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.