

On Spectroscopic Measurements. 339 



This question has been discussed by Ebert*, who concludes 

 that the width of the spectral lines due to this cause is not 

 consistent with the results obtained by interference. 



Lord Rayleigh f has shown that this conclusion does not 

 hold ; and that the apparent inconsistency is, at least in part, 

 due to the arbitrary assumption of a concentration of light at 

 the edges of the line. Proceeding to investigate the case of 

 uniform distribution, he arrives at the result that for this case 

 the visibility-curve is periodic. 



It will appear later that this is the fact in most, if not all, 

 of the radiations thus far examined. This is at variance with 

 the result obtained by Lord Rayleigh for a distribution result- 

 ing from Maxwell's law of velocities ; but it is expressly 

 stated that " the case of electric discharge may require further 

 consideration." 



The general formula for the visibility of fringes due to 

 interference of two streams of light whose difference of path 

 is variable, from a source which is not homogeneous, is the 

 same as that for a source of finite area whose " parallax " is 

 variable. 



For the resulting intensity of two equal homogeneous 

 streams of light is 



T A 2 D 



J.! = 4: COS" 7T — • 



A 



If the light be included between wave-numbers n± and n 2 

 and the illumination from dn be ^(^n)dn % 



1=1 1^1/1 = 4: I ^(n)coi^irD)idn. 



= 1 1^ = 4:1 



If for n we substitute n + x, in which n is the mean wave- 

 number, and for yfr(n) put (j>(x), we have 



1=1 " <j>(x) cos 2 7rD(/t + x)dx 



Expanding and omitting the factor 2, putting 



J c/> (x) dx — P, J (/) (x) cos 27rDx dx = C, 



27rD7i = S, and J <f> (x) sin 2ttDx dx = S, 



we have 



I = P + CcosS-SsinS. 



* Wied. Ann. vol. xxxvi. p. 466 (1889). 

 t Phil. Mag. April 1889. 



