268 Prof. A. Anderson on Kirchhof's 



time which vanishes except at points where there are 

 sources, and that the solution of the equation is 



-rM* 



V = i 1 1 — * dx dy dz 



throughout all space, we have KirchhofFs formula for the 

 most general^ case by writing V for <f>. If, in addition to 

 volume distributions, there are surface distributions of 

 sources at which 



Thus V the value of Y at any point outside a surface 

 enclosing all volume and surface distributions of sources is 

 given by the formula 



4:7rJJ \0n r r on, r \/ 



\ a' 



r being the distance of the point from an element of the 

 surface. In the first term the differentiation with respect to 

 the normal is performed on r alone and, in the second term, 



t is written for t after differentiation. KirchhofFs 



a 



formula has thus been shown to follow directly from a 

 generalization of Green's theorem. 



As remarked above, the development of (f>(t — -^— — -\ 



and of -rcbit 1 °) by Taylor's theorem must conform 



dl^\ a J " 



to the conditions of validity, and these conditions must hold 



in the application of the series to any question considered. 



The time t is the time at which the actual disturbance 



reaches B, while t~— is the time at which a secondary 



disturbance starts from A. The resultant at B of the 

 secondary disturbances is made up of components which 

 start from A at different times, and what is shown is 

 that this resultant is the same as the actual disturbance at B 

 at the time t. 



