president's address. 197 



so on. In brief, when the slide is once set everything on the 

 slide is metrical, and everything on the rule is inches. 



The subject chosen for this evening is on the construction of 

 lenses. I will endeavour to make it as interesting as the nature 

 of the case will permit, and will leave out all mathematical 

 formulas. 



We will first touch on spherical aberration in lenses, and in 

 particular in that known as Herschel's doublet. There can be 

 no reason or need for a chromatic doublet made of one kind of 

 glass for visual purposes when an achromatic aplanat might be 

 constructed for the same cost ; nevertheless, for illuminating 

 purposes the subject is of much importance. This doublet 

 appears in the "Ency. Metrop. " in that classical article on 

 "Light " by Sir John Herschel, who was a Senior Wrangler. 

 Coddington, also a Senior Wrangler, quotes it in his excellent 

 treatise on " Optics," where he gives the radii but not the foci. 

 Sir D. Brewster gives it in the " Ency. Brit.," 7th ed., and 

 interpolates an error in one of the radii. Parkinson, a fellow 

 and tutor of St. John's, quotes it in his " Optics." That it has 

 attracted so much attention is therefore not to be wondered at. 

 I have worked out the aberrations of both Herschel's doublets, 

 and find that neither of them is free from aberration ; the 



aberration of the high power is — "296 — and the other has 



F 

 just a trifle more. The focus of the high power combination is 

 also wrong,* and this mistake is copied both by Brewster and 

 Parkinson. 



There is no doubt that the aplanatism of this doublet cannot 

 any longer be maintained. It is very easy to generalise on this 

 subject and say that as both the lenses of which the doublet is 

 composed are converging ones, therefore they both must have 

 the same kind of aberration ; the case, however, is not so simple. 

 For example, let us suppose that a pencil is converging directly 

 on the plane surface of a block of glass (refractive index 

 //, = 1 '5) to a point on the axis inside the glass and one inch 

 from that surface ; on entering the glass these rays will be 



* This is, of course, a very serious error, for any optician constructing a 

 lens of any given focus from this formula would use this erroneous focus as 

 a divisor ; the result would be that all his radii would be wrong. 



