494 



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



fact that the different sets of electrons are shifted by dif- 

 ferent amounts does not, however, afreet the total number 

 which pass through the gap, which number will consequently 

 be the same as if the force X s were absent, except for a 

 small error at one end of the plane, which only exists, how- 

 ever, for a length of the plane comparable with the mean 

 free path*. Thus, in the general case (23) represents the 



condition which must hold between the value of V at a 



gap, 



Fi< 



and the normal component of the force resolved perpendicular 

 thereto. 



Now returning to the complicated cell-structure cited on 

 p. 476, we see that the fields inside the groups and the 

 drops of potential at the gaps must satisfy three conditions. 



(1) If we draw parallel to the applied field X a line of 

 length L great compared with the dimensions of a group, 

 and if ds is an element of this line, we must have 



XL = f L X'^+2V 



Jo 



for all such lines parallel to the field X. Here 2 V repre- 

 sents the sum of all the drops of potential occurring at gaps 

 along the line of length L, and X' is the field at any point. 



(2) If ABO (fig. 8) represent three regions separated by 

 bounding gaps it is easily seen by con- 

 sidering the state of affairs at the point 

 0, for instance, that we must have 



aV b = a V c + c V e . 



(3) The force and the potential drop 

 at each point in the neighbourhood of a 

 bounding gap must satisfy the relation 



Now in the general ease the condition 

 (1) is readily satisfied 

 averaging effect due to 



* It may be noted that if we consider the electrons coming from any 

 one element, and draw a plane through that element perpendicular to 

 the gap and to the force X. n , then since the electrons which strike the 

 gap on the side of the plane to which the force X s points have had their 

 journeys increased by the action of the force, fewer of them will reach 

 the plane than would otherwise have done so. It is to be noticed, how- 

 ever, that this effect is cancelled by the diminution in the journey 

 travelled by the corresponding set of electrons striking the gap on the 

 other side of the plane ; at least this is true if we neglect the second 

 order of small quantities. 



owing to the 

 the integration 



