April 19, 1880.] Lord Bayleigh, On the aberration of a lens. 373 



April 19, 1880. 

 Peofessor Newton, President, in the Chair. 



Asa Gray, Professor of Natural History in Harvard University, 

 Cambridge, Mass., having been nominated by the Council, was 

 ballotted for and duly elected an honorary member of the 

 Society. 



W. W. Cordeaux, St John's College, and C. M. Prior, Trinity 

 Hall, were ballotted for and duly elected Associates of the 

 Society. 



The following communications were made to the Society : — 



(1) Lord Rayleigh, M.A., On the minimum aberration of a 

 single lens for parallel rays. 



It is well known that when the material of a lens is plate 

 glass (//,= 1'5), the aberration is least when the lens is double 

 convex, the radius of the anterior surface r being equal to -^^ of 

 the focal length f and that of the posterior surface (— s) equal to 

 \f The residual aberration 8/" is then given by 



¥=-il^ (1). 



y being the semiaperture *. 



In the older works on Optics the special supposition that 

 fjb = 1'5 is introduced at the beginning of the calculations, so that 

 the results are not available for an examination of the effect of a 

 varying refractive index ; but it has been repeatedly asserted that 

 lenses formed of diamonds or of other precious stones of high 

 refracting power have an almost inappreciable aberration "f. In 

 Coddington's Optics, § 89, the minimum aberration for /a = 2 is 



stated to be only ^ ^ , but no algebraical calculation is given. 



* Parkinson's Opiics, §§ 130, 131. 



t E.g. Optics. EncijclopcccUa Britannica, 1842. 



