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

 4. Contact Potentials. 



Richardson has developed a relation for contact potentials 

 in the form 



eY c = Wx-Wa + t, 



where Y c represents contact potential, e the charge on an 

 electron, Wi and W2 work done on an electron in leaving 

 and entering the metallic surfaces, and yfr a term of the 

 order of the Peltier effect. 



This expression may be written in terms of <£ as 



Y c = </>i — $2, (8) 



where the Peltier term is neglected. This expression gives 

 the contact potential as the difference of the <£'s for the two 

 metals ; so that to test the much discussed question as to 

 the existence of intrinsic potentials, it is only necessary 

 to measure $ for a series of metals and substitute in 

 equation (8). Measurements of <£ for metals far enough 

 apart in the voltaic series to test the above equation have 

 not been made with sufficient accuracy for the purpose. 

 However, Richardson noticed that the values of the heating 

 effect lor the metals examined by Richardson and Cooke 

 lay close together. In explaining this seeming coincidence, 

 he suggested, as stated above, that the heating effect is 

 connected with the cooling effect through the relation 



0i = 2 + V c (9) 



He recognized that the non-existence of contact potentials 

 would explain the results as well. 



It has been shown ihat the observations on iron cannot 

 be taken to support the relationship as he expressed it. 

 Moreover, it was shown that the heating effects measured 

 by (/ooke and Richardson did not equal the cooling effect 

 of the hot emitter as measured by the same experimenters, 

 although the theory demanded that they should, since the 

 effect measured as the heating effect was supposed to be 

 (<£ 2 + V c ). The c/Zs so far determined from the cooling 

 effect have been identical within their limits of accuracy, 

 so that between the metals for which this effect has been 

 measured, no contact potential exists as great as two-tenths 

 of a volt. 



It was observed that quite different values of </> were 

 obtained when active residual gases were present. For this 

 case there would ordinarily be differences in the <j/s for 

 different metals, and the differences would be of an order 

 of magnitude sufficient to account for contact potentials. 



