200 Profs. Richardson and Cooke on the Heat developed 



When there is no thermionic current, the rate of total heat 

 production 



= R tfds. 



J-'o 



80 that the increase, 8Q, due to the thermionic current 



As an illustration, let us suppose that;* has the same value 

 at every point. Then 



SQ = «■(./-, +.r )f;/(.6' l -.r ) + J/(.r 1 2 -.r l a- + .r a )}. 



We can determine the position of the point M from the 

 conditions which have to be satisfied in order that there 

 should be no current through the galvanometer G (fig. 1) 

 when the thermionic current is turned on. For, we shall 

 have that the drop of potential from M along S through the 

 resistance Ej, shunted by the battery circuit and the resis- 

 tance R 2 to K, is equal to the drop of potential from M along 

 S to L, so far as the thermionic current is concerned. The 

 drop of potential from M to K due to the thermionic current 

 is equal to 



Rj;^> + Pf>, where P=|gM, 



B being the resistance of the battery circuit. The drop from 

 MtoL 



f *° f '' • 

 = R 1 dx I jdx. 



*o Jo 



In addition, the potential drop due to the thermionic current 

 from K to E 



Cxi i% 



jdx = the drop from L to E = R 5 \ j 

 «,u ' Jo 



dx. 



In the particular case when j is constant, these two relations 

 become 



jj*i'+j*F = jj**\ or W + 2P# 4 = R«V • • (1) 



and 



jxjli = >r R 5 , or .^4 = XqR 5 . . ■ ■ (2) 



We see, therefore, that xjx x - R4/R5. In the experiments 



