the Photoelectric Eftect. 589 



This makes the energy lost proportional to the initial 

 energy for different wave-lengths, and the relation between 

 the observed T m and v a linear one. The slope, measured by 

 k m , of the experimental line would then be less than that (h) 

 of the theoretical line. The two lines would intersect at 

 T TO = 0. This is in accordance with the experimental results 

 if the experimental values of v are really identical with the 

 least frequencies which would cause airy electrons to be 

 emitted from a perfectly clean surface. It might be, how- 

 ever, that the true values of v would be less than those 

 observed, on account of the slowest electrons being com- 

 pletely stopped by such a layer. In that case the relation 

 between T and x would have to be of the form 



T=T f(x)-g(z), (15) 



when T is the maximum initial energy. 



There is at present, so far as we are aware, no experi- 

 mental evidence bearing on the law of loss of energy with 

 matter traversed for these slowly moving electrons, but 

 Sir J. J. Thomson * has deduced a formula of type (14) with 

 f(x) = constant, on theoretical grounds. The application of this 

 formula can hardly be regarded as having much cogency in 

 the present instance, but it is of some interest to see what it 

 leads to, in the way of an estimate of the thickness of inactive 

 matter required to produce the observed differences between 

 theory and experiment. In the least favourable case, that 

 of bismuth, assuming the inactive matter to be Bi 2 3 , we find 

 a = 2'5x 10~ 4 cm. In the other cases the thickness would 

 vary down to about one-tenth of this. Thicknesses of inactive 

 matter of this magnitude should produce distinct optical 

 effects. The only case in which we observed visible changes 

 of this kind was that of copper, the surface of which became 

 darker during the experiments. The existence of photo- 

 electric fatigue shows that the surfaces of the metals do 

 become covered with a layer of inactive matter. Tests which 

 we have carried out show that the change in the maximum 

 energy and in the distribution of energy of the emitted 

 electrons due to photoelectric fatigue is uncertain, but is 

 certainly inappreciable in comparison with the change in the 

 number of electrons emitted. However, a layer of inactive 

 matter might easily have the effect of reducing the number 

 of escaping electrons very considerably without causing any 

 comparable change in the distribution of velocity among 

 those which got through, particularly as the mode of dis- 

 tribution is fairly irregular to start with. It is significant 



* ' Conduction of Electricity through Gases,' 2nd edition, p. 379. 



