416 Dr. L. Silberstein on the Electron 



Let us therefore make the assumption (which, as far as I 

 know, has actually been made by the leading electronists) 



that p/ne is a small fraction. Then log (1— p/ne) = — , and 

 eq. (5) becomes 



2k . 1 Cp'dr' 



The coefficient on the left hand is a certain squared length, 

 since such is the dimension of the ratio of <£ and p. Calling 

 the coefficient in question L 2 , we have, by (I), 



U=\^ (6) 



The length L is identical, in fact, with J. J. Thomson's 1/p 

 which he takes as the measure of the thickness of the layer 

 in the example mentioned above. As concerns the value of 

 the fundamental length Z, we have, by (6), for, say, 

 T=300 (or 27° C), 



2 . 1Q- 14 1^_ 1-7.10 4 



4tt.9-5.10- 20 "n" n > 



i. e. in round figures, 



L=l30/\/n. 



Thus, for instance, if there is one free electron per each 

 atom of the metal, say, of copper, or w=10 22 , then L is of 

 the order of 1*3 . 10 _9 . But as far as is known, there may 

 be only one free electron for every 1000 or 10,000 atoms: 

 in the latter case we should have jL=10 -7 cm. As a matter 

 of fact the number n is not even coarsely known, so that all 

 such estimates, especially in the domain of electrostatics, are. 

 for the present, pretty useless. (See also the preceding- 

 footnote. ) 



With the above notation the last approximate equation 

 for p becomes 



-!*-*.+ £ j«£, ... (I) 



or written shortly, 



—£*/> = £,+ pot/o, 



a linear integral equation of the second kind, the integral on 

 the right hand to be extended over the volume of all con- 

 ductors of the system which, with $ e and the total charges 

 of the conductors given ? suffices for the determination of p. 



