Aberrations of a Symmetrical Optical Instrument. 273 

 Approximating in (5) we have, rejecting 3rd order terms, 



Pi -\ X i _ M"+l (Q\ 



V 



This is obviously true, for by considering the points K t -, 

 Ki+i in the figure, we have 



*i—n Si' — n 



and the positions of the Gaussian image-planes are connected 

 by the relation 



*-»(£-£)"*(£-?) (7) 



To the next approximation including 3rd order terms we 

 have 



ft-A r t . i/i i\ £ 2 +^ 2 , 65 + W< 

 "IT I 2U 5J « 



_ 1 *i+y* \ Pi-Ay,- >\\ 



_ 1 < + ,+//?+, 1 

 2 u" i 



*< a *»■' — n 



Making use of (6) and denoting the equal expressions in 

 (7) by the symbol Q t -, we have as the simplified form of the 

 last equation, 



ow 



_1/1 1_\ / 1 ___1_\ 



Pfcl. Mag. S. C. Vol. 30. No. 176. Aug. 1915. 



