10S VISION WITH THE (.'<LMP<rM .MICROSCOPE 



y-b'=m'(x-OW) . (3) 



Let the equation to Sj bey- 6'=m // (a;O 1ST') . . (4) 



Prom (2) and (.".) 



//_/,=/' (ON' ON) = //'X'X = >//fZ . 

 Now sin C B. A=;u . sin C R B ; 







(' A .-iiid (' I! are the v.-ilues of // in equations (1) and ('2) 

 .'==( ) C ; 



.-. C A=& + (OC-ON) = /' + m r; 



ami >imilarlv CB=6 + ?>(/?'; 



.-. (ft+mr) sin C A R=/t (6 + m' ) sin C B R. 

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

 other. xi that for a first approximation we may consider them to be 

 equal. 



/. k -\--JH r=n(h-\-m' ?), i.e. u. m f =m . f>. 



r 



= ; then ju m'=m b n . . . ((>). 

 Similarly, sin C' S B'=p . sin C' S A' ; 



^ n C' B' S=^ - sin C' A' 8 ; 

 and, as before, 



C' B'= / + m" ', C' A'= // + //// ' from equations (4) and (:}) ; 

 .'. as before we may lake 



Let ~ = "'- tll( ' n M in' = m" !>' >' . (7) 



Krom (-)) and ((}) // = /, + '"-'' ",/ = A ^ ^ * 



/' \ M / fJ. 



this and (7) m"=u m' + b H' (\ - <f "} _^' 



V A' / " A* 



and t'roin ((}) =, }, + /, M / 'i r/ " \ . ;// 



/' 



Assume 



'^A , ' 7 "' <l U U f 



.'' ' ,=.'/-!+ =/, / // - 



* /' 



t '"' 11 I>'<J /> + /! /// 



^ be the coordinates of P, the -point from wliidi the 

 r.-'\ "i bghl proceeds : 



6=Y-j (X-O.X, : 



