PLATES. The PLATES are wrong numbered, but may be distinguished by observing that some are marked with Arabic and some with Roman numerals. PLATE 1. refers to Mr. Airy's Paper on the Spherical Aberration of Eye-pieces, No. I.. 2. refers to Mr. Airy's Paper on the Theory of Escapements, No. III. I. refers to Mr. Willis's Paper on the Pressure of a Stream IV. refers to Mr. Morton's Paper on the Focus of a Conic 4. refers to Mr. Willis's Paper on Vowel Sounds, No. X. 7. refers to Mr. Miller's Paper on Crystals, No. XV. 8. No. XIX. 9. refers to Mr. Coddington's Paper on the Microscope. ADVERTISEMENT. THE Society as a body is not to be considered responsible for any facts or opinions advanced in the several Papers, which must rest entirely on the credit of their respective Authors. I. On the Spherical Aberration of the Eye-pieces of I. Telescopes. BY GEORGE BIDDELL AIRY, M. A. FELLOW OF TRINITY COLLEGE, AND OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, [Read May 14 and May 21, 1827.] In a paper on Achromatic Eye-pieces, which was read before this Society about three years since, and is printed in the second Volume of the Transactions, after giving the equations which must be satisfied in order that an eye-piece may be truly achromatic, I stated my intention of laying before the Society, at some future time, investigations of the conditions most favourable for the destruction of spherical aberration. I now proceed to fulfil this promise, by presenting to the Society an investigation, which I hope will be found pretty complete, of the course of a small pencil of homogeneous light after refraction by a lens; and by pointing out the application of the resulting expressions to the theory of eyepieces. I have not considered the general case of a small pencil incident in any direction, but have confined myself to the cases in which the axis of the pencil passes through the axis of the lens: a limitation which, however, includes every thing relating to the eye-pieces of telescopes and microscopes. The importance of these investigations, has been acknowledged by every scientific artist, and by every writer who has endeavoured to assist, by practical rules, the common workman. But the complication of symbols has prevented most writers from entering upon Vol. III. Part I. A the subject at all: and those who have made some steps, have confined themselves to the simplest cases. I am not aware that any writer has investigated the conditions which must be satisfied that an object may be seen distinctly in all parts of the field of view, though this is the most important point in the construction of eye-pieces. The effects of spherical aberration may be described as follows. The first is a distortion of the object. If, after examining an object in the center of the field of view, we bring it to the outside, we shall frequently find that it is extended in the direction of a radius of the field of view, and that it is increased, though in a smaller degree, in the other dimension. If we look at a square, it will appear to be drawn out at the corners, so that the sides are all convex towards the center. Sometimes the contrary effects will be produced an object being less magnified at the circumference of the field than near the center. This defect may, in many cases, be entirely removed. The second effect is, that if an object be distinctly visible in the center of the field of view, it is necessary to push in the eye-piece farther, in order to see clearly the objects at the outside of the field. In consequence of this, it is impossible, with the same position of the eye-piece, to see distinctly all parts of the field, or to see an object distinctly as it passes the field of view. This defect can never be destroyed. The third effect is, that no adjustment of the place of the eye-piece will make an object distinctly visible when it is far from the center of the field of view. If a brilliant point, as a star, be viewed in this situation, with one position of the eye-piece, it appears a bright line in the direction of a radius of the field, and with another position it appears a bright line in a direction perpendicular to the former: with other positions it appears an ellipse, or a circle. In the case last mentioned, different parts of the last image are formed at different distances from the eye: in this case, no distinct image is formed at all, except in the center of the field; the rays of other pencils never converging accurately to a point. This defect may frequently be entirely corrected, though it is sometimes prudent to leave it partially uncorrected. But upon pursuing the investigations, it will appear that these conditions frequently interfere with one another, so that the construction, which is most advantageous for obviating one defect, makes another pretty large. And this has occasioned some anomalies in the practical rules which workmen have established. The lenses commonly in use are double equi-convex lenses, and plano-convex lenses: and the general rule of workmen is to place these in such a manner that the angle made by the incident ray with the first surface, shall be nearly equal to the angle made by the emergent ray with the second surface. This I believe is to diminish the distortion; and, for that purpose, the rule is not very far from the truth. But there is a remarkable departure from this law in the construction of the common eye-piece (Ramsden's) for transit instruments, and, generally, for all telescopes to which micrometers are applied. The eye-glass, nearest the object-glass, is a plano-convex, with its plane side towards the object-glass. This construction (which makes the angles above-mentioned extremely unequal) is adopted for the purpose, as workmen express it, of procuring a flat image; that is, for the purpose of making all parts of the image, after refraction, at the same distance from the eye. In this construction, then, the first condition is given for the second: and the third is not at all considered, no general rule having been given for it. up It is necessary, then, to consider on which of these conditions the greatest stress should be laid. When the aperture of the telescope is very small, or its magnifying power very great, the breadth of a pencil is very small, and the second and third defects become |