642 Prof. 0. W. Richardson on Distribution of the 



in obtaining (16) terms have been dropped which cannot be 

 disregarded under the experimental conditions. To find the 

 value of i it is therefore necessary to proceed rather differ- 

 ently. By eliminating U between equations (2) and (3) we 

 see that for particular values of V and T the corresponding- 

 value of x satisfies the equation 



2RT 



5N/i 



or, if 





(28) 



f(,) = l f ' V%d y ,nd O- 2 RT /^ V i\ # M (29^ 

 /( -^l ^ 3_1 5M\"9N"j M ' • (29) 



/(»0=iO,-i (30) 



If we plot the curves y=/( t r 1 ) and y=C#i — -J- their points 

 of intersection determine the value of x x which corresponds 

 to a given value of C, that is to say to given values of T and 

 "V*!. If we disregard the constants of integration, which 

 disappear from the final result, we have, corresponding to 

 equation (13), 



Nw 1 = U 1 + 3NRT|| 1 + log (l-e-'i)}. . . . .(31) 



=^{ifS-S^-log(l— ).} 



from (2) . From this, together with (30), 



Wi = 3Rt{|(V- \x x - log (I-* - * 1 ) J. . (32) 



This is true (apart from the omission of the constants of 

 integration) for all values of x x . By combining this with 

 the corresponding expression for w 2 , using the expansion, 

 appropriate to very small values of x 2 , which is required for 

 the case of thermionic emission, one finds 



, JNAV9JN \3^. —4 



, T f/l-*-^Y « a -» 1+ 3ii(iJ v * . .(33) 



The term on the right containing V 2 is always quite 

 negligible. Dropping this term and making use of (27) one 

 finds 



V2W3AtMR3 eT ,/ l-«- y e -^P . . m 



