TIIK THEORY OF OPTICAL INSTRUMENTS. 



Let their curvatures be concave towards the instrument, their radii being 

 , and /, respectively, then, 



We must now insert these values in equation (5), but, for the sake of 

 Minplicity, we shall suppose the planes of reference to pass through the principal 







We now Hnd f t = * /, = 



Jj jj 



'* 2tf, 



'"i+i' a ' = ITi < 17 )- 



Hamilton's function for a symmetrical instrument is of the form 



tf+V) 



K + 6 3 ')' 

 (tt.rt, + 6,6,) (,' + 6,') + q (,' + 6,') (a./ + 6, J ) 



+ r ( a i* + 6, s ) (a,a, + 6,6,) (18). 



hiffcrentiiiting. and making 6, and 6, zero, we find 



- 1 = 81 + 3a, s + 6ra,a, + (6 + f/) ,* 



B-84-3fa 1 i +(26+2j)a 1 a-J-3po, f (19), 



C = 6 + (6 + q) a? + 6pa,a, + Sea, 1 



x4' = 21 + art, 1 + 2raja, + qa? \ 



1? = Q + ra* + b<i l ti, + j>af I (20). 



C = G + ^a, 1 + 2paa, J + ca,' ) 

 It' tlu- pliiiies of reference pass through the principal foci, 



21 = and 6 = (21). 



Substituting in ^nations (5) and (7), and putting 





