Interference Phenomena. 543 



interfere, it is necessary that their effects should overlap. 

 When an interference pattern is produced either in a spectro- 

 scope, or with the help of a medium like the eye snowing 

 selective absorption, it always means that each impulse is 

 spread out so as to overlap the one which follows. Looked 

 at from a different point of view, we may say that two perio- 

 dicities are involved in every case of interference. We have, 

 in the first place, a retardation of path of the two interfering 

 rays. Whatever the nature of light, if analysed by Fourier's 

 theorem, this retardation is seen to produce a periodicity, 

 which, however, alone is not sufficient to give rise to inter- 

 ference effect. The prism or grating which analyses the 

 light, or some medium showing selective absorption, intro- 

 duces the second period. If there is without such means an 

 interference which can be objectively observed with a ther- 

 mopile or bolometer, it means that there must be some pre- 

 vailing period in the original light. The light may be homo- 

 geneous or it may only show like sunlight a maximum of 

 intensity in some region of the spectrum. 



22. We have calculated the disturbance produced by a 

 grating with the help of an equation (1) § 8, which may be 

 proved in a more rigorous manner. Let (f> be a function 

 satisfying the differential equation 



5 =aV< k (7) 



and having given values cj> and -~ at the boundaries of the 



space we are considering. Kirchhoff* has shown that at any 

 point P within that space (f>(t) may be expressed by 



where the integration is extended over the boundary of the 

 space, and 



n= d K'-'a) 4"^) , 



dN 

 f( t ) = &t 



N is the normal directed to the inside of the space, and r 

 is the distance of the point P from the element dS of the 

 surface. The differentiation in the first term of H is to be 

 carried out as if r were the only variable. The expression 



* " Zur Theorie der Lichtstrahlen," Wied. Ann. Bd. xviii. p. 663 (1883), 

 and Gesammelte Abhandlungen, jNachtrag-, p. 22. 



2 P 2 



