76 Prof. A. E. H. Love. The Advancing Front of the [May 9, 

 These equations express the same relations between the forces and the 

 direction of the normal to 2 as are expressed by (4). 



In the application of conditions (4) to the problem of the Hertzian 

 oscillator, the external field (X , Y , Z ), K ft, 7o) is that which is 

 established at the instant when the vibrations begin. At this instant 

 the brass balls of the oscillator are so highly charged that the electric 

 strength of the air between them gives way. The initial field is that 

 due to the charges at this instant, so that it can most appropriately be 

 represented as the electrostatic field of a fixed doublet. If B denotes 

 the moment of this doublet, the field in question is expressed by the 

 equations ^ 



70) = o 



Now write down the complete expressions for X, Y, Z, and a, /3, y, 

 in accordance with equations (2). Denoting differential coefficients of 

 the function f with respect to its argument by accents, these expressions 

 are 



X = (3^ + 3rf + ?*f '), Y = (3^ + 3rf 



r/ * T V / o I O / ' 9 / "\ & 



h ( OY + o?y + r y ) + 



r 5 ? 





(6). 



J 



In like manner, complete expressions for X , Y , Z , as given by (5), 



are 



Let t = be the instant when the vibrations begin. Then r = cHs 

 the equation of the surface separating at time t the field expressed by 

 (6) from that expressed by (7), and the direction cosines J, m, n of the 

 normal to this surface are x/r, y/r, z/r. When these values of X,... are 

 substituted in (4) it will be found that f disappears, and that the 

 equations (4) give 



= 0, 2(^-B) + 2rf = 0, 



which must hold when r = c/, i.e., when the argument of ^ is zero. 

 Hence we must have 



t (0) = B, f (0) = 0. 



Now take ^ to have the form (3). We find 



