HALL. — ELECTRIC CONDUCTION AND THERMOELECTRIC ACTION. 73 



junctions. Let us therefore consider carefully what may be the 

 nature of the equilibrium which exists in a detached piece of wire 

 having a temperature gradient.. 



The Boltzmann Aerostatic Equation. 



I shall make use of the idea that each metal exercises a specific 

 "intrinsic" attraction for electrons. Helmholtz long ago assumed 

 such an attraction n for electricity in discussing the "double layer" at 

 the surface between different substances. Several years since I made 

 the suggestion that this attraction might be a function of the tempera- 

 ture of the metal. More recently O. W. Richardson 12 has made use 

 of the Boltzmann formula 



w 

 "' = e-RT (4) 



in dealing with the forces exerted upon electrons by electrical charges 

 or by the attracting metal atoms. In this formula "wi is the con- 

 centration of the electrons at a point .4 and n 2 that at a point B," 

 and " W is the work done in taking an electron from .-1 to B and R is 

 the gas constant in the equation pv = R9[— RT], reckoned for a 

 single electron." 



I feel greatly indebted to Professor Richardson for his discussion 

 of this matter, and when I took up the question now before us I 

 expected to use his ideas and conclusions, except in so far as they 

 might be modified by my assumption that R for an electron is less 

 than R for a gas molecule. I have, however, upon close examination 

 of the matter, been forced to the conclusion that, in applying formula 

 (4) to a discussion of the Thomson effect, involving of course a 

 difference of temperature between the two points .4 and B, he has 

 fallen into error. 



Boltzmann gives the equivalent of the formula in question under 

 the heading Aerostatilc, 13 and it is very easily derived, as follows, for an 

 atmosphere of uniform temperaturean equilibrium: 



II This at least is my interpretation of certain passages in his papers; for 

 example, the following sentence from an article in the Monatsbericht d. k. Akad. 

 d. Wiss. zu Berlin, Nov. 3, 1881, S. 951 : "Soil in einen Leiter, (lessen Potential 

 (elektrostatisch gemessen) p und dessen galvanische Constante A - ist, ein 

 neues Quantum Elektricitat dE eingefuhrt werden, so ist dazu die Arbeit 

 (p~k) dE nothig." 



12 Phil. Mag.; Vol. 23 (1912), pp. 263-278. 



13 Gastheorie, Vol. I, § 19. 



