432 Prof. Richardson and Dr. Bazzoni : Experiments 



is within the limits set by the errors of measurement, but 

 between 7 volts and 13 volts the observed currents are 

 uniformly below those given by the Y 3/2 law. Above 

 14 volts the observed currents exceed the values calculated 

 in this way. 



It is known that electron currents between a hot and a 

 cold electrode in a very good vacuum vary as V 32 for small 

 values of V, and the phenomenon has been accounted for 

 satisfactorily by Langmuir*. No doubt a similar explanation 

 will apply to those of the present experiments in winch the 

 pressures were very low, bui it will scarcely cover a case 

 •such as that oE the numbers in the last table, since an essential 

 feature of Langmuir's explanation lies in the assumption 

 that the electrons move freely between the electrodes under 

 the acceleration due to the electric field without interference 

 • or collisions with gas molecules. This condition will certainly 

 be far from being satisfied with gas pressures of the order of 

 a millimetre. 



The following considerations show that with monatomic 

 gases a similar law for low potential differences is to be 

 •expected even at high pressures. According to the researches 

 of Franck and Hertz, if the potential difference is less than 

 a critical value \ l characteristic for each monatomic gas, the 

 electrons undergo collisions with the gas molecules without 

 loss of energy; so that if they are assumed to start from the 

 hot electrode (V = 0) with negligible velocity, their kinetic 

 energy on reaching a point in the field where the potential 

 is Y (V<Y 1 ) will be given by 



imv 2 = eV (1) 



Owing to the presence of electrons in the space between 

 the electrodes, V will have to satisfy Poisson's equation 



V 2 V = 47rp (2) 



The average velocity of the electrons in the direction of 

 the electric intensity will be governed by the acceleration 

 between successive collisions, so that the current density at 

 any point will be given by the expression | 



. n e 2 \ p e X dV 



2 in v ^ 2 m v o% 



where X is the mean free path of the electrons in the gas. 



* Phvs. Review, vol. ii. p. 457 (1913'). 



t Cf. l Electron Theory of Matter/ 2nd Ed. p. 410. 



