276 ADAMS : RAYLEIGH-ZEISS INTERFEROMETER 



of the solution with respect to water by the relation 



vp- v c 



/3 = 



then {B, - B^jv = /S'/l-Ql- Finally therefore 



iV^ 2(^'-g/3") &'-q^" 



(13) 



N^ (.58)2 X 1.91 0.320 



This expression gives the numbers of fringes iV( through 

 which the comparison band apparently shifts, in relation to the 

 total number of fringes N t corresponding to the position of the 

 compensator; in actual practice it is more convenient to put 

 jV"^ = r Ir^ where r^ denotes the number of divisions on the drum 

 corresponding to one fringe in white light. Making this sub- 

 stitution, and putting N'y^ = 1, we find the corresponding read- 

 ing ri to be 



(13 a) ri = 0.320 r^jifi' - q&") 



in other words, for each interval of 0.320 rj/{^' —q^") divi- 

 sions the achromatic fringe will have shifted one fringe to the 

 left of the original bright band. Consequently for any solu- 

 tion or mixture for which ^' is known, the amount of shift can 

 be accurately calculated in advance;^ the shift can therefore 

 be allowed for, and any error from this source obviated. 



In conclusion it may be remarked that in two of the three 

 forms of Zeiss instrument — viz., in the portable gas interferom- 

 eter and the water interferometer — the light passes twice 

 through the compensator plate and hence the right hand member 

 of equations 1 to 7 inclusive must be multiplied by 2 when 

 applied to these instruments. Only slight modification of the 

 formulae is required to enable them to be applied to any form 

 of compensation interferometer. 



^ Examples of the application of this formula may be found in the paper 

 already referred to, now in course of publication. 



