11)6 Profs. Richardson and Cooke on the Heat developed 



In some cases it has been observed that for very small 

 values of V the thermionic current had a small value 

 independent of the voltage. In this case we have 



/(V) = v* or /(V„)/g = 4, 



where V is the potential fall along the hot wire. 

 When V is greater than I ^— , 



so that to obtain /(V) as a function of V we proceed as 



^hen th< 

 -dVdi 



follows :— First take V = Vj between and I -"— . Then the 



value of f(Vi) is equal, by what has gone before, to w 



o® oV 



Next take 

 Then 



Ox 



3 V/ S .,, /(V - ) = BV + BV/ 9 .,/( V ')- 



Since /(V]) has already been determined, differentiation of 

 the current-E.M.F. curve enables us to determine /(V 2 ). 

 We then take 



and thus deduce the value of /(V 3 ). Proceeding in this 

 way, we can obtain the values of f(V) corresponding to a 

 series of constantly increasing values of V. We now multiply 

 each value of /(V) by the corresponding value of V. V is 

 the potential difference driving the current f(Y)dx which 

 originates from the element dx of the hot wire, so that it is 

 clear that the average potential difference through which the 

 electrons fall, corresponding to any observation where the 

 thermionic current is i, will be equal to 



(V(V)A, lP i ri 



J f(Y)d* » J« i|J>: 



