The star, to which we wish to call especial attention, is situate (see Fig. [82]) opposite the bottom of the “fauces,” the name given to the indentation which gives rise to the appearance of the “fish’s mouth.” This object, which has been designated the “trapezium,” from the figure formed by its principal components, consists, in fact, of six stars, the fifth and sixth (γ´ and α´) being excessively faint. Our previous remark, relative to the increased brightness of the stars, applies here with great force; for the fifth escaped the gaze of the elder Herschel, armed with his powerful instruments, and was not discovered till 1826, by Struve, who, in his turn, missed the sixth star, which, as well as the fifth, has been seen in modern achromatics of such small size as to make all comparison with the giant telescopes used by these astronomers ridiculous.
Sir John Herschel has rated γ´ and α´ of the twelfth and fourteenth magnitudes—the latter requires a high power to observe it, by reason of its proximity to α. Both these stars have been seen in an ordinary 5-foot achromatic, by Cooke, of 3¾-inches aperture, a fact speaking volumes for the perfection of surface and polish attained by our modern opticians.
Let us now try to form some idea of the perfection of the modern object-glass. We will take a telescope of eight inches aperture, and ten feet focal length. Suppose we observe a close double star, such as ξ Ursæ, then the images of these two stars will be brought to a focus side by side, as we have previously explained, and the distance by which they will be separated will be dependent on the focal length of the object-glass. If we refer once again to Fig. [39] we shall see that this distance depends on the focal length and on the angle subtended by the images of the stars at the object-glass, which is of course the same as the angle made by the real stars at the object-glass, which is called their angular distance, or simply their distance, and is expressed in seconds of arc.
If we take a telescope ten feet long and look at two stars 1° apart, the angle will be 1°; and at ten feet off the distance between the two images will be something like 2⅒ inches, and therefore, if the angle be a second, the lines will be the 1
3600th part of that, or about 1
1700th part of an inch apart, so that in order to be able to see the double star ξ Ursæ, which is a 1˝ star, by means of an eight-inch object-glass, all the surfaces, the 50 square inches of surface, of both sides of the crown, and both sides of the flint glass, must be so absolutely true and accurate, that after the light is seized by the object-glass, we must have those two stars absolutely perfectly distinct at the distance of the seventeen hundredth part of an inch, and in order to see stars ½˝ apart, their images must be distinct at one-half of this distance or at 1
3400th part of an inch from each other.
We know that both with object-glasses and reflectors a certain amount of light is lost by imperfect reflection in the one case, and by reflection from the surfaces and absorption in the other; and in reflectors we have generally two reflections instead of one. This loss is to the distinct disadvantage of the reflector, and it has been stated by authorities on the subject, that, light for light, if we use a reflector, we must make the aperture twice as large as that of a refractor in order to make up for the loss of light due to reflection. But Dr. Robinson thinks that this is an extreme estimate; and with reference to the four-foot reflector which has recently been constructed, and of which mention has already been made, he considers that a refractor of 33·73 inches aperture would be probably something like its equivalent if the glass were perfectly transparent, which is not the case, and when the thickness of such a lens came to be considered, it was calculated that instead of its being equal to the four-foot reflector, it would only be equal to one of 37¼ of similar construction, and that even a refractor of 48 inches aperture, if such could be made, would not come up to the same sized reflector just referred to in illuminating power.
On the assumption, therefore, that no light is lost in transmission through the object-glass, Dr. Robinson estimates that the apertures of a refractor and a reflector of the Newtonian construction must bear the relation to each other of 1 to 1·42. In small refractors the light absorbed by the glass is small, and therefore this ratio holds approximately good, but we see from the example just quoted how more nearly equal the ratio becomes on an increase of aperture, until at a certain limit the refractor, aperture for aperture, is surpassed by its rival, supposing Dr. Robertson’s estimate to be correct. But with specula of silvered glass the reflective power is much higher than that of speculum metal; the silvered glass, being estimated to reflect about 90 per cent.[[8]] of the incident light, while speculum metal is estimated to reflect about 63 per cent.; but be these figures correct or not, the silvered surface has undoubtedly the greater reflective power; and, according to Sir J. Herschel, a reflector of the Newtonian construction utilizes about seven-eighths of the light that a refractor would do.
Speaking generally, refractors of sizes usually obtainable are preferable to reflectors of equal and even greater aperture for ordinary work; as in addition to the want of illuminating power of reflectors, the absence of rigidity of the mounting of the speculum militates against its comfort of manipulation.
In treating of the question of the future of the telescope, we are liable to encroach on the domain of opinion and go beyond the facts vouched for by evidence, but there are certain guiding principles which are well worthy of discussion. There are the two classes of telescopes, the refractors and reflectors, each possessing advantages over the other. We may set out with observing that the light-grasping power of the reflector varies as the square of the aperture multiplied by a certain fraction representing the proportion of the amount of reflected light to that of the total incident rays. On the other hand, the power of the refractor varies as the square of the aperture multiplied by a certain fraction representing the proportion of transmitted light to that of the total incident rays. Now in the case of the reflector the reflecting power of each unit of surface is constant whatever be the size of the mirror, but in that of the refractor the transmitting power decreases with the thickness of the glass, rendered requisite by increased size, although for small apertures the transmitting power of the refractor is greater than the reflecting power of the reflector; still it is obvious that on increasing the size a stage must be at last reached when the two rivals become equal to each other. This limit has been estimated by Dr. Robinson to be 35·435 inches, a size not yet reached by our opticians by some 10 inches, but object-glasses are increasing inch by inch, and it would be rash to say that this size cannot be reached within perhaps the lifetime of our present workers, but up to the present limit of size produced, refractors have the advantage in light-grasping power.
The next point worthy of attention is the question of permanence of optical qualities. Here the refractor undoubtedly has the advantage. It is true that the flint glass of some objectives gets attacked by a sort of tarnish, still, that is not the case generally, while, on the other hand, metallic mirrors often become considerably tarnished after a few years of use, and although repolishing is not a matter of any great difficulty in the hands of the maker, still it is a serious drawback to be obliged to return mirrors every few years to be repolished. There are, however, some exceptions to this, for there are many small mirrors in existence whose polish is good after many years of continuous use, just as on the other hand there are many object-glasses whose polish has suffered in a few years, but these are exceptions to the rule. The same remarks apply to the silvered glass reflectors, for although the silvering of small mirrors is not a difficult process, the matter becomes exceedingly difficult with large surfaces, and indeed at present large discs of glass, say of four or six feet diameter, cannot be produced. If, however, a process should be discovered of manufacturing these discs satisfactorily and of silvering them, there are objections to them on the grounds of the bad conductivity of glass, whereby changes of temperature alter the curvature to a fatal extent, and there is also a great tendency for dew to be deposited on the surface.
The next point to be considered is the general suitability for observatory work, and this depends upon the quality of the work required, whether for measuring positions, as in the case of the transit instrument, where permanency of mounting is of great importance, or for physical astronomy, when a steady image for a time is only required. For the first purpose the refractor has decidedly the advantage, as the object-glass can be fixed very nearly immovably in its cell, whereas its rival must of necessity, at least with present appliances, have a small, yet in comparison considerable, motion.