16 Mr. R. A. Houstoun on the Effect of a 



As the one wedge is moved past the other, $ 2 changes ; and 

 each o£ the six terms gives a similar system of maxima and 

 minima. It is the system with the phase § 1 — <$ 2 + a on which 

 the working of the instrument depends. Its intensity is 



— times the intensity of the others ; and the position of its 



minima is not appreciably affected by the other systems. 



Hence we can disregard the other systems, i. e., we can 

 disregard the second terms in the expressions (I.) and (II.). 

 On entering the second plate the first terms become 



(E 2 + E'V)^ I (i_*2) sin /T-n-tan- 1 ^ +^sin(j-r 1 -tan -^-) 



+ (E /2 + EV)*|^cos('T / -/ 1 ~tan- 1 ^V/ccos('T'-Z 1 -tair ] ^)} 

 and 



(E^ + E'V^j^cos^T-^-tan-^^-^cos^T-n-tan- 1 ^)} 



+ (E'* + EV) I | (l-^sin^T'-Zi-tan-^U^sin^T'-Zx-tan-^)! 



If we disregard the k 2 terms, on leaving the second plate 

 the two components are 



(E 2 + E / V)*sin(T-r 1 ~r 2 -tan- 1 ^-^ + (E /2 + EV)^ 



{/ccos^-/ 1 -/ 2 -tan- 1 J)-^cos(r-/ 1 -r 2 -tan- 1 ^ E j} 

 and 

 (E^E^^JKCOs/T-n^ 



(E^ + EV^sin^r-Zi-Zo 



tan-i^5 



We can disregard the third term in the first component 

 and the second term in the second component for the same 

 reason that the second terms were disregarded above. If we 

 multiply the first component by cos ty and the second by 

 sin ty and add, we get the vibration in the principal plane of 

 the analysing nicol 



\ (E 2 + E'V) cos 2 ^ + EVsin 2 ^psin(T-r 1 -~r 2 -tan- 1 ^- / +tan~ 1 k tan tJtJ 

 + {(E' 2 + E 2 /c 2 )sin 2 ^ + E / Vcos 2 ^Psin(T / -/ 1 -/ 2 -tan- 1 ^+tan-- 1 ^cot^ 



