lOi S. R. Williams — An Achromatoscqpe. 



in changing the thickness of the film. To put it in other 

 words, if a yard contains a certain number of sheep and a 

 greater number are driven in on one side than are let out on the 

 other the number in the yard will be increased. When the 

 difference in path is made any multiple of what it was before 

 the change, then that same number will also indicate the ratio 

 of the number of bands lying between any two wave lengths 

 before and after the change was made. For instance, let 

 N'd/ISFd = 2, 3, 4 or 5, etc., then p 2 /p 1 will also equal 2, 3, 4 or 

 5, etc. Let us makep 2 /p 1 = r and then 



"N ' "NT ' n 



£-5=-^=^ = r. (11) 



We are now in a position to obtain a numerical value for N D 

 even if we have not commenced to count when j^" d = 0, for 

 from (5) and (11) we obtain 



N D =— . (12) 



Equation (12) is the one obtained by the late Professor D. B. 

 Brace* in a paper on the use of spectral bands. This rather 

 visualized method for deducing it is given here in the hope 

 that attention may be drawn to the importance of the equa- 

 tion in certain optical measurements. The form of the equation 

 as first derived by Bracef and used by his pupils was 



mr 



The only difference in the two formulae is that the r in one is 

 the reciprocal of the r in the other. Either form is correct if 

 properly interpreted. 



Suppose we have a thin transparent film of any substance, 

 refracting or otherwise, and if light, reflected from the front 

 and rear surfaces of the same, is allowed to illuminate the slit 

 of a spectrometer, a channeled spectrum will appear in the 

 field of view. If we count the number of bands, p t , between 

 any two definite points in the spectrum and by any means 

 whatsoever we can vary continuously the thickness of the film 

 so that m bands pass a selected wave length and again count 

 the number of bands, p 2 , between the two definite points 

 between which p x was counted, then the order of interference 

 ma} 7 be determined for the wave length past which m bands 

 defiled in changing the thickness of the film. This is an 

 interpretation of equation (12). 



* Brace, Phvs. Rev., vol. xxi. p. 289, Nov., 1905. 



t Brace, Phil. Mag, p. 350, Oct,, 1899 ; Phvs. Rev., vol. xviii, p. 280, Apr., 

 1904. 



