ADAMS: RAYLEIGH-ZEISS INTERFEROMETER 269 



eliminating e from equation (3) we have 



which reduces with sufficient approximation to the power series 



(5) V 



V'2 



1_^ 1_J__ J:^_l 



R ^-^ - R—-r^^ + ^'-^^-^^3 — 



a 2 a a^ 



Now let R'~^ be a quantity such that 



a / I 



hi 



then 



1 



(6) R' = R-R' , , - + R 



J_ 1_ _ 1 



^1.5 „ Vh 2 



2a(l-4^^ a^(l- ' 



V'hJ ^ V H/ 



As an example, in our instrument (the Zeiss Water-Interferom- 

 eter) a = 110 mm. and 7ij) = 1.514; moreover, if r represents 

 the number of divisions on the drum corresponding to a given 

 value of R, r = 200 R (also r' = 200 R') ; for these values formula 

 (6) reduces to the expression 



in which the last term is almost entirely negligible. Values of R' 

 (and hence also of r') calculated in this way are proportional to 

 the decrease in optical path resulting from the tilting of the 

 compensator plate, and therefore strictly proportional to the 

 quantity p, the refractive index difference of the solutions. 



Another use to which fornmla (3) may be put is the calculation 

 of the variation with refractive index ?i of the path difference 

 p corresponding to a given angle 6. Thus by differentiation, 



