250 Theory of Electric Inertia. 



15. The interpretation of this result considered alone is 

 that, the velocity having been increased or diminished at S 

 by ~&u, the effect of the magnetic reactions is at every point 

 in the subsequent course partially to restore the velocity 

 gained or lost, as the case may be, when the sphere was at S. 

 To maintain u constant we should have to apply a force in the 



Q 2 Jj. 



direction of the motion equal at each instant t to -=- e'dii-^,. 



6 vt 2. 



Or we should have to do work in the whole equal to 



— 7r - from the lower to. the higher limit of t. Neglecting 



3 vl ^ 



as we may the value of — at the higher limit, we have for 



the whole work required -^ . In fact, there will be 



3 vt 



strictly two forces to be applied at every point. One which is 

 proportional to ~du and ot opposite sign, and does not contain 

 the factor k. The other, which is always in the direction of 

 the motion, and contains the factor /c 3 , and which is therefore, 

 except perhaps for very small values of t 0) inappreciable 

 compared with the first. The first force, which is proportional 

 to ~d*i, expresses the effect of the magnetic reactions against 

 the acceleration denoted by ~dii. Divided by ~d>t it represents 

 the electric inertia. It does not appear, however, from this 

 investigation that the sphere having charge e and velocity u 

 can correctly be said to possess inertia as a function of e only, 

 because the magnetic reactions do not depend only on the 

 instantaneous velocity u. 



16. For the lower limit of the integration for t, which I 



r> 

 have denoted by t , Lodge takes -, where c is the radius of 



the charged sphere. It may be admitted that c is the least 

 distance for which the formulae employed have any meaning. 

 But I would here ask whether it would not be safer to take 

 for c the least distance for which the lormuke employed 



(e.g.. H = eu — g- J are capable of being verified experi- 

 mentally? In like manner in the ellipsoidal integration, 

 art. 13, should not the limits be, instead of = and = 7r, 



0= - and = 7T •, where c is the least distance for which 



r du 



6 'cii 



the formula, electric force = can be verified ex- 



r 



perimentally ? 



