﻿276 Prof. 0. W. Richardson on the Elect 



ron 



readily calculated. This minimum value is in every case 

 greater, and in nearly all cases much greater, than the 

 measured values o£ a. Thus it follows, as J. J. Thomson has 

 already pointed out, that the two terms must be nearly equal 

 to one another. If the electrons have no internal momentoids 

 7= If, and it is necessary that n the number of free electrons 

 inside a metal should for most metals be nearly proportional 

 to 6 3 ' 2 . If, on the other hand, 7=1 J, which is another possi- 

 bility, w T e should have to have n x # 3 nearly. 



An expression * for a equivalent to the above has been 

 deduced by H. A. Lorentz, on the assumption that the 

 colliding electrons behave like hard elastic spheres. 



Thermoelectric Circuits. 



Now return to the four conductors AA' B and B', of 

 which A and A' are of the same material, as also are B and 

 B', but the material nature of A and A" is different from 

 that of B and B'. A and B are maintained at the fixed 

 temperature O , and A' and B' at the fixed temperature 6' . 

 The four conductors are connected together as before. 

 Consider the transportation of a number N of electrons 

 round the circuit thus formed, without leaving the metal. 

 In this case the only work done on balance, if any, is that 

 done against the electrical forces. This is equal to NTe, 

 where T is the thp.rmoelectromotive-force of the circuit. 

 This must be equal to the net absorption of heat during the 

 transference so that 



r9' 

 Ne 



where P' and P are the Peltier effects at the hot and cold 

 junctions, and <r 2 and a 1 are the specific heats of electricity 

 in B and A respectively. Substituting the values of P' P cr 2 

 and o-j already obtained we find, after integrating by parts, 

 that 



where P 2 and Pi are the pressures of the free electrons in B 

 and A respectively at the temperature #, and P is the Peltier 

 effect at a junction formed of A and B at that temperature. 



* Quoted bv J. Kcenigsberger und J. Weiss, Ann. der Phusik, 

 vol. xxxv. p. 43(1913). 



