408 Lord Rayleigh on the Interfere nee Bands 



the spectnil line <j>(.v) can be deduced from the " visibility- 

 curve." By Fourier's theorem, 



<£(#) = - I du < cos u.r 1 cos uv </>{v) dv 



+ sin ux \ sin uv <f>(v) dv V ; 

 J— » J 



or in your notation, if we identify u with 2ttD } 



</>(#) = - I du < C cos i&» + S sin ?<# ?• . 



Hence, if C and S are both given as functions of m, 

 <£(,r) is absolutely, and uniquely, determined. However, the 

 visibility-curve by itself gives, not both C and S, but only 

 C 2 + S 2 ; so that we must conclude that in general an inde- 

 finite variety of structures is consistent with a visibility- 

 curve given in all its parts. 



But if we may assume that the structure is symmetrical, 

 S = 0; and <f> is then determined by means of C. And, since 

 V 2 =C 2 /P 2 , the visibility-curve determines C, or at least C 2 . 

 In practice, considerations of continuity would always fix tbe 

 choice of the square root. Thus, in the case of a spectral 

 band of uniform brightness, where 



V 2 = sin 2 7Tfl/7r 2 n 2 , 

 we are to take 



C = sin irnlirn, 

 and not 



C = + N /(sin 2 7r?V'7rV). 



In order to determine both C and 8, observations would 

 have to be made not only upon the visibility, but also upon 

 the situation of the bands. You remark that u it is theoreti- 

 cally possible by this means to determine, in case of an 

 unequal double, or a line unsym metrically broadened, whether 

 the brighter side is towards the blue or the red end of the 

 spectrum." But I suppose that a complete determination of 

 both C and S, though theoretically possible, would be an 

 extremely difficult task. 



If the spectral line has a given total width, the "visibility" 

 begins to fall away from the maximum (unity) most rapidly 

 when the brightness of the line is all concentrated at the 

 edges, so as to constitute a double line. 



It is interesting to note that in several simple cases the 

 bands seen with ever increasing retardation represent the 



