﻿604 Prof. 0. W. Richardson : Some Applications 



so small that the difference between this formula and 

 equation (20) is almost negligible. If an electron has only 

 three degrees of freedom ry=5/3 ; so that 



p = A^V^ (22) 



In (21) and (22) A : and R are independent of 0, but the 

 same is not true of w. It is difficult to say how w will 

 depend on 0, but it is practically certain that it will do so. 

 The expansion of the material alone would change the value 

 of w. If the variation of w is small, it could probably be 

 represented with sufficient accuracy by making w a linear 

 function of 6. Such a property of w would make no change 

 in the form of (21) and {22). For if we substitute 

 w — w Q -\-a6, where w and a are constants, in (21) we have 



y _w +aQ _ a y _ w 



p = K^- Y e "^ = A t e *6y~e ™ 



y _^o 



= A s ffy- 1 e m , ... (23) 



where A 2 is independent of 6. 



Thus (23) is of the same form as (21). In order to 

 change the power of 6 which multiplies the exponential 

 factor in equations (20) to (22), it is necessary that w should 

 contain a term proportional to 6 log 6. 



In order to deduce the value of the saturation current from 

 the equilibrium pressure, it is usual to suppose that the 

 number of electrons emitted is equal to those returned to 

 the metal in a given time. This state of affairs holds good, 

 undoubtedly, under such conditions as give rise to an equi- 

 librium pressure, but it is questionable whether the number 

 calculated in this way is equal to the saturation current. In 

 fact experiments have shown that a considerable proportion 

 of these slowly-moving electrons are reflected when they 

 strike the surface of a metal ; so that the number calculated 

 in this way will be greater than the saturation current. We 

 do not, as yet, know enough about this phenomenon of 

 reflexion to be able to make proper allowance for it. If we 

 leave it out of account tentatively, we may put 



p = «N0* - /3#, 



where a. and ft are independent of temperature. We then 

 find 



w 



i = A z 6 2 e~™ (23 a) 



In this formula A 3 is independent of 6, and the form of the 



