f (^70 ) 



for the Dieaii Iciiüllis <>f tlic IVcc pallis. .\\, X,^, . . . for llie iimnl»or 

 of electrons of llie several Uiiids, coiilaiiied i)) unit of voliinie. We 

 shall liiiallv sii|>|)ose, as Diudi', lias done, thai foi- eveiT kind of 

 electrons, the mean kinetic eneruv of one of these |»articles i« equal 

 In ihat of a niolecnie of a ,uas at the same tenifXM-atnre : we mav 

 rc|tiesent it \)y (i 1\ if 7' is the absolute temperalnic, and ^f a constant. 

 In these notations Dkidk's value is ^) 



^ = Y~rr C^"-' '^ ^ ". + •'•/' ^'^ /-' ". -\- ••••)• • • • i-1) 

 4« / 



s(i that {?)) becomes 



A = -^ (e,-^ a; h ", f <' ^\ '. ". + ....) ^- . . (•>) 



4 « (• i 



It i> to be icmarked that the foi-mida '4) has been obtained in the 

 supposition that the electric force remains constant, or at least that 

 it keeps its direction and maunitude durinji- an interval of time in 

 which an electi'on has nnderuoiu' a larji'c mnnber of collisions against 

 particles of the metal. The results of I! \(ii:N and ivrm-.Ns ai-e theref(n-e 

 la\(>rable to the \ iew that even the period of vibration of the i-avs 

 is verv large in comparison with the tinu' between two siu-ceeding 

 im[)acts. Part of the following calculations are baseil on this assumption. 



^ 4. AV'e have now to examine the emission bv the jtlate. It 

 follows from the fundamental eipialions of the llieorv of electrons, that 

 evei'v c/ii(i/(/r. wlxMher in dii-ectioJi <tr in magnitude, of the velocity 

 of an el(M-tron produces an electromagnetic disturbance ti-avelling 

 (Uitwards in the surrounding aethei-. Ileiu-e, it will be at the instants 

 of the collisions that the electrons become cetitres of radiation. We 

 shall calculate the amount of energy, radiated in this way, in so far 

 as it is emitted aci-oss a detinite part w of the front surface of the 

 plate; this part of the emission is due to the electrons contaiiUMl in 

 a Ndliime o)L. of the nuMal. 



Let (f be a ]>oint within the area oj. (tP the normal in this |»oint, 

 drawn towards the side of tlu^ aether, and I* a point on this line, 

 at a distance r fr(;ni (f. which is \ery large in comparison with the 

 dimensions of v). In this poim I* we ]>lace an element of surface w', 

 perpendicular to I f I*-, our ])robiem will be to calculate the energy 

 radiate<l across this element. 1 cho(>se (f as (u-igin of coordinates and 

 ()l* as the axis of :. The components of the velocity of an electron 

 \\'\\\ be denoted by u,-, v,/, U-. 



1) Dp.ude, i. c, p. .j7(J. This fuiuiula does not change by the intiodiulion of our 

 new units. 



