﻿602 Prof. 0. W. Richardson : Some Applications 



number N of electrons emitted in unit time from unit area of 

 a hot body at temperature 6 was given by the expression 



N = n \/i> > ( 15 



V 2mir v ' 



where n is the number per unit volume of the free electrons- 

 inside the material, m is the mass of an electron, co is the 

 work it has to do in order to escape, and R is the constant in 

 the equation pv = H0 reckoned for a single molecule. If it 

 is assumed that n is independent of the temperature, it 

 follows that the negative thermionic saturation current i 

 from a hot body is of the form 



i = A6h-»l*\ (16) 



where A is independent of temperature. 



Formula (15) has been deduced theoretically in an inde- 

 pendent manner by Sir J. J. Thomson * and other writers, 

 and there seems to be no doubt that it is accurate to the 

 extent to which n has a precise meaning, a point which will 

 be considered in § 5. The point of chief interest in the 

 discussion in this section is that it relates the emission o£ 

 electrons to thermoelectric effects. 



The following calculation is very similar to a method o£ 

 computing the value of the Thomson effect which I described 

 in the 'Philosophical Magazine/ vol. xxiii. p. 263. It assumes- 

 that the emission and absorption of electrons and the Thomson 

 heating effect are reversible phenomena subject to the law s 

 of thermodynamics. It also assumes that the electrons 

 outside the conductor obey the law of a perfect gas, pv = l$6. 

 Admitting these hypotheses, the conclusions as to the equi- 

 librium pressure of the external electrons appear to be exact. 



Consider two conductors, A and A', made of the same 

 material and maintained at the absolute temperatures 

 and &. These are of sufficiently great size and are connected 

 by a thin conductor. The atmospheres of electrons around 

 them are separated by a suitable insulating partition. If 

 contact difference of potential depends upon temperature, 

 the potential V at the surface of A' will not be the same 

 as the potential V at the surface of A. Around A place a 

 potential filter at the potential V f. N electrons are then 

 taken out of A by means of the usual piston and cylinder 

 arrangement at temperature 6, potential V', and pressure p . 



* Phil. Trans. A. -vol. cci. p. 502 (1903). See also H. A. Wilson, 

 Phil. Trans. A. vol. ccii. p. 243 (1904), and P. Debye, Ann. der Physik, 

 vol. xxxiii. p. 469(1910). 



t Cf. Phil. Mag. vol. xxiii. p. 263 (1912). 



