Plummkr — On die Symmetrical Optical tristrumenti 1\ 



where 



'<(^ + ^)=^ 



H ~Z 



Mi'V I'i 



n - p 



i -"t 



T ■" 



f*i-i>'i _ (H-fi 



Ufl & - TQ 



/'. — * c . /> . — 



i js ■// ■ t tr > " t-1 v t-l ~ 



KILl 



(5) 



Let the ray intersect the planes through C;_ v V,-, 0;'_ v C( in the points 

 (Ci-v >/i- v 2£-i), (c» Vi, %), {Ci'-v Ui'- V s/-i). (''/ Vi, ~i)- By '1), to the lowest 

 order ( W = W t u or Vf), 



K"lli = KiVi-x 





m Hi = A- Vi -i = 



m - m 



(6) 



with similar equations in (z, n), (z, n) ; since, when Wf, Ui" are neglected 



- mm = 



vwp 



ij-i-i'ji- 



dw? 



dim' r " ll/l - 1 ~ dm H ' 



By the equation of the ray in the two media 



ft ~ Cj = Vi ~ Hi = '4 - Zj 

 k »k ih 



r r f 



C t -_j - Cj_j 2/i -1 ~ yt-1 -I '■' 1 



kl 



■>»,-. 



%. 



The neglect of the third order in »!,-, ui^, ... by putting /,• = /,_j = 1 

 will affect Wi in the sixth order only. Therefore to this order 



m _ Vi ~ !H _ K"W (Vi - Vi) m LC/Lj (i//^ - i/j.J 



1 " c/ - Ci ~ f#t (Zt - IQ ' "** „^ (Z< - JQ ■■■ [ ' ) 



and the {in, y) part of Wp becomes 



Wi' 



2( J u i - w . 1 )n'(i;,-Jfi) s 



Ll'dn ->id-L; {,/{., -n;.^. 



,l- 



