86 Mr. E. Howard Smart on a Formula for 



Proceeding to a third approximation we may assume A as 



of the order Ay 2 and neglecting powers of & above the 

 fourth, r * 



^{'-K>-l)('-S(t)'}-^] 



= a similar expression in ft t , A t , and */. 



We can use the relation 6i-\Si s= &•«/ se ?/; again correct to 

 this order of approximation. 



+ \vl » (_i L. Wtf f-i L.^ 



-i^[4^a(^a)(i-fc)_^(i-3)(i-*)] 

 +*-["f-^] 



where A' denotes the value of A as obtained from the last 

 approximation. 



Summing the difference equations for the system of 

 refracting surfaces and putting © t for 



we get 



