the Photoelectric Effect. 587 



emitting and receiving electrons. Of the incident group 

 some will be absorbed and others reflected. Let the propor- 

 tion absorbed be a. Then the proportion reflected is 1— a. 

 Some of the electrons in the group under consideration have 

 greater speeds than others; so that as the proportion reflected 

 out of any group having a given speed is a function of the 

 speed, the proportion of the energy, in a mixed incident 

 group, which is reflected, will be different from the propor- 

 tion of the incident number which is reflected. Let be 

 the proportion of the energy of the group, incident in the 

 state of thermal equilibrium, which is absorbed. Then 

 s = 8\x. As the proportion of incident electrons absorbed is 

 smaller the higher the speed, it follows that 5 is a positive 

 quantity which is less than unity. 



The deduction of formulae (9) and (10) does not depend 

 on the unitary theory of light except in so far as the unitary 

 assumption may implicitly underlie Planck's radiation formula, 

 or rather Wien's form 



E(v<9)=^Av 3 <rfe, .... (11) 



which is used instead, as a sufficient approximation. 

 If we put w = hv we have instead of (9) and (10) 



T m =h(v-v ), T r = sh(v-v ) . . . (12) 



or, in wave-lengths, putting c = v\ = v Q X 



\T m = ch(l-~\ \T r = sch(l-^). . (13) 



A more comprehensive test of these formulae is afforded 

 by PI. XIII. fig. 9, which contains all the observations which 

 we have made. The points corresponding to the different 

 metals are indicated thus : — 



Na«, Alo, Mg*, ZnA, Sn + , BH, Cu x , and PU. 



The values of X which have been used in constructing the 

 figure are those given by plotting T r , the mean energy, 

 against v. The points near the lines OB and 00 represent 

 values of T m and those near OD and OE values of T r . OA is 

 the theoretical line for T m = h(v— v ) using the value of h 

 given by radiation measurements, viz. h = 6*55 X 10 -27 erg cm. 

 Except in the case of copper and bismuth, all the values of 

 T m lie very near the line OB and all those of T very near 

 the line OD. The slope of the line OB corresponds to 

 £^=5"4x 10" 27 erg sec. instead of 6*55 xl0~ 27 erg sec. 



