(3) 



of Stationary States of Motion. 247 



obtained by eliminating d and h between equations (1) : 



^■4divC = 0, %-divK=0. . . . (2) 

 cot cot 



In all other respects the four quantities are to be regarded 

 as completely arbitrary, so that there is no limitation o£ the 

 generality of the electromagnetic equations for the interior 

 of the electron. For convenience of analysis we shall sup- 

 pose that surface distributions are to be treated as limiting 

 cases of surface layers in the usual way, so that the electric 

 and magnetic forces, d and h, are continuous everywhere 

 together with their first differential coefficients. 



7. Using the Poynting energy flux Oseen derives the 

 following expression for the radiation across any fixed 

 surface S enclosing the radiating system : — - 



16tt 2 cR = | ( uv/n, '. 



— n-jft[g»]i] + e«]-(g*.i>} 



and t = t 1 -\- (rl)/c ^ 



Square brackets denote vector multiplication, round scalar 

 multiplication as usual, dSl denotes an element of solid angle 

 in the direction of the unit vector 1, r denotes the radius 

 vector drawn from the origin to the vector element of sur- 

 face dS, whilst ti is a constant time, the same for all surface 

 elements, and t a time varying from element to element as 

 indicated. The units are Lorentz units. 



By means of (1) we can express the vector U in the 

 following more convenient form : 



— tifflf ♦[»?]}»]■ ••'•w 



where dN is an element of volume of the electron, that is, 

 of the region throughout which C, or K, or both differ 

 from zero. 



8. In applying Oseen 's formulae (3) and (4) to our problem 

 we shall find it convenient to use cylindrical coordinates 

 (2, ot, %) and to choose c } the speed of light, as the unit of 

 velocity to save writing. 



Let denote the colatitude and (/> the longitude of the 

 unit vector 1 ; then the time t is given by the equation 



£ = ^4- ^ cos + -cram cos (<£ — %). . . . (5) 



