476 



Dr. W. F. G. Swarm on the Electrical 



If we fix our attention on the groups of molecules we can 

 imagine each group as separated from 

 its neighbours by a kind of equipotential 

 surface (represented by the dotted lines 

 in fig. 3), these surfaces being such that 

 if an electron leaves one of the groups 

 with sufficient velocity to reach a sur- 

 face, it will escape to the next group. 

 Since one of these surfaces must surround 

 each group, it is obvious that they will 

 be polygonal surfaces with approximately 

 plane faces, and will be of such a nature 

 as to fit together perfectly, nowhere 

 enclosing a space unless that space con- 

 tains one of the groups. They will divide up the whole 

 region into a kind of honeycombed cell structure. We 

 shall imagine that in the absence of the electric field, the 

 electrons in these cells obey Maxwell's law, the number dn 

 having a velocity between c and c + dc being given by 



dn = Ae- hmc2 c 2 dc, 



(3) 



where 



A _ 4n(7tm) 3 / 2 3 



ol6 is the kinetic energy of a gas molecule at a temperature 

 0, n is the number of electrons per c.c, and m is the mass 

 of an electron. 



We shall suppose that it is only in the very small regions 

 or gaps * separating the groups that the molecular forces 

 come into play. These regions we shall suppose to be very 

 narrow compared with the width of the group as a whole. 

 We shall further suppose that those electrons whose velocity 

 resolved perpendicular to the gap is greater than u, when the 

 electron leaves the group in the absence of the field, will be 

 able to get across. 



The problem which we shall first consider is one where 

 the metal is divided as it were into a large number of slabs 

 of width I by gaps crossing the metal with their planes per- 

 pendicular to the direction of the field. We shall afterwards 

 give reasons for assuming (see Appendix, page 493) that the 

 result so obtained for the conductivity is practically true for 

 the more complicated cell structure cited above. 



* It is not necessary to imagine an actual separation between the 

 groups. All that is necessary is that there shall be regions (typified by 

 the above gaps), on crossing which the molecular forces change with 

 considerable abruptness. 



