262 Prof. A. Anderson on KircTilwff's 



form of an integral taken over the surface. The formula 

 thus obtained can then be applied to the case of a single 

 source or that of several sources of light emitting vibrations 

 which travel through the aether with constant speed. It 

 is, however, instructive and interesting to proceed dif- 

 ferently, and begin with the case of a single source. It 

 is assumed that the vibrational velocity or vibrational 

 displacement at a distance r from a source of disturbance 



is equal to — </>(£ J, where M is a constant and a the 



velocity of propagation. 



Let S, fig. 1, be a closed surface, and A, B two points 

 outside it, and let r u r be the distances of A and B from 



an element dS of the surface at P, n being the outward 

 drawn normal at that point. Many integrals whose 

 subjects of integration depend on r ± and r and their 

 rates of variation along the normal vanish when taken 

 over the surface S. Thus, if F 1 (r 1 , r ) and F 2 (r u r ) be 

 two functions of r x and r that are finite, continuous, and 

 single- valued throughout the space S, 



IK 



On on / 



d$ 



will vanish if the integrand can be separated into a number 

 of terms 



on On on on On o» 



&c, . 



