132 Dr. J. Moser on the Division of Induction in the 



" inducteous." In this arrangement the division of the induc- 

 tion corresponds to the division of the current in flowing 

 electricity. 



But before I proceed further with the physical considera- 

 tions, which would appear hypothetical, I shall deduce the 

 mathematical from the theory of potential. 



If we look upon the differential inductometer as formed of 

 two condensers, the total electricity, E, on the middle plate 

 consists of two parts, e x and e 2 ; 



E=^ + g 2 (1) 



so that <?! is the charge on one plate, and e 2 on the other. 

 The value of each of these is found in the following manner. 

 According to Green *, if e be the charge on a plane conden- 

 ser whose plates have the surface S and the distance r, and 

 if the potential-function on the one is Y, while the other is 

 connected with the earth, then 



= YS 

 4:7rr' 



In the derivation of this equation it is assumed that r is 

 small in comparison with the diameter of the plates, an as- 

 sumption to which I will return afterwards. 



We will apply this formula to the two condensers of the 

 differential inductometer. All three plates have the same 

 surface S. The middle one has the potential V; the two 

 outer ones are connected with the earth. Let the distance of 

 the plate of which the charge is e-i be r 1; that of the one with 

 charge e 2 be r 2 . Then 



YS 



e,= 



and 



and, accordingly, 



1 4tt?V 



YS 



1 1 ,™ 



? 1 7 2 



In other words, the charges are inversely proportional to 

 the distances. The values of the two charges are derived 

 immediately from equations (1) and (2). According to these, 



^=-5-E (3) 



e 2 = -^-E (4) 



* Green, Essay, § 8j Thomson, Papers, § 53. 



