806 otherwise when the bars are turned through a right angle so as to be perpendicular to the focal line. In extreme cases a remedy may be applied in the form of glasses of different curvatures in perpendicular planes, so adjusted both in form and position as to compensate the corresponding differences in tlae lens of the eye. The use of a lens as a magnifier has been explained under MICROSCOPE. The simplest view of the matter is that the lens, consistently with good focusing, allows of a nearer approach, and therefore of a higher visual angle, than would otherwise be possible. Telescope, d c. In a large class of optical instruments an imaye of the original object is first formed, and this image is examined through a magnifier. If we use a single lens merely for the latter purpose, the field of view is very restricted. A great improvement in this respect may be effected by the introduction of a^/zW^-lens. The ideal position for the field -lens is at the focal plane of the object-glass. The image is then entirely uninfluenced, and the only effect is to bend round the rays from the margin of the field which would otherwise escape, and to make them reach the eye -lens, and ultimately the eye. If the field -lens and the eye-lens have nearly the same focal length an image of the object-glass will be formed upon the eye-lens, and through this small image will pass every ray admitted by the object-glass and field-lens. However, to obtain a sufficient augmentation of the field of view it is not necessary to give the field-lens the exact position above mentioned, and other considerations favour a certain displacement. For example, it is not desirable that dust and flaws on the field-lens should be seen in focus. In Huygens s eye-piece the field-lens is dis placed from its ideal position towards the object-glass. In Ramsden s eye-piece, on the other hand, the focal plane of the object-glass is outside the system. This eye-piece has the important advantage that cross wires can be placed so as to coincide with the image as formed by the object-glass. The component lenses of a Ramsden s eye-piece are some times achromatic. For further particulars, with diagrams, on the subject of eye-pieces, see MICROSCOPE. In large telescopes the object-glass is often replaced by a mirror, which may be of speculum metal, or of glass coated chemically with a very thin layer of polished silver. The mirror presents the advantage (especially important for photographic applications) of absolute achromatism. On the other hand, more light is lost in the reflexion than in the passage through a good object-glass, and the surface of the mirror needs occasional re-polishing or re-coating. For fuller information see TELESCOPE. The function of a telescope is to increase the "apparent magnitude" of distant objects; it does not increase the
- apparent brightness." If we put out of account the loss
of light by reflexion at glass surfaces (or by imperfect reflexion at metallic surfaces) and by absorption, and suppose that the magnifying power does not exceed the ratio of the aperture of the object-glass to that of the pupil, under which condition tl.j pupil will be filled with light, Ave may say that the "apparent brightness" is absolutely unchanged by the use of a telescope. In this statement, however, two reservations must be admitted. If the object under examination, like a fixed star, have no sensible apparent magnitude, the conception of "apparent brightness" is altogether inapplicable, and we are con cerned only with the total quantity of light reaching the eye. Again, it is found that the visibility of an object seen against a black background depends not only upon the "apparent brightness" but also upon the apparent magnitude. If two or three crosses of different sizes be cut out of the same piece of white paper, and be erected against a black background on the further side of a nearly dark room, the smaller ones become invisible in a light still sufficient to show the larger. Under these circum stances a suitable telescope may of course bring also the smaller objects into view. The explanation is probably to be sought in imperfect action of the lens of the eye when the pupil is dilated to the utmost. The author of this article has found that in a nearly dark room he becomes distinctly short-sighted, a defect of which there is no trace whatever in a moderate light. 1 If this view r be correct, the brightness of the image on the retina is really less in the case of a small than in the case of a large object, although the so-called apparent brightnesses may be the same. However this may be, the utility of a night-glass is beyond dispute. The general law that (apart from the accidental losses mentioned above) the "apparent brightness" depends only upon the area of the pupil filled with light, though often ill understood, has been established for a long time, as the following quotation from Smith s Optics (Cambridge, 1738), p. 113, will show. "Since the magnitude of the pupil is subject to be varied by various degrees of light, let NO be its semi-diameter when the object PL is viewed by the naked eye from the distance OP ; and upon a plane that touches the eye at 0, let OK be the semi-diameter of the greatest area, visible through all the glasses to another eye at P, to be found as PL was ; or, which is the same tiling, let OK be the semi-diameter of the greatest area inlightened by a pencil of rays flowing from P through all the glasses ; and when this area is not less than the area of the pupil, the point P will appear just as bright through all the glasses as it would do if they were removed ; but if the inlightened area be less than the area of the pupil, the point P will appear less bright through the glasses than if they were removed in the same proportion as the inlightened area is less than the pupil. And these proportions of apparent brightness would be accurate if all the incident rays were transmitted through the glasses to the eye, or if only an insensible part of them were stopt." Resolving Power of Optical Instruments. According to the principles of common optics, there is no limit to the resolving power of an instrument. If the aberrations of a microscope were perfectly compensated it might reveal to us worlds within a space of a millionth of an inch. In like manner a telescope might resolve double stars of any degree of closeness. The magnifying power may be exalted at pleasure by increase of focal length and of the power of eye-pieces ; and there are at any rate some objects, such as the sun, in dealing with which the accompanying loss of light would be an advantage rather than the contrary. How 7 is it, then, that the power of the microscope is subject to an absolute limit, and that if we wish to observe minute detail on the over-lighted disk of the sun we must employ a telescope of large aperture ? The answer requires us to go behind the approximate doctrine of rays, on which com mon optics is built, and to take into consideration the finite character of the wave-length of light. A calculation based upon the principles of the wave- theory shows that, no matter how perfect an object-glass may be, the image of a star is represented, not by a mathe matical point, but by a disk of finite size surrounded by a system of alternately dark and bright rings. Airy found that if the angular radius of the central disk (as seen from the centre of the object-glass) be 0, 2R the aperture, A the wave-length, then 0=1-219725, showing that the definition, as thus limited by the finite- ness of A, increases with the aperture. In estimating theoretically the resolving power of a telescope on a double star we have to consider the illu mination of the field due to the superposition of the two independent images. If the angular interval between the components of the double star w r ere equal to 29, the central 1 Cmiib. Phil. Proc., vol. iv.
