PfiUMMER — On the Symmetrical Optical Instrument. 7o 



define the successive formation of //,-, h/ : and 



- 47JV - AAWi 2 ' %V + 4WW 



+ 2D i h*h i ' i Pi . lPi ' - 4#,A,V,,> M r / - tFikiWpi'Ti 

 where the coefficients A„ . . ., F ( have the meanings found in *J 4. 



6. It follows at once from (10) that 



. . . = if,-! = «,=..., . . . = £,-_! = K; = . . . 

 ...= )),_! = >;,=..., . . . = c,,- _! = <;,• 



when the third order is neglected. Therefore to the third order, by 

 addition, 



, dW iv dW™ 



>)j - »Jo = -5 — . '(/ " la = n / > 



yi yf _dW iv dW" 



Cj - 5. - % , lj - U - - -gj , 



where / is the number of the final refracting surface, 

 - 4^* = -42 W? 



4=1 



= ,4,>„ 2 + 5/>/ 2 + 46V,/ i 20/irf./ - 4%r UI - - 4%'r,,,- 



' t Y ¥ ' 2 . y '' ' '2 . ?* '9 



r »/ = 'w + 4o£/ : p = ijo t- S > py - i • + s/ ", 

 and in terms of the quantities already found (§ 4) 



A = ^A;h;\ B = ZBihi' 1 , G = SCJW, 

 D = ZDih ?h i'\ F = 22V V> i, F = SFJi Ji ,' 3 . 



Let di = «, n - c<i be the distance (from left to right) between the 

 surfaces i and i + 1. Then 



di = («; n ~ C;) - (a; - Ci) = (C(; n - C;') - ((( ; - ('/), 



and, to repeat the notation, 



A; = w\ + - = p; i 



K[ = A>,- - p;_ v K;" = A'/', - /( ,-, 



Li = Z,)-, - p ; _ v L" = Lffi - /<,-, 



