o22 Mr. T. H. Blakesley on 



axis passes the centre o£ a surface before it encounters the 

 surface itself. 



The variables 9\, rg, and d being three in number may 

 then be looked upon as sufficient to determine all the pro- 

 perties relating to focussing for small central pencils of light. 



If we contemplate the relations -^, ■—, and symbolize 



them under the letters .v and i/, or, in other words, if we 

 consider d as unityj we reduce the variables to two in number, 

 and can then represent all the ordinary properties of lenses 

 under a simple system of coordinates, where cV implies the 

 relation of the radius of the first surface to the thickness or 

 length of the lens, and ?/ a similar magnitude applying to the 

 second surface. 



The first diagram is based upon this principle. If \ye take 

 any point upon the paper its position will indicate some 

 particular lens, and all lenses haAdng some one the same 

 property will lie upon a line draw^n upon the diagram. If 

 two such lines meet the point of intersection will correspond 

 to a lens having the properties appertaining to both the lines. 

 The general characters of a lens depend upon its shape and 

 not upon its scale. But if the general characters of a lens 

 are knowai, and the point on the diagram determined, the 

 strength of a lens is then simply dependent upon the scale, 

 and can be raised as desired. 



The diagram presented is based upon the supposition that 

 jbL = l'b, a supposition which, though it was long employed 

 for glass as sufficiently exact for academical approximation 

 in the casual text-books of Cambridge University, when it 

 w^as certainly not so, has, under the laborious care of German 

 experiment, become not inapplicable to the glasses of low- 

 dispersion produced by Schott. 



It may make the use of such a diagram simpler to take an 

 example or two. 



Suppose the condition which it is desired to obtain to be 

 that the second principal focus shall lie upon the second 

 surface. 



Then from any table of optical properties, e. g. that given 

 of lens quantities in my ' Geometrical Optics,^ this condition 

 implies that the following equation must hold good : — 



Hence r^ ^i — l 



or if /A = l-5, x= — 



d fi 



1 

 3* 



