362 Mr. S. D. Chalmers on the Sine Condition 



Thus 



a? t> \ 7 fju sin A / v ; 



Even though the value of Hi be large, the relation 

 /xoOOi sinPOxN^^IIa rinQIjNj 



holds good ; but the point Q is no longer the theoretical 

 image of P or even on the ray OPI. 



The relation (II.) above, expressed in the form 

 jul . m . IIj is invariant 



furnishes a convenient check upon the results of trigono- 

 metrical calculations for oblique rays. 



Rays in one Plane. 



For the case of rays in one plane we may adapt the method 

 of Hockin to give further information. In this method the 

 optical length, i. e., 2/t* x actual length, is stationary for the 

 actual path. We cannot, since aberrations are present, 

 assume that all optical paths between the same points are of 

 the same length, merely that the difference between two 

 neighbouring rays is zero. 



All the rays are in one plane. 



Oi, 2 are two neighbouring object points ; 



~P 1} P 2 two neighbouring points on the stop plane ; 



Nx the centre of the stop ; 



OiP], OiP 2 , and OiNx pass through the system and meet 



2 Pi, 2 P 2 , and 2 N! in the points Q x , Q 2 , and Q 3 and 

 intersect the image plane in I 1? I 2 , and L ; 



2 Pi, 2 P 2 , and 2 Ni meet the image plane in J 1} J 2 , and J 



Q1I1, and Q 2 I 2 meet in E]_ ; 



QiJx and Q 2 J 2 meet in F { . 



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