456 



Dr. J. Hopkinson. 



[Dec. 16, 



Hitherto we have made no assumption excepting that energy is not 

 dissipated in a condenser by charge and discharge. We now make an 

 assumption concerning /(V), namely, that it is, of the form 0(Y/aj), 



i.e., that ^X = — , or in words, that the capacity of a condenser varies 



dx x 



inversely as the distance between the plates. 

 Then we have — 



= 2K-K S (9) 



In words, the specific inductive capacity as determined by charge or 

 discharge of a condenser at any given potential and distance between 

 the plates is the arithmetic mean of the inductive capacity deter- 

 mined by the force resisting separation of the plates and of that deter- 

 mined by lateral pressure, the potential and distance being the same. 

 This is true whatever be the relation between charge and potential 

 difference, but it is at variance with the experimental result that 

 and K s are both greater than K. 



Further J* = jV(V)«*V/iV/(V). 



In the accompanying curve, let abscissa of any point P of the curve 

 OQP represent V, ordinate /(V). If Kp>K area ONPQO>area of 

 triangle ONP, i.e., unless the curve y = (fx) has a point of inflexion 

 between and P, the fact that > K implies that K increases with 

 V, — a conclusion again at variance with experimental results. 



We are thus unable to account for the observation on the hypo- 

 thesis that the capacity varies inversely as x. Let us now suppose that 

 /(V) = V<fi(x), that is to say, that however the capacity may depend 

 on the distance, it is independent of the charge, or is constant for any 



