200 Mr. H. H. Lester: Determination of Work Function 



and cold electrodes, <f> 1 the cooling effect at the hot, and 

 <£ 2 the heating effect at the cold electrode. 



Langmuir has shown that the big effects due to the 

 presence of residual gases disappear only with the last 

 traces of the gases * ; hence, in view of the lack of ideal 

 conditions, it is not surprising that Richardson and Cooke 

 did not find that changes in gas-pressure affect the heating 

 effect. 



The dependence of the heating effect of the anode upon 

 the cooling effect of the cathode was shown by some 

 peculiar results obtained in experiments with osmium as 

 the source of the thermions and iron as the receiving 

 surface. It was found that the osmium developed two 

 ranges of thermionic emission ; i. e., for a given tempe- 

 rature two values of the saturation current were possible. 

 Apparently two values of <f> were involved. The larger 

 saturation current gave larger values of the heating effect, 

 and the lower saturation current gave lower values of the 

 heating effect. 



The theory of the dependence of the heating upon the 

 cooling effect regards the work done when an electron 

 is taken completely around the circuit. If Wi and W 2 

 represent the work-functions at the surfaces of the hot 

 and cold electrodes respectively, and if V c is the contact- 

 potential between the two metals, then this work may be 

 expressed as 



W 1 -*V c -W 2 +<^ = 0, 



where i|r includes work done against external resistance, 

 gas pressure, and Peltier potential. The terms in ty are 

 negligible in comparison with the first three ; hence we 

 have 



W X -=W, + «V C (1) 



According to this relation, (W 2 + eV c ) varies directly 

 with Wi. 



Now the thermionic currents at a given temperature vary 

 inversely with b. Hence, since <f> and b are supposed to be 

 equivalent, it is evident that the observed change in the 

 heating effect should have been inverse to the change in 

 current ; that is, W 2 + eV c , the effect measured, should have 

 been smaller for the larger current. This was contrary to 

 their observation. It is possible that a contrary change 

 in eY c more than compensated for the change in W. 



The same experimenters later measured the cooling effect 

 * Phys. Rev. Dec. 1913. 



