372 On Mutual Electromagnetic Mass. 



of comparatively large distances *. In fact, Prof. Nicholson 

 himself states (p. 227, loc. cit.) that "under this condition " 

 (r of the order of a) his formula " ceases to give the mutual 

 mass etc/'' Why, then, not calculate the rigorous expression, 

 which, if the problem is appropriately treated, is as easily 

 obtained as the approximate one ? 



In view of these circumstances it may be useful to recall 

 here, without repeating details of the calculation (which was 

 based on the electromagnetic momentum of the system of 

 the two charges), my final formulae for the mutual mass of 

 a pair of charges as specified above, for the cases 1 and 2. 

 They are : — 



When the spheres exclude one another. 



U N e^/c 2 ^ 1 a 2 + a 2 2 ~\ 



) ™ l2 = -i-2- 1 - - K -i-T- 2 ; r> a x - a 2 , 

 7 Zirr l. o r 2 J ' = x " 



or, in virtue of (1), 



ir L r 2 j' 



where + corresponds to charges of equal, and — to charges 

 of opposite signs. 



When the sphere 1 is entirely contained in the sphere 2. 



(B) m "=2?ra~l ] - -5a,»-J' 

 or, again, by (1), 



(BO m 12 = ±x/^7 2 . A 1 [5- 2^1. 

 V a 2 L a 2 J 



The signs being interpreted as above. It is worth noticing 

 that B follows from (A) by a cyclic permutation of a l9 r, a 2 . 



These formulae are rigorously valid for any value of r. 

 Examples illustrating them will be found in my papers quoted 

 above. 



London, July 1915. 



* /. e. small values of (« 1 2 +« 2 2 )A* 2 . 



