Aberrations of a thin Lens of XJniaxal Crystal. 293 

 Accordingly these values give 



in the second member of which we have 



T*~~ W + ** = W " r ) \2*~ V ~ r /• 



and may write 



\ * / Z /ub — I \z' Z / 



the formula for an ordinary spheric refraction is therefore thus 

 found to be 



~ ju,- 1 V i a'/ V* ?V 2' 



/ i l \ 2 



in which it may be remarked that ( , f J 2 is the square 



of the angular deviation, and which is easily seen to agree 

 with known results. 



7. Returning to the crystal, let it be bounded by a second 

 surface of revolution, infinitely near to the former, and about 

 the same axis; and let the light emerge at this second surface 

 into a vacuum again. The equation of the second surface 

 being 



r' = Y'' r + t 5 '*' 4 ' (270 



and the ordinate of the intersection of the emergent ray with 

 the axis being z", the formula (24.) will apply to this new 

 case by merely changing r, s, z 1 , z respectively to — r\ — s 1 , 

 — z", — z, without changing jut, v, £; and we have 



And, adding the two equations (24.) and (28.), we find 



. . (26.) 



