1886.] 



On Specific Inductive Capacity. 



457 



given condenser. It at once follows that K S =K, which is discordant 

 with observation. Consider, however, the ratio — 



X 



since 0= ^0(ff) + V0'( a5 ) when e is constant. Suppose ~- = m, a, 



CtX £±_ 



positive constant quantity greater than unity — 

 mc/)(x) + x(})'(x) = 0, 



x m (j)(x) = C, a constant as regards 

 or <j)(x) cc ar m . 



We could, therefore, account for Kp being greater than K by sup- 

 posing that the potential difference with given charge per unit of 

 area does not vary as a? but as x m . Such a supposition would be sub- 

 versive of all accepted ideas of electrostatics. 



There remains one other consideration to be named. We have 

 assumed throughout that the charge of the condenser depends only 

 on the distance of the plates and their difference of potential, and is 

 independent of previous charges or of the time the difference of poten- 

 tial has existed. We have ignored residual charge. It is easy to see 

 what its effect will be on determinations of K made by measuring the 

 potential and charge of the condenser. It is not so obvious what its 

 effect will be in all cases on the force between the plates. Consider a 

 complete cycle of operations : the condenser is charged with quantity e, 

 the distance between the plates is increased from x to x + dx, the con- 

 denser is discharged and the plates return to their initial position. 

 The work done respectively in charging the condenser, separating the 

 plates, and recovered in discharging the condenser, will depend on 

 the rate at which these operations are performed. There are ideally 

 two ways of performing them, so that no energy is dissipated by 

 residual charge, first, under certain reservations, so rapidly that no 

 residual charge is developed ; second, so slowly that at each potential 

 the residual charge is fully developed ; in either case the potential is 

 a function of the then charge, and not of the antecedent charges. 

 The attraction between the plates will differ according as the charge 

 is an instantaneous one or has been long applied. If a liquid were 

 found exhibiting a considerable slowly developed residual charge, the 

 capacity determined by attraction with continuous charge would be 

 greater than the capacity determined by an instantaneous discharge 

 of the condenser through a galvanometer or into another condenser* 



vol. xli. 2 I 



