414 BELL SYSTEM TECHNICAL JOURNAL 



or its equivalent 



logioi = logio^n + n logio T - (bn/2.3T). (lb) 



An and 6„ are constants characteristic of the surface. Their value 

 depends on the value assigned to n. From such experiments it is 

 impossible to decide whether n should equal or 4 or any value 

 between these. There are good theoretical reasons, which are given 

 below, why n = 2. In that case 



or 



i= AT^exp (- b/T), (2a) 



log * - 2 log r = log A - b/2.3T. (2b) 



If log i — 2 log T is plotted versus 1/T, a straight line is usually ob- 

 tained. Call this line a Richardson line. Its slope is — b/2.3, and 

 its y intercept is log A. Since we shall have numerous occasions to 

 refer to the slope and intercept of a Richardson line, we shall find it 

 convenient to refer to them by their equivalents — b/2.3 and log A, 

 respectively. On those rare occasions when the Richardson plot 

 yields a curved line, we can draw a tangent at any point on the curve. 

 Equation (2) will then represent the equation for this tangent ; 

 — b/2.3 and log A will depend on the particular point at which the 

 tangent is drawn, so that b and A will depend on T. 



The Thermodynamic Equation 

 The slope and intercept of experimental Richardson plots are to be 

 correlated with certain quantities in one or the other of two theoretical 

 equations. The first of these * is based on the first and second law 

 of thermodynamics and the assumption that the electron vapor acts 

 like a perfect gas.f The equation is : 



log ir = log ir' + log [(1 - r)/(l - /)] + I log V 



- I log r + (1/2.3) r {L,/RT')dT, (3) 



in which T' is any fixed temperature in the experimental temperature 

 range; r and r' are the electron reflection coefficients at T and T', 

 respectively ; Lp is the heat of vaporization per g. mole of electrons at 

 constant pressure ; R is the gas constant per g. mole. 



TJiermodynamics cannot tell us how Lp varies with T and until we 

 know this we cannot perform the integration indicated. By consider- 



* For a recent critical derivation see Becker and Brattain.' 

 t This assumption is suljse(|uently justified by experiment. 



