MOTION OF ELECTRIFIED SYSTEMS OF FINITE EXTENT, ETC. 183 



included in the calculation, and our equations show that the relation between ^, 

 and the exciting field is not so simple as that generally assumed. 



We have shown in Section 3 that the motion here considered is associated with a 

 dissipation function 



It thus appears natural to suppose that the rate of radiation is 2D, and we have 

 shown in Section 10 that this agrees with the calculation by means of POYNTING'S 

 Theorem when the motive force is purely mechanical and the proper relation between 

 X and f is observed. 



In the present case it appears that I) may become negative, a result which can only 

 be interpreted as meaning absorption and not emission of radiation. Although this 

 result is somewhat novel, it is quite consistent with the common-sense view that there 

 may be circumstances in which a vibrating particle absorbs radiation and others in 

 which it emits radiation. 



Substituting the values of ^ and f in D, and taking the mean value for a complete 

 period, we find that the average rate of radiation is given by 



/ 1 f / in' ' m' 



-\ k 2 a~) sin ka ka cos ka \ \( \ -\ lfa~ } sin ka I 1 + - - ) ka cos ka ^ 



m / in \ m / 



3 



4 > J 4 ~ > 



* Sl^l ' tffi 



l + 2L_jfcV +A-V 



in 

 Now the roots of the equations 



tan ka = ki 

 and 



tan ka = ( I + 



m'\ , //, , in' ,., .A 

 -}kal{ 1 + /"", 



in / I \ m I 



which are real, are in general different. We therefore have regions for which there is 

 radiation, separated by regions for which there is absorption. 



The above expression for the radiation is true only if ka is a small quantity, and 

 this must be observed in discussing the application of the expression to actual fact. 



The positively charged particles associated with the electric discharge appear to be 

 of atomic size and to have a ratio of mass to charge of the order of the electro- 

 chemical equivalent of hydrogen. For such a particle the ratio of electric mass to 

 ordinary mass is comparatively small. 



If we take provisionally 



=lxW~ M , m=lxKT a4 , a=lxl(T 8 , 



