404 Prof. L. Natanson on the 



§17. Electromagnetic Dissipation. — The electromagnetic dis- 

 sipation function is 



F^ffldxdydzCCEl + FJ + El), ... (1) 



the symhols being defined as in § 13. The disturbance settles 

 down obeying the well-known equations 



K dI' = ~ 4,rCE * ; K ^ = ~ 47rCE ^ ; K TF = ~ 47r °^ ; (2) 



they are therefore the electromagnetic iC coercion " equations. 

 If we take t = K/47tC, as has been done by Maxwell and 

 many others, we see that 



F=- 4 J3J^^^rC(E^ +B ,^ + E^) . (3) 



and 



DF 2F 



DF = ~V W 



Prof. J. J. Thomson has shown * that for water with 

 8*3 per cent, of H 2 S0 4 , t cannot diiFer much from 2.10 -11 of 

 a second ; and for glass at 200° C. from about 10~ 5 of a 

 second. 



§ 1 8. Irreversible Dynamics. — In the case of § 17 the energy 

 we have called T is proportional to the dissipation function F; 

 the same holds in § 16 if we have p 1 u 1 + p 2 u 2 =Q (see Maxwell, 

 Phil. Trans. 1867_, pp. 73-74). Hence, in such cases equa- 

 tion (V.) becomes DT/Dt= — 2T/t. Again, in the Irreversible 

 Dynamics of § 9, if the additional dissipative forces — R/ be 

 proportional to the corresponding components of momentum, 

 the same proportionality holds. For example, let 



represent the additional dissipative force acting in the ^.-direc- 

 tion ; then T = tF ; and since from (5), § 9, it is easily shown 

 that 



DT 



W = ~ 2F ' ( 2 ) 



* 4 Notes on Recent Researches in Electricity and Magnetism/ 1893, 

 o2i. 



