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XX. Intelligence and Miscellaneous Articles. 



ON THE FORMS OF LENSES PROPER FOR THE NEGATIVE EYE- 

 PIECES OF TELESCOPES. BY G. B. AIRY, ESQ., ASTRONOMER 

 ROYAL. 



TN the ' Monthly Notices ' for June and November last, there are 

 ■*- discussions on the forms of lenses proper for the negative eyepiece. 

 Perhaps I shall not do wrong in stating to the Society that as long 

 ago as the year 1827 I made a most elaborate investigation of the 

 properties of eyepieces as depending on the curvatures of their sur- 

 faces. The paper is entitled " On the Spherical Aberration of the 

 Eyepieces of Telescopes," and is printed in the ' Transactions of the 

 Cambridge Philosophical Society,' vol. iii. This paper had been 

 preceded by one " On the Chromatic Aberration of the Eyepieces of 

 Telescopes," from which 1 had been able to infer the proportions of 

 the focal lengths and intervals of the lenses which (independently of 

 their curvatures) destroy colour at the sides of the field, using but 

 one kind of glass ; and had selected some of these as examples to 

 which the formulae for spherical aberration were to be applied. One 

 of these is the Huyghenian eyepiece, with the following very com- 

 mon proportions: — focal length of first lens or field-glass =3M ; 

 focal length of second lens or eye-glass =M ; interval between the 

 two lenses =2M. 



The principal results as applying to the cases before us are the 

 following : — 



First, as regards distortion. 



I must refer to page 15 of the Memoir for the general formula; 

 but I may quote the following special results : — 



(a) It is possible to destroy distortion entirely, but not by the use 

 of common forms (equiconvex or plano-convex). 



(b) The most favourable combination of common lenses is, — the 

 first, equiconvex ; the second, plano-convex, with its convex side 

 towards the first lens, or with its plane side next the eye. 



Second, as regards indistinctness at the edge of the field. 



From the general formulae in page 35, it appears that it is impos- 

 sible in any eyepiece whatever, in which the lenses are all convex, 

 to secure distinctness in the approach to the edge of the field, 

 except in some cases by movement of the eyepiece ; and the problem 

 always is to diminish the indistinctness as much as possible. For 

 this purpose, in the Huyghenian eyepiece, 



(c) The different points of the image may be made distinct by a 

 little sliding of the eyepiece, by a form very nearly the same as the 

 following : — 



(d) The best form is, for the field-glass, a meniscus, with convex 

 side towards the object-glass, and radii as 4 : 11 ; and for the eye- 

 glass a convex lens, the mere convex side towards the field-glass, and 

 radii as 1 : 6. The constants by which the indistinctness in the two 



j- a 95 , 61 



dimensions is expressed are — — and — — , 



126 12o 



