210 Mr. C. Y. Raman : The Experimental 



indefinitely near the positive side of the surface 



=-j£(^)^* cos0 



where N is the indefinitely small distance of the point from 

 the nearest element of the surface and 6 is the angle between 

 n and r. 



e -iW 



In the particular case in which S is an infinite plane and cj> is 

 constant over the whole of it, the expression (b), instead of 

 being an approximation true in the limit (N = 0), is perfectly 

 rigorous for all values of N and expression (a) reduces to 



which is the velocity potential of two sets of aerial waves 

 proceeding from the infinite plane, on opposite sides of it, 

 to an infinite distance. 



If the surface over which the integration is effected is part 

 only of an infinite plane, the integral (a) can be written as 



At points on that part of the infinite plane over which the 

 integration is not effected, the integral (c) is zero, for (fig. 3) 



= o and cos 6 = for all such points. This part of the 



Fig. 3. 



71 



L 6 



as 



infinite plane is therefore one of 'silence.' This is true 

 whether <f> is or is not constant over the whole of the surface 

 of integration. 



