitors in the process. He it
was who made the great 40-inch lens for the Yerkes Observatory.
As optical glass is now made, the material is constantly stirred with
an iron rod during all the time it is melting in the furnace, and after
it has begun to cool, until it becomes so stiff that the stirring has
to cease. It is then placed, pot and all, in the annealing furnace,
where it is kept nearly at a melting heat for three weeks or more,
according to the size of the pot. When the furnace has cooled off, the
glass is taken out, and the pot is broken from around it, leaving only
the central mass of glass. Having such a mass, there is no trouble in
breaking it up into pieces of all desirable purity, and sufficiently
large for moderate-sized telescopes. But when a great telescope of two
feet aperture or upward is to be constructed, very delicate and
laborious operations have to be undertaken. The outside of the glass
has first to be chipped off, because it is filled with impurities from
the material of the pot itself. But this is not all. Veins of unequal
density are always found extending through the interior of the mass, no
way of avoiding them having yet been discovered. They are supposed to
arise from the materials of the pot and stirring rod, which become
mixed in with the glass in consequence of the intense heat to which all
are subjected. These veins must, so far as possible, be ground or
chipped out with the greatest care. The glass is then melted again,
pressed into a flat disk, and once more put into the annealing oven. In
fact, the operation of annealing must be repeated every time the glass
is melted. When cooled, it is again examined for veins, of which great
numbers are sure to be found. The problem now is to remove these by
cutting and grinding without either breaking the glass in two or
cutting a hole through it. If the parts of the glass are once
separated, they can never be joined without producing a bad scar at the
point of junction. So long, however, as the surface is unbroken, the
interior parts of the glass can be changed in form to any extent.
Having ground out the veins as far as possible, the glass is to be
again melted, and moulded into proper shape. In this mould great care
must be taken to have no folding of the surface. Imagining the latter
to be a sort of skin enclosing the melted glass inside, it must be
raised up wherever the glass is thinnest, and the latter allowed to
slowly run together beneath it.
[Illustration with caption: THE GLASS DISK.]
If the disk is of flint, all the veins must be ground out on the first
or second trial, because after two or three mouldings the glass will
lose its transparency. A crown disk may, however, be melted a number of
times without serious injury. In many cases--perhaps the majority--the
artisan finds that after all his months of labor he cannot perfectly
clear his glass of the noxious veins, and he has to break it up into
smaller pieces. When he finally succeeds, the disk has the form of a
thin grindstone two feet or upward in diameter, according to the size
of the telescope to be made, and from two to three inches in thickness.
The glass is then ready for the optician.
[Illustration with caption: THE OPTICIAN'S TOOL.]
The first process to be performed by the optician is to grind the glass
into the shape of a lens with perfectly spherical surfaces. The convex
surface must be ground in a saucer-shaped tool of corresponding form.
It is impossible to make a tool perfectly spherical in the first place,
but success may be secured on the geometrical principle that two
surfaces cannot fit each other in all positions unless both are
perfectly spherical. The tool of the optician is a very simple affair,
being nothing more than a plate of iron somewhat larger, perhaps a
fourth, than the lens to be ground to the corresponding curvature. In
order to insure its changing to fit the glass, it is covered on the
interior with a coating of pitch from an eighth to a quarter of an inch
thick. This material is admirably adapted to the purpose because it
gives way certainly, though very slowly, to the pressure of the glass.
In order that it may have room to change its form, grooves are cut
through it in both directions, so as to leave it in the form of
squares, like those on a chess-board.
[Illustration with caption: THE OPTICIAN'S TOOL.]
It is then sprinkled over with rouge, moistened with water, and gently
warmed. The roughly ground lens is then placed upon it, and moved from
side to side. The direction of the motion is slightly changed with
every stroke, so that after a dozen or so of strokes the lines of
motion will lie in every direction on the tool. This change of
direction is most readily and easily effected by the operator slowly
walking around as he polishes, at the same time the lens is to be
slowly turned around either in the opposite direction or more rapidly
yet in the same direction, so that the strokes of the polisher shall
cross the lens in all directions. This double motion insures every part
of the lens coming into contact with every part of the polisher, and
moving over it in every direction.
Then whatever parts either of the lens or of the polisher may be too
high to form a spherical surface will be gradually worn down, thus
securing the perfect sphericity of both.
[Illustration with caption: GRINDING A LARGE LENS.]
When the polishing is done by machinery, which is the custom in Europe,
with large lenses, the polisher is slid back and forth over the lens by
means of a crank attached to a revolving wheel. The polisher is at the
same time slowly revolving around a pivot at its centre, which pivot
the crank works into, and the glass below it is slowly turned in an
opposite direction. Thus the same effect is produced as in the other
system. Those who practice this method claim that by thus using
machinery the conditions of a uniform polish for every part of the
surface can be more perfectly fulfilled than by a hand motion. The
results, however, do not support this view. No European optician will
claim to do better than the American firm of Alvan Clark & Sons in
producing uniformly good object-glasses, and this firm always does the
work by hand, moving the glass over the polisher, and not the polisher
over the glass.
Having brought both flint and crown glasses into proper figure by this
process, they are joined together, and tested by observations either
upon a star in the heavens, or some illuminated point at a little
distance on the ground. The reflection of the sun from a drop of
quicksilver, a thermometer bulb, or even a piece of broken bottle,
makes an excellent artificial star. The very best optician will always
find that on a first trial his glass is not perfect. He will find that
he has not given exactly the proper curves to secure achromatism. He
must then change the figure of one or both the glasses by polishing it
upon a tool of slightly different curvature. He may also find that
there is some spherical aberration outstanding. He must then alter his
curve so as to correct this. The correction of these little
imperfections in the figures of the lenses so as to secure perfect
vision through them is the most difficult branch of the art of the
optician, and upon his skill in practising it will depend more than
upon anything else his ultimate success and reputation. The shaping of
a pair of lenses in the way we have described is not beyond the power
of any person of ordinary mechanical ingenuity, possessing the
necessary delicacy of touch and appreciation of the problem he is
attacking. But to make a perfect objective of considerable size, which
shall satisfy all the wants of the astronomer, is an undertaking
requiring such accuracy of eyesight, and judgment in determining where
the error lies, and such skill in manipulating so as to remove the
defects, that the successful men in any one generation can be counted
on one's fingers.
In order that the telescope may finally perform satisfactorily it is
not sufficient that the lenses should both be of proper figure; they
must also both be properly centred in their cells. If either lens is
tipped aside, or slid out from its proper central line, the definition
will be injured. As this is liable to happen with almost any telescope,
we shall explain how the proper adjustment is to be made.
The easiest way to test this adjustment is to set the cell with the two
glasses of the objective in it against a wall at night, and going to a
short distance, observe the reflection in the glass of the flame of a
candle held in the hand. Three or four reflections will be seen from
the different surfaces. The observer, holding the candle before his
eye, and having his line of sight as close as possible to the flame,
must then move until the different images of the flame coincide with
each other. If he cannot bring them into coincidence, owing to
different pairs coinciding on different sides of the flame, the glasses
are not perfectly centred upon each other. When the centring is
perfect, the observer having the light in the line of the axes of the
lenses, and (if it were possible to do so) looking through the centre
of the flame, would see the three or four images all in coincidence. As
he cannot see through the flame itself, he must look first on one side
and then on the other, and see if the arrangement of the images seen in
the lenses is symmetrical. If, going to different distances, he finds
no deviation from symmetry, in this respect the adjustment is near
enough for all practical purposes.
A more artistic instrument than a simple candle is a small concave
reflector pierced through its centre, such as is used by physicians in
examining the throat.
[Illustration with caption: IMAGE OF CANDLE-FLAME IN OBJECT-GLASS.]
[Illustration with caption: TESTING ADJUSTMENT OF OBJECT-GLASS.]
Place this reflector in the prolongation of the optical axis, set the
candle so that the light from the reflector shall be shown through the
glass, and look through the opening. Images of the reflector itself
will then be seen in the object-glass, and if the adjustment is
perfect, the reflector can be moved so that they will all come into
coincidence together.
When the objective is in the tube of the telescope, it is always well
to examine this adjustment from time to time, holding the candle so
that its light shall shine through the opening perpendicularly upon the
object-glass. The observer looks upon one side of the flame, and then
upon the other, to see if the images are symmetrical in the different
positions. If in order to see them in this way the candle has to be
moved to one side of the central line of the tube, the whole objective
must be adjusted. If two images coincide in one position of the
candle-flame, and two in another position, so that they cannot all be
brought together in any position, it shows that the glasses are not
properly adjusted in their cell. It may be remarked that this last
adjustment is the proper work of the optician, since it is so difficult
that the user of the telescope cannot ordinarily effect it. But the
perpendicularity of the whole objective to the tube of the telescope is
liable to be deranged in use, and every one who uses such an instrument
should be able to rectify an error of this kind.
The question may be asked, How much of a telescope can an amateur
observer, under any circumstances, make for himself? As a general rule,
his work in this direction must be confined to the tube and the
mounting. We should not, it is true, dare to assert that any ingenious
young man, with a clear appreciation of optical principles, could not
soon learn to grind and polish an object-glass for himself by the
method we have described, and thus obtain a much better instrument than
Galileo ever had at his command. But it would be a wonderful success if
his home-made telescope was equal to the most indifferent one which can
be bought at an optician's. The objective, complete in itself, can be
purchased at prices depending upon the size.
[Footnote: The following is a rough rule for getting an idea of the
price of an achromatic objective, made to order, of the finest quality.
Take the cube of the diameter in inches, or, which is the same thing,
calculate the contents of a cubical box which would hold a sphere of
the same diameter as the clear aperture of the glass. The price of the
glass will then range from $1 to $1.75 for each cubic inch in this box.
For example, the price of a four-inch objective will probably range
from $64 to $112. Very small object-glasses of one or two inches may be
a little higher than would be given by this rule. Instruments which are
not first-class, but will answer most of the purposes of the amateur,
are much cheaper.]
[Illustration with caption: A VERY PRIMITIVE MOUNTING FOR A TELESCOPE.]
The tube for the telescope may be made of paper, by pasting a great
number of thicknesses around a long wooden cylinder. A yet better tube
is made of a simple wooden box. The best material, however, is metal,
because wood and pasteboard are liable both to get out of shape, and to
swell under the influence of moisture. Tin, if it be of sufficient
thickness, would be a very good material. The brighter it is kept, the
better. The work of fitting the objective into one end of a tin tube of
double thickness, and properly adjusting it, will probably be quite
within the powers of the ordinary amateur. The fitting of the eye-piece
into the other end of the tube will require some skill and care both on
his own part and that of his tinsmith.
Although the construction of the eye-piece is much easier than that of
the objective, since the same accuracy in adjusting the curves is not
necessary, yet the price is lower in a yet greater degree, so that the
amateur will find it better to buy than to make his eye-piece, unless
he is anxious to test his mechanical powers. For a telescope which has
no micrometer, the Huyghenian or negative eye-piece, as it is commonly
called, is the best. As made by Huyghens, it consists of two
plano-convex lenses, with their plane sides next the eye, as shown in
the figure.
[Illustration with caption: THE HUYGHENIAN EYE-PIECE.]