﻿of the Electron Theory of Matter. 623 



According to Einstein the energy communicated to an 

 electron by light of frequency v is /u>, where h, as also the h 

 of equation (59), is Planck's constant. Part of this is used 

 up in doing work P necessary to escape from the substance, 

 the remainder forms part of the kinetic energy of the electron 

 after it has escaped. Let us see to what extent the con- 

 sequences of this type of theory are consistent with the 

 conditions of statistical equilibrium. 



To simplify the calculations we shall suppose that the 

 work P is equal to the heat developed within the substance 

 by the escaping electrons. This enables us to identify P 

 with the w in (54). We shall also suppose that the reflexion 

 coefficient of the electrons returned to the surface is inde- 

 pendent of temperature. The properties deduced may there- 

 fore only be strictly true for an ideal body which absorbs all 

 the electrons that fall on it. If we work out the value of /3 

 we find that 



;N"=an<y/ 



m / r y . Ji* 



2/717T \2m7T/ 



'«(*==) A#« . • (60) 



and in a similar way the kinetic energy E carried away from 

 unit area of the surface in unit time is 



Jw 

 ,"»*. . (61) 

 \mir J \m.ir / v J 



We also have by the substitution of (59) in (53) 



N=27r/c 2 .f 'dvcF{v)Jufie~ mV . . • • (62) 



Now, subject to the assumptions P ~ iv and a is independent 

 of 0, equations (60) (61) and (62) are not consistent with 

 Einstein's suggestion that the whole of the energy of the 

 emitted electi ons arises from the energy hv of a light unit. 

 Let us see if they are consistent with a fraction y of it 

 arising in this way. If the energy given to each electron is 

 hv the part of the kinetic energy of each electron which 

 escapes, which arises from this cause, will be hv - 10, so that 



7 E= ~ f (hv-w)€F(y)hv z e'™" dv 



c Jo 



W reF (v)hv* e " ™ V dv - Nw. . (63) 



Jo 



2irh 



