170 Prof. Richardson and Mr. Robertson : Effect of 



Now we have seen (p. 164, ante) that T a varied in the 

 different comparative experiments, being a function of the 

 temperature T 2 of the hot wire in the high vacuum experi- 

 ments jand the pressure p of the gas. It was in fact the 

 temperature which at the pressure p gave the emission its 

 high vacuum value and is therefore determined by the 

 equation 



ATi ^-5/T 1=rA ^ 2 ^-57T 2 ( 19) 



In this equation the factors T^ and T 2 * can be treated with 

 sufficient exactness as equal • so that to such approximation 

 as we require 



Tl= 6' + T 2 logA/A' T2 ' • • • • ( 2 °) 



and using equations equivalent to toe. cit. p. 112 (15) and 

 (17), 



V — -log (1 +ap c ) 

 Ti= ff-T a \og(l+ap°) T * ' ' ' ' (21) 

 and the operative contact potential in volts is 



b<-^iog(r+ap*) j 



30o _ U'-T 2 log(l + a^) °' °J 



;(|+log ll + ap-;)} - \ T % *dT. (22) 



Equations (21) and (22) express V as a function of the 

 temperature T 2 of the hot wire in the high vacuum experi- 

 ments, T that of the cold electrode, the pressure p of the 

 hydrogen, the universal constants k and e, the constants a, c, 

 and a defined already, the emission constant V for the metal 

 in a vacuum, and the specific heat of electricity a in platinum. 

 The term in a is unimportant, but is added for the sake of 

 completeness. 



If this theory is correct the observed displacements of the 

 curves will be equal to the differences in the values of V, for 

 a given value of T 2) corresponding to the gas pressures used. 

 Neglecting the unimportant term in cr and substituting the 

 known values of the constants, the values of V given by 

 equation (22) are : — * 



For T 2 = 1200°K: when ^=0-112 mm. V=0;452 volt, and 

 when p = .0-0013 mm. V = 0374 volt. 



