Theory of Radiation. 49 



When u m is for all values of m zero, H is constant, so that 



r—l (■<"■<■ r 



and dJI_ m ^"d^/ r = n dH , \ 



m ^ m ( r ^ l dH \ 

 + X *m\X -rzXr,™). . . . (17) 



The aBthereal energy is 



»=• 1 /^„A 2 1 9 



■£i2?V57 + ^"* 



The rate of increase of the sethereal energy is by (1) 



»i = oo J 



^=' (18) 



By adding (17) and (18) we have the total rate of increase 

 of the purely material and the purely sethereal energy. The 

 total energy, since there is conservation, must be expressible 

 in the form 



H+ JAh(^h\<< + ^A- ■ (19) 



And on making the total rate of change vanish, 



^ jrA».) + i+i =0 ( 20 ) 



* 1 dT r * r -" i > + ~dT =0 ' (21) 



£ S^,«)+S -Sj/r-O (22) 



In passing from (21) to (22) I write 



dt r = 1 CvXf 



neglecting terms involving the a's which are here small 

 quantities compared with those retained. (20) and {22) are 

 conditions necessary for the conservation of energy. 

 Phil. Mag. S. 6. Vol. 25. No. 145. Jan. 1913. E 



