Gases on Contact Potential Difference between Metals. 169 



For platinum when it is sensitive to hydrogen the constants 

 a, e, and a have the values a = l*27xl0 4 , c = 0'73, and 

 « = 2*43 x 10 3 when p is in millimetres of mercury. 



The contact potential which is operative during the experi- 

 ments is not Y lt which refers to a gap between two metal 

 surfaces both at temperature r L\ when one is in a gas-free 

 space and the other in hydrogen at pressure p, but it is the 

 potential difference between two surfaces at temperatures T : 

 (that of the hot wire) and T (that of the cold cylinder), both 

 in an atmosphere of hydrogen at pressure p. Let us call this 

 potential difference il. To find the value of O consider the 

 gap between two blocks of the metal, one maintained at 

 temperature T x and the other at T , both immersed in hydrogen 

 at pressure/? and connected together by a platinum wire. Next 

 consider the work done in taking an electron round a closed 

 circuit starting inside the metal at T 1} across the boundary 

 of T l5 across the gap, then across the boundary of T , and 

 finally down the wire to the starting point. This consists of 

 the algebraic sums of the amounts of work done in crossing- 

 five surfaces, viz. that between the pure and contaminated 

 metal at T\ (77J, that between the contaminated metal at T^ 

 and the gas ($1), that across the gap ( — ell), that from the 

 gas to the contaminated metal at T (<JE> ), and that between 

 the pure and contaminated metal at T (t) ) . Thus by the 

 energy principle 



e£i = 4>i + Vi-(<l>o + Vo) (4) 



The notation is the same as that in 'Emission of Electricity 

 etc' p. 109. In the same notation (p. 109 equation 34') we 

 have 



eV L =4h!+Vi-0h-+Vi) 9 .... (5) 

 and similarly 



eVo = 0</ + V-W>o + *?<>) (6) 



Now 97/ = i7o / = ; so that 



.a = <Y o -V 1 ) + 0/-^o' (7) 



Now, from loc. cit. p. 33 equation (16) (equation (15) 

 p. 32 is more accurate but the difference is hardly material) 



*i'-*o'=j*(Ti-To), .... (16) 



and substituting for V and V 1 from (3) above and the 

 similar equation for V 



a=*(T 1 -T„).{|+log(l + ar )}, . . (17) 

 or, a little more accurately, 



Q=*(T 1 -T ) [| + log(l+a^) } - P" crdT. (18) 



