XVIII. 



VELOCITY OF PROPAGATION OF ELECTROSTATIC FORCE. 



[Nature, vol. Lin. p. 509, April 2, 1896.] 



As we may have to wait some time for the experimental solution 

 of Lord Kelvin's very instructive and suggestive problem concerning 

 two pairs of spheres charged with electricity (see Nature of February 

 6, p. 316), it may be interesting to see what the solution would be 

 from the standpoint of existing electrical theories. 



In applying Maxwell's theory to the problem it will be convenient 

 to suppose the dimensions of both pairs of spheres very small in 

 comparison with the unit of length, and the distance between the 

 two pairs very great in comparison with the same unit. These 

 conditions, which greatly simplify the equations which represent the 

 phenomena, will hardly be regarded as affecting the essential nature 

 of the question proposed. 



Let us first consider what would happen on the discharge of (A, B), 

 if the system (c, d) were absent. 



Let ?7i/ be the initial value of the moment of the charge of the 

 system (A, B), (this term being used in a sense analogous to that 

 in which we speak of the moment of a magnet), and m the value 

 of the moment at any instant. If we set 



m = F(t), (1) 



and suppose the discharge to commence when = 0, and to be 

 completed when t = h, we shall have 



F() = m when <0, (2) 



and F(Q = when t>k, (3) 



Let us set the origin of coordinates at the centre of the system 

 (A, B), and the axis of x in the direction of the centre of the 

 positively charged sphere. A unit vector in this direction we shall 

 call i, and the vector from the origin to the point considered p. 

 At any point outside of a sphere of unit radius about the origin, 

 the electrical displacement ($)) is given by the vector equation 



/ \ (/ "" * O / I v \ J? I 



\ / J ' \ / 



where F denotes the function determined by equation (1), F' and F" 

 its derivatives, and c the ratio of electrostatic and electromagnetic 



