436 Prof. Richardson and Dr. Bazzoni : Experiments 



Since U and z vanish when V= Vi and #=# l5 we have 



/ =~(2fl)^ 1 =~2V l % .... (20) 



from the solution for the space between the cathode and the 

 critical surface. Thus if the distance between the cathode 

 and the anode is I and the potential difference between 

 them Y h 



Vi* 



{za)° = 



and 



(«./= ?{ 2+ F(I^.)} 



*~~16tt 



( e \ iy ^ /2 iu v '- 2 n> iY /2 4- x ^ -iY— ^ ( Yi i\ ll + 



1.4.7.... (3n-2) 2 /^.A^ 1 3 fl | 



This formula makes the currents for values of V between 

 Vx and 2 Vj increase with V less rapidly than the requirements 

 of the V 3/2 formula which holds for Y<Y 1 . The calculated . 

 falling off is indicated roughly by the following numbers: — 



V,/Vi— ► 1*25 1-5 1-8 2-0 



i/V * ''73 '57 -4 -4 



The values of iji{ are the currents calculated by (21) 

 divided by the corresponding currents calculated on the 

 assumption that the Y 3/2 law which holds for V< Vi is valid 

 also for V>V 1 . The calculated falling off is much greater 

 than that shown by the results on p. 431. This might be 

 expected, as the theoretical conditions are very imperfectly 

 realized in the experiments. Apart from the quite different 

 system of electrodes used, there was a drop of potential down 

 the cathode due to the heating current of about 2' 5 volts. 

 This makes the effective critical potential about 1*5 volts 

 too high. The sharpness of the effects arising from the loss 

 of energy at the critical value also tends to be obliterated, 

 owing to the occurrence of the initial distribution of velocity 

 which will prevent the average kinetic energy from actually 

 vanishing at any point. The larger observed currents might 

 also be attributed to the liberation of positive ions at the 

 critical collisions ; since we should expect any considerable 

 development of positive ions to permit a much closer 

 approach to saturation, owing to the consequent reduction 

 of p in equation (2). 



