270 ADAMS : RAYLEIGH-ZEISS INTERFEROMETER 



dp ^^ I \ 1 \ 



(7j 



dn- ^^^'''Wl{~ V 



dn ^^""Wh VH+sm2d/ 

 whence by combination with (3), we have 



1 1 



,o\ dp ^ J Vh Vh + sin 2 e 



(8; -i = 2 n dn . . ^ = 



V V i7 - 1 - y/E + sin 2 + sin + cos ^ 



For small values of Q (the usual case) we may write sin 6 = 

 and cos 6 = 1. The above expression then reduces with suf- 

 ficient approximation to the following: 



Ap 2n An 



(9) ^ 



P hW H - I) 



For ordinary crown glass n = 1.52 and the above formula 

 reduces to 



(9a) -^ = 0.94 An 



Now for the change of path p, caused by the insertion of suc- 

 cessive plane-parallel plates perpendicular to the direction of 

 the light, pi = h{n — 1) and therefore dpi/p = dn{n— 1). 

 But dn/{n — 1) is the ordinary ''relative dispersion." Hence 

 if we write (9) in the form 



(lOA) 



where 



(lOB) 



q is then the factor by which we must multiply the relative dis- 

 persion of the glass plate in order to obtain the proportional 

 change of path (Ap/p) resulting from a given increase (An) 

 of the refractive index of the plate. The value of q for ordinary 



