108 VISION WITH THE COMPOUND M1CKOSCOPE 



or, yb'=in'(xOX') . (X) 



Let the equation to Sp be y -b'= in' '(, O X') . . (4) 



From (2) and (3) 



b'-b=m' (ON'-ON)=m'X'X = /y/^ . . (">) 



Xo\v sin C R A=/^ . sin ORB; 



^ . sin C A R =J u . V* . sin C B R. 



Now C A and C B are the values of // in equations (1) and (2) 

 when #=0 C ; 



.; C A=&-fw(OC-OX)=+wr; 



and similarly C B= ?; + ?/&' ; 



/. (b + mr) sin C A R=/w, (b+m 1 r) sin C B R. 

 Now CAR, GBR do not in general differ much from each 

 other, so that for a first approximation we may consider them to be 

 equal. 



.'. b-\-m r=p(b-}-m f r), i.e. p m f =.in . b. 



r 



Let =u ; then u. m'= i m b n 



r " 



Similarly, sin C' S B'= M . sin C' S A/ ; 



or, . sin C' B' S= . sin C' A' S ; 



and, as before, 



C r ~B'=b' + m"<>' / , C' A'=b' + m' r' from equations (4) and (3) ; 

 .-. as before we may take 



Let _ = %', then /u m' = m" b' ,,' . . (7> 



C1 /K\ 1 /r\ I/ 7 , W - &** 7 7 / ^W\ ?> '' ^ 



From (5) and (6) ?/=/>+ - =;6 I j _ 14. 



/i V P/M 



.,. j /_ x / . 7 / /i (Z?fc\ in d id 



this and (7) m" = um f + bn' (1 14- 



V A* / /" 



and fi-om (6) =m-?y // + /; v// (\ - 



d 



Assume 



d d u du f <1 n u' 



- =h [ = g 1 + -=/, w n =/.' 



P H V P 



then 



Now let X, Y be the coordinates of P, the point from which the 

 ray of light proceeds ; 



then by (1) 6=Y w (X-O N) ; 



