Electromagnetic Theory of Radiation. Ill 



magnetic charges. The volume density of the magnetic 

 charge mav he written in the form 



and this is equivalent to the expression given by Page when 

 we write 



W= -£( 1 -?) <B - 



where o> is a vector representing the angular velocity of the 

 electron or its field in the case when v = 0. 



5. The rate of radiation of energy in a field of type (5) is 

 found to be 



; 2 {v. (axw)} "] 



c l (v.a) 2 + ^v . w)~ | . 



32 



r' 77 ' 



{C 2_ V ? ) 2 {C 2_ V 2 } 



.2 , 3 



The vectors a and w are at present at our disposal. If we 

 take a=0 and choose the above value of w, assuming also 

 that (v.w) = 0, we obtain for the rate of radiation 



2 e 2 co' 2 



3T' 



2tt 

 and the amount of energy radiated in an interval ~ - is * 



toJ CO 



— K- — , which is approximately ^— 6'4(10)~ 27 , when e is 



ijC tfc IT 



assumed to be 4*77 x 10" 10 E.S.U. 



6. The possibility of radiation in quanta having been 

 established the next step must be to justify our assumption 

 that a = 0. When the electron is stationary or moving 

 uniformly in a straight line this assumption seems quite 

 natural, but there must be some occasion when an electron 

 moves in a curve, and so we must consider "the possibility 

 that a may be zero in a general type of motion. 



In the case of a moving electric pole the expression for 

 o is t 



tt __f_f"(..-£) +v"(//-v) +?"■-- ?)+--F->r-r , , r > 



4 „. f <(,,_ f)+ v(y-^)+r(---r)-<' 2 ('-T) 



* A similar result may be obtained without the introduction ot 

 magnetic particles by putting w = and regarding a as a multiple ol* an 

 angular velocity about an axis perpendicular to v. 



I Cf. R. Hargreaves, Proc. Oamb. Phil. Soc. 1915. 



