44 Lord Rayleigh on the Incidence of Aerial 



being proportional to e ihYt , all satisfy the fundamental 

 equation 



( V 2 + ^)=0; (92) 



and they are connected together by such relations as 



^dt~dy dz> [ * 6) 



or 



^=47rY#-^\ .... (94) 

 at \dz ay J 



in which any differentiation with respect to t is equivalent to 

 the introduction of the factor ikV. Further 



d l + d £ + ^ = ^ + ^ + ^ = o. (95) 



dx dy dz dx dy dz v 



The electromotive intensity (P, Q, R) and the magnetization 

 (a, b, c) are connected with the quantities already defined by 

 the relations 



/, g, A = K(P, Q, R)/4tt ; a, b, c=^a, 0, y) ; (96) 



in which K denotes the specific inductive capacity and /j, the 

 permeability ; so that V -2 =K/Lt. 



The problem before us is the investigation of the disturbance 

 due to a small obstacle (K ; , //) situated at the origin, upon 

 which impinge primary waves denoted by 



f =0, g =0, k =<***,. . . . (97) 



or, as follows from (94), 



a = 0, /3 = 47rV^, 7o = 0. . . (98) 



The method of solution, analogous to that already several 

 times employed, depends upon the principle that in the 

 neighbourhood of the obstacle and up to a distance from it 

 great in comparison with the dimensions of the obstacle but 

 small in comparison with \, the condition at any moment 

 may be identified with a steady condition such as is determined 

 by the solution of a problem in conduction. When this is 

 known, the disturbance at a distance from the obstacle may 

 afterwards be derived. 



We will commence with the case of the sphere, and consider 

 first the magnetic functions as disturbed by the change of 

 permeability from /a to ///. Since in the neighbourhood of 

 the sphere the problem is one of steady distribution, a, /3, yare 

 derivable from a potential. By (98), in which we may write 



