WEBSTFR. — PI ANCK'S RADIATION FORMULA. 135 



Moreover, as possible modes of vibration, we have not only a rigid 

 displacement of the magneton as a whole, but also a disturbance of the 

 flow of electricity around it, that may give electrical oscillations. 

 These may be thought of as superposed on the continuous flow just 

 as they would be in the case of a large ring of wire, heavily charged 

 with negative electricity and at the same time carrying a current 

 around the ring and performing electrical oscillations which may dis- 

 place the centre of charge to any point in its plane. The displacement 

 of the center of mass of the magneton during these oscillations might 

 be anything, depending on how the charge was distributed and on 

 what changes of thickness of the ring might be caused by the changes 

 in distribution of its charge. We shall assume here, purely for con- 

 venience, that the center of charge and the center of mass move 

 together. We shall also assume that any number of these waves may 

 be superposed without disturbing one another, except by electro- 

 static action, as in the case of the ring of wire. 



Let us now consider a magneton whose geometric center is dis- 

 placed in the plane of the ring by a distance £', and whose center of 

 charge and mass is displaced relative to the ring by a distance £", 

 or in all a distance £ = £' + (•". We shall divide the intra-atomic 

 forces acting on it into the following five classes : 



(1) The resultant of the attraction of the positive electricity through 

 which it moves and the repulsions of the other magnetons, equal to — /£, 

 and acting on the electricity itself, rather than on the rest of the 

 structure; 



(2) The resultant of the magnetic attractions and all non-electro- 

 static repulsions between them, equal to — /'£' and applied to the 

 structure of the ring; 



(3) The internal forces of the magneton, giving a force — /"|" on 

 the electricity and +/"£" on the ring; 



(4) The force of inertia,— m — -} due to radiations caused by the 



at- 



acceleration of the electricity, and acting on it; 



2 e 2 d 3 £ 



(5) The damping force + - -= — f due to radiation, equal for 



o c* dr 



d£ 

 simple harmonic motions depending on sin wt to — g -j where 



g= 3?"- 



d£" 



(6) Another damping force — g" ~~ due to an assumed tendency 



(76 



