Mr. Lubbock on the Double Achromatic Object Glass, 165 



-"■{-i(l— s)(*+6)} 



,.,A'-,)--{.-i(-!:- i)(/ + £)} 



j_ J i <Y 11 , n i\nj T\/Y i_w 



r A'"ffi\r A J \r Aj\r~ A/\A mA'J 2 



" jti&XF* ~A\7~A r )j F + ,&C * 



Neglecting y\ 

 I 1 m / 1 lA JL 1 _ 1 /I Yv 



r A != 7»-lVA' A/ r A' == w— 1\A' aV 



Hence, neglecting j/ 4 , 



A'~ mr + wA + \wA' AJ\A' A J 2(w-l) 2 ' 



Hence, if r v r 2 , r 3 , r 4 are the radii of four spherical sur- 

 faces; A v A 2 , A 3 , A 4 , the distances from the vertex at which 

 the ray intersects their common axis after refraction at the 

 first, second, third, and fourth surfaces respectively, neglect- 

 ing the thicknesses; m, the index of refraction for the substance 

 of which the lens is formed which is bounded by the first 

 and second surfaces ; m\ the index of refraction for the sub- 

 stance of which the lens is formed which is bounded by the 

 third and fourth surfaces ; then, neglecting y 1 , 



A = mr + mA + \ mA x A ) \ A t A J 2(m — ly 



Ag "" r 2 + Ai I A 2 »»Ai/\A 2 Ai / 2(m— I)* 



JL_ _ w'-l 1 f J| i S |JL JM 8 my 



A 3 ~ r 3 "TaT \ wt'As "" A 2 ) \ A 3 """ A 2 / 2 (»?»'— 1)* 



J_ _ m'—\ m' f 1 1 ) f 1 1 \ 8 m*^ 



A 4 ~ ~~ rT" + A 3 + lA 4 ?/*'A 3 /\A 4 A 3 / 2(?/«' — 1)* 



A 4 y \ r 4 r 3 ) 'Irj ^ J A 



