I)R R A. SAMPSON ON A 

 It i. ** that the ten,,, in ,, i come to the value, B iven. Leaving these aside 



n n 



This appears, multiplied by -(1 -) B + B', and added to Wtf + W,* which is 



n 

 the whole is 





n 



~ n? n 9 



+ B* x - 3 (l-n)(\-n + n 3 ). 



This may be written 



= K'+KX 



where 



X = nBM-rr 



This is the given expression if finally we write small letters for capitals. 



It will be noticed that q, which contains the reference to the distribution of 

 curvatures, apart from their effect upon focal length only presents itself in the forms 

 in which it is introduced by S l k, S t g. It is somewhat remarkable that the same is 

 true when we have any number of thin lenses in contact.; thus, if we have a system 

 of thin lenses in contact, giving a set of coefficients S&, ..., and add a single thin lens 

 to it for which we have Stf, ..., then, noticing that 



