Mutual Electromagnetic Mass. 371 



the appropriate name for m 12 = m 2 i, which I have employed 

 since 1909, is the mutual electromagnetic mass of 1 and 2. 



Let 1, 2 be spheres of radii a 1? a 2 , and let r be the distance 

 apart of their centres. Let each of these spheres have a 

 homogeneous volume charge. It will be enough, for the 

 purposes of the present Note, to consider the limiting values 

 of the masses for small velocities, or the so-called rest-masses 

 (although, as I have shown in papers to be quoted presently, 

 there is no difficulty in treating any velocity common to the 

 two spheres and directed along the central line). Then, in 

 Heaviside's rational units, 



/?? 1= = J _'__ m 2 = — — > .... (1) 

 Oira 1 D7ra 2 



where c is the velocity of light in empty space. The expression 

 for the mutual mass m l2 of these spherical charges assumes 

 different forms according as — 



(1) the spheres exclude one another (r >a l + a 2 ), 



(2) one is entirely contained in the other, or 



(3) the spheres are only partly overlapping. 



In a communication to the IV. Congress of the Societa 

 Italiana per ii Progresso delle Scienze, Naples, December, 

 1910, L developed the complete and general formula? tor the 

 first two cases*, the third being more complicated and of 

 little physical interest. 



Quite recently I have been surprised to see this very 

 problem treated by* Prof. Nicholson -J-, without any mention 

 of my previous work. It seems, in fact, that Prof. Nicholson 

 lias had no knowledge of my Italian communication, although 

 it has appeared also, with some more details, in the more 

 widely circulated l J h;js. Zeitschrifl (vol. xii. p. 87, 1911), 

 and was shortly afterwards reviewed in Journal de Physique. 

 Now, if it were only for the sake of claiming priority, the 

 matter would hardly be worth mentioning, especially as the 

 mathematical side of the problem is of utter simplicity. But 

 it so happens that Prof. Nicholson's solution — formula (12), 

 he. cit. — is wrong in its numerical coefficient, and, what is 

 more important, would (if correct) apply only to the case 



* Cf. the Atti of the said Meeting. 



| J. YV. Nicholson, Proceedings of the Hi vs. So.\ Lond. vol. xxvii. 

 Tart 3, April 15, 1915, pp. 217-228. 



2 B3 



