HALL. — ELECTRIC CONDUCTION AND THERMOELECTRIC ACTION. 87 



It is to be observed that the very important part played by v in the 

 equations (21) and (21') does not imply that n, the number of free 

 electrons per cu. cm. of the metal, is so large as to be of the same 

 order of magnitude as the number of atoms per cu. cm. The value 

 of {dF -5- (IT), by way of which v gets into the equations in question, is 

 not dependent upon the absolute value of n at any place, but upon the 

 ratio of the n of one temperature to the n of another temperature. 

 Thus it is possible for a comparatively small number of free electrons 

 to have a great effect upon a, by way of the (A) electrons which are 

 subject to the (dF -r dT) established by the (B) electrons. 



As to the term Ayr T ( - w ~ :) in equation (21) and (21'), although we 

 are hardly at liberty to assume k v to be small in comparison with k r , t, 

 which we suppose to be negative, may be small, and the factor T^~ 1) 

 is less than T~ l . It seems not unlikely, then, that this term is 

 small compared with the T p term. 



If we are satisfied that equations (21) and (21') accord in a general 

 way with the known phenomena of the Thomson effect, we must next 

 inquire whether either of these formulas will give a good quantitative 

 account of the Thomson coefficient a as found by experiment in certain 

 metals. Let us consider lead, with a = 0, very nearly; cobalt, with 

 <r = 2000 20 ; and antimony, with a = — 1000. 20 I take cobalt and 

 antimony because they have the limiting values known to me. 



Taking the first term in the value of a as the dominating one, we 

 see that, if we take p = 1, as we do in other cases, a = 0, according 

 to (21), if v = \ + \ p = 1 or, according to (21'), if v = 1 + p = 2. 

 Neither 1 nor 2 seems a very improbable value for v. 



Substituting R for l: r T p in this first term we have, approximately, 

 for cobalt, 



a = l(± + B - v y = 2000 (22) 



or 



a = \ (l + p - v ) R = 2000 (22') 



e 



The value of R g , reckoned for a single molecule of an ordinary gas, 

 is about 137 X 10 -18 . If we for a moment assume this as the value 

 of the electron R in (22) and (22') and take e = 159 X 10" 22 in electro- 

 magnetic units, and p = 1, we get from (22), v = 0.77, and from (22'), 

 v = 1.77. 



20 These are approximately, the values given for the metals in question 

 at 0° C. in the Recuil de Constantes Physiques (1913) of the Societe Fran- 

 chise de Physique. 



