In the preceding essay on the structure of the universe, we have pointed out several features of the universe showing the unity of the whole. We shall now bring together these and other features with a view of showing their relation to the question of the extent of the universe.

The Milky Way being in a certain sense the foundation on which the whole system is constructed, we have first to notice the symmetry of the whole. This is seen in the fact that a certain resemblance is found in any two opposite regions of the sky, no matter where we choose them.

If we take them in the Milky Way, the stars are more numerous than elsewhere; if we take opposite regions in or near the Milky Way, we shall find more stars in both of them than elsewhere; if we take them in the region anywhere around the poles of the Milky Way, we shall find fewer stars, but they will be equally numerous in each of the two regions. We infer from this that whatever cause determined the number of the stars in s.p.a.ce was of the same nature in every two antipodal regions of the heavens.

Another unity marked with yet more precision is seen in the chemical elements of which stars are composed. We know that the sun is composed of the same elements which we find on the earth and into which we resolve compounds in our laboratories. These same elements are found in the most distant stars. It is true that some of these bodies seem to contain elements which we do not find on earth. But as these unknown elements are scattered from one extreme of the universe to the other, they only serve still further to enforce the unity which runs through the whole. The nebulae are composed, in part at least, of forms of matter dissimilar to any with which we are acquainted. But, different though they may be, they are alike in their general character throughout the whole field we are considering. Even in such a feature as the proper motions of the stars, the same unity is seen. The reader doubtless knows that each of these objects is flying through s.p.a.ce on its own course with a speed comparable with that of the earth around the sun. These speeds range from the smallest limit up to more than one hundred miles a second. Such diversity might seem to detract from the unity of the whole; but when we seek to learn something definite by taking their average, we find this average to be, so far as can yet be determined, much the same in opposite regions of the universe. Quite recently it has become probable that a certain cla.s.s of very bright stars known as Orion stars--because there are many of them in the most brilliant of our constellations--which are scattered along the whole course of the Milky Way, have one and all, in the general average, slower motions than other stars. Here again we have a definable characteristic extending through the universe. In drawing attention to these points of similarity throughout the whole universe, it must not be supposed that we base our conclusions directly upon them. The point they bring out is that the universe is in the nature of an organized system; and it is upon the fact of its being such a system that we are able, by other facts, to reach conclusions as to its structure, extent, and other characteristics.

One of the great problems connected with the universe is that of its possible extent. How far away are the stars? One of the unities which we have described leads at once to the conclusion that the stars must be at very different distances from us; probably the more distant ones are a thousand times as far as the nearest; possibly even farther than this. This conclusion may, in the first place, be based on the fact that the stars seem to be scattered equally throughout those regions of the universe which are not connected with the Milky Way. To ill.u.s.trate the principle, suppose a farmer to sow a wheat-field of entirely unknown extent with ten bushels of wheat. We visit the field and wish to have some idea of its acreage. We may do this if we know how many grains of wheat there are in the ten bushels. Then we examine a s.p.a.ce two or three feet square in any part of the field and count the number of grains in that s.p.a.ce. If the wheat is equally scattered over the whole field, we find its extent by the simple rule that the size of the field bears the same proportion to the size of the s.p.a.ce in which the count was made that the whole number of grains in the ten bushels sown bears to the number of grains counted. If we find ten grains in a square foot, we know that the number of square feet in the whole field is one-tenth that of the number of grains sown. So it is with the universe of stars. If the latter are sown equally through s.p.a.ce, the extent of the s.p.a.ce occupied must be proportional to the number of stars which it contains.

But this consideration does not tell us anything about the actual distance of the stars or how thickly they may be scattered. To do this we must be able to determine the distance of a certain number of stars, just as we suppose the farmer to count the grains in a certain small extent of his wheat-field. There is only one way in which we can make a definite measure of the distance of any one star. As the earth swings through its vast annual circuit round the sun, the direction of the stars must appear to be a little different when seen from one extremity of the circuit than when seen from the other. This difference is called the parallax of the stars; and the problem of measuring it is one of the most delicate and difficult in the whole field of practical astronomy.

The nineteenth century was well on its way before the instruments of the astronomer were brought to such perfection as to admit of the measurement. From the time of Copernicus to that of Bessel many attempts had been made to measure the parallax of the stars, and more than once had some eager astronomer thought himself successful. But subsequent investigation always showed that he had been mistaken, and that what he thought was the effect of parallax was due to some other cause, perhaps the imperfections of his instrument, perhaps the effect of heat and cold upon it or upon the atmosphere through which he was obliged to observe the star, or upon the going of his clock. Thus things went on until 1837, when Bessel announced that measures with a heliometer--the most refined instrument that has ever been used in measurement--showed that a certain star in the constellation Cygnus had a parallax of one-third of a second. It may be interesting to give an idea of this quant.i.ty. Suppose one's self in a house on top of a mountain looking out of a window one foot square, at a house on another mountain one hundred miles away. One is allowed to look at that distant house through one edge of the pane of gla.s.s and then through the opposite edge; and he has to determine the change in the direction of the distant house produced by this change of one foot in his own position. From this he is to estimate how far off the other mountain is. To do this, one would have to measure just about the amount of parallax that Bessel found in his star. And yet this star is among the few nearest to our system. The nearest star of all, Alpha Centauri, visible only in lat.i.tudes south of our middle ones, is perhaps half as far as Bessel's star, while Sirius and one or two others are nearly at the same distance. About 100 stars, all told, have had their parallax measured with a greater or less degree of probability. The work is going on from year to year, each successive astronomer who takes it up being able, as a general rule, to avail himself of better instruments or to use a better method. But, after all, the distances of even some of the 100 stars carefully measured must still remain quite doubtful.

Let us now return to the idea of dividing the s.p.a.ce in which the universe is situated into concentric spheres drawn at various distances around our system as a centre. Here we shall take as our standard a distance 400,000 times that of the sun from the earth. Regarding this as a unit, we imagine ourselves to measure out in any direction a distance twice as great as this--then another equal distance, making one three times as great, and so indefinitely. We then have successive spheres of which we take the nearer one as the unit. The total s.p.a.ce filled by the second sphere will be 8 times the unit; that of the third s.p.a.ce 27 times, and so on, as the cube of each distance. Since each sphere includes all those within it, the volume of s.p.a.ce between each two spheres will be proportional to the difference of these numbers--that is, to 1, 7, 19, etc. Comparing these volumes with the number of stars probably within them, the general result up to the present time is that the number of stars in any of these spheres will be about equal to the units of volume which they comprise, when we take for this unit the smallest and innermost of the spheres, having a radius 400,000 times the sun's distance. We are thus enabled to form some general idea of how thickly the stars are sown through s.p.a.ce. We cannot claim any numerical exactness for this idea, but in the absence of better methods it does afford us some basis for reasoning.

Now we can carry on our computation as we supposed the farmer to measure the extent of his wheat-field. Let us suppose that there are 125,000,000 stars in the heavens. This is an exceedingly rough estimate, but let us make the supposition for the time being. Accepting the view that they are nearly equally scattered throughout s.p.a.ce, it will follow that they must be contained within a volume equal to 125,000,000 times the sphere we have taken as our unit. We find the distance of the surface of this sphere by extracting the cube root of this number, which gives us 500. We may, therefore, say, as the result of a very rough estimate, that the number of stars we have supposed would be contained within a distance found by multiplying 400,000 times the distance of the sun by 500; that is, that they are contained within a region whose boundary is 200,000,000 times the distance of the sun.

This is a distance through which light would travel in about 3300 years.

It is not impossible that the number of stars is much greater than that we have supposed. Let us grant that there are eight times as many, or 1,000,000,000. Then we should have to extend the boundary of our universe twice as far, carrying it to a distance which light would require 6600 years to travel.

There is another method of estimating the thickness with which stars are sown through s.p.a.ce, and hence the extent of the universe, the result of which will be of interest. It is based on the proper motion of the stars. One of the greatest triumphs of astronomy of our time has been the measurement of the actual speed at which many of the stars are moving to or from us in s.p.a.ce. These measures are made with the spectroscope. Unfortunately, they can be best made only on the brighter stars--becoming very difficult in the case of stars not plainly visible to the naked eye. Still the motions of several hundreds have been measured and the number is constantly increasing.

A general result of all these measures and of other estimates may be summed up by saying that there is a certain average speed with which the individual stars move in s.p.a.ce; and that this average is about twenty miles per second. We are also able to form an estimate as to what proportion of the stars move with each rate of speed from the lowest up to a limit which is probably as high as 150 miles per second.

Knowing these proportions we have, by observation of the proper motions of the stars, another method of estimating how thickly they are scattered in s.p.a.ce; in other words, what is the volume of s.p.a.ce which, on the average, contains a single star. This method gives a thickness of the stars greater by about twenty-five per cent, than that derived from the measures of parallax. That is to say, a sphere like the second we have proposed, having a radius 800,000 times the distance of the sun, and therefore a diameter 1,600,000 times this distance, would, judging by the proper motions, have ten or twelve stars contained within it, while the measures of parallax only show eight stars within the sphere of this diameter having the sun as its centre. The probabilities are in favor of the result giving the greater thickness of the stars. But, after all, the discrepancy does not change the general conclusion as to the limits of the visible universe. If we cannot estimate its extent with the same certainty that we can determine the size of the earth, we can still form a general idea of it.

The estimates we have made are based on the supposition that the stars are equally scattered in s.p.a.ce. We have good reason to believe that this is true of all the stars except those of the Milky Way. But, after all, the latter probably includes half the whole number of stars visible with a telescope, and the question may arise whether our results are seriously wrong from this cause. This question can best be solved by yet another method of estimating the average distance of certain cla.s.ses of stars.

The parallaxes of which we have heretofore spoken consist in the change in the direction of a star produced by the swing of the earth from one side of its...o...b..t 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 s.p.a.ce 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 s.p.a.ce. 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 s.p.a.ce. 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 s.p.a.ce 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 s.p.a.ce, 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 pa.s.sage through s.p.a.ce. 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 s.p.a.ce, 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 s.p.a.ce, 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 antic.i.p.ate 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 pa.s.sing 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-gla.s.s, 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-gla.s.s is composed of two lenses--a concave one of flint-gla.s.s and a convex one of crown-gla.s.s, 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-gla.s.s, 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-gla.s.s requires two completely distinct processes: the making of the rough gla.s.s, which is the work of the gla.s.s-maker; and the grinding and polishing into shape, which is the work of the optician. The ordinary gla.s.s of commerce will not answer the purpose of the telescope at all, because it is not sufficiently clear and h.o.m.ogeneous. OPTICAL GLa.s.s, 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 gla.s.s. In the time of Dollond it was found scarcely possible to make good disks of flint-gla.s.s 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 princ.i.p.ally in the constant stirring of the molten gla.s.s 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 gla.s.s 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 gla.s.s 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 compet.i.tors in the process. He it was who made the great 40-inch lens for the Yerkes Observatory.

As optical gla.s.s 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 gla.s.s is taken out, and the pot is broken from around it, leaving only the central ma.s.s of gla.s.s. Having such a ma.s.s, 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 gla.s.s 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 ma.s.s, 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 gla.s.s 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 gla.s.s 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 gla.s.s 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 gla.s.s in two or cutting a hole through it. If the parts of the gla.s.s 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 gla.s.s can be changed in form to any extent.

Having ground out the veins as far as possible, the gla.s.s 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 gla.s.s inside, it must be raised up wherever the gla.s.s is thinnest, and the latter allowed to slowly run together beneath it.

[Ill.u.s.tration with caption: THE GLa.s.s 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 gla.s.s 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 gla.s.s 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 gla.s.s is then ready for the optician.

[Ill.u.s.tration with caption: THE OPTICIAN'S TOOL.]

The first process to be performed by the optician is to grind the gla.s.s 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 gla.s.s, 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 gla.s.s.

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.

[Ill.u.s.tration 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.

[Ill.u.s.tration 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 gla.s.s 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-gla.s.ses, and this firm always does the work by hand, moving the gla.s.s over the polisher, and not the polisher over the gla.s.s.

Having brought both flint and crown gla.s.ses 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 gla.s.s 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 gla.s.ses 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 gla.s.ses of the objective in it against a wall at night, and going to a short distance, observe the reflection in the gla.s.s 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 gla.s.ses 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.

[Ill.u.s.tration with caption: IMAGE OF CANDLE-FLAME IN OBJECT-GLa.s.s.]

[Ill.u.s.tration with caption: TESTING ADJUSTMENT OF OBJECT-GLa.s.s.]

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 gla.s.s, and look through the opening. Images of the reflector itself will then be seen in the object-gla.s.s, 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-gla.s.s. 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 gla.s.ses 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 circ.u.mstances, 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 a.s.sert that any ingenious young man, with a clear appreciation of optical principles, could not soon learn to grind and polish an object-gla.s.s 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.