.CAS8EGRAIN KKFLECTOR WITH CORRECTED FIELD. 41 



These expressions are identical, except for notation, with results given by 

 SCHWARZSCHILD ; they contain the complete theory of the Cassegrain combination, 

 corrected by figuring for coma and spherical aberration, except as regards distortion, 

 and this could i-asily I" 1 added by calculating >'. II. 



\\. read IV. mi <-<\\i:i\ ins (L'n) tliat l'i a ^i\.-n d.-i^n !' in-t ruiii.-nt , as -|..-.-iti.-d in 

 the values of *, *', u at r, we can adjust the figures of the two mirrors so as to annul 

 spherical aberration and coma at the principal focal plane, and then the curvature of 

 the field and astigmatism amount to determinate quantities. Coma is annulled only 

 f>r the purpose of getting a larger field for photography, and there is very little use 

 in annulling it if the field possesses pronounced curvature, or in less degree, if the 

 focal circles are not reasonably small. Hence the practical questions are : can the 

 design be made such that curvature is nearly absent and astigmatism small, and 

 can the corresponding values assigned to the deformations be realised in practice ? 

 All these questions are treated more or less explicitly by SCHWAIIZHCHILD, and I 

 shall traverse the ground again only in order to connect the problem with its 

 subsequent development and bring out the points which I require. 



Itegarding the expression for curvature, v u is the positive distance from the 

 principal focus of the great mirror to the principal focus of the combination. In 

 the Cassegrain form the latter point is, as a rule, not far beyond the surface of the 

 ^n-at mirror, so that v u is not far from the focal length of the great mirror and 

 I+K (?* + ') will be a small fraction ; also K'U is numerically less than unity. Hence 

 the curvature of the image will differ very little from 1/w, the reciprocal of the 

 distance from the second mirror to the principal focus of the great mirror, a distance 

 which would seldom be more than one-third or one-fourth of the focal length of the 

 great mirror, or one-tenth to one-twentieth of the focal length of the combination. 

 The common Cassegrain is subject to the same objection. The values of its errors 

 may l>e read from the equations (19) on p. 40, if we have the means to determine e, e'. 



As an illustration we may take the great 60-inch reflector of Mount Wilson 

 Observatory, which can be used either as a Newtonian, with a focal length of 

 25 feet, or in three different forms as a Cassegrain ; taking the form designed for 

 direct photography, it has an effective focal length of 100 feet, so that v/u = 4. 

 If we take the final focus at the great mirror, which is nearly the case, we have 

 u = 5, v = +20, and K = +3/20. Now since the telescope is corrected as a 

 Newtonian, the great mirror is parabolic, or e = ; and therefore taking it as 

 corrected for spherical aberration as a Cassegrain, ^-eVw = 1, or e' = 16/9, which 

 is a hyperboloidal form, the deformation from a sphere being nearly three times that 

 which would produce a paraboloid. Substituting ^eVttu = 1 in the equation for S a G, 

 we have, after some reductions, ^ a G = ru/r = ^K, or the coma of such an 

 arrangement is the same as for a simple mirror of the same focal length. Also we 

 find (? :1 G = 15, $ 3 G <S S H = 11, so that the radius of curvature of the field is 

 one-nineteenth of the focal length or about 5^ feet only. As to the astigmatism 



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