394 Royal Society : — Sir William Thomson on an Apparatus 

 jecting stems. If a tube (fig. 3) be added to the lid to prevent 



Pig. 3. 



currents of air from circulating into the interior of the jar, the 

 insulation may be so good that the loss may be no more than 

 one per cent, of the whole charge in three or four days. Two such 

 jars may be kept permanently charged from year to year by very 

 slow water-dropping arrangements, a drop from each nozzle once 

 every two or three minutes being quite sufficient. 



The mathematical theory of the action, appended below *, is 

 particularly simple, but nevertheless curiously interesting. 



The reciprocal electrostatic arrangement now described, presents 

 an interesting analogy to the self-sustaining electromagnetic system 



* Let c, c' be the capacities of the two jars, I, V their rates of loss per unit 

 potential of charge, per unit of time, and D, D' the values of the water-drop- 

 pers influenced by them. Let -\-v and — v' be their potentials at time t, v and 

 v' being both of one sign in the ordinary use of the apparatus described in the 

 text. The action is expressed by the following equations : — 



at ^t 



If c, D, I, c r , D', V were all constant, the solution of these equations would be, 

 for the case of commencing with the first jar charged to potential 1, and the 

 second zero, 





jrt 



/=D- 



c(p-o) 



with the corresponding symmetrical expression for the case in which the second 

 jar is charged, and the second at zero, in the beginning ; the roots of the quadratic 



(cx+l)(c , x+l')--DTy=0 



being denoted by p and <r. When IV > DD', both roots are negative ; and the 

 electrification comes to zero in time, whatever may be the initial charges. But 

 when IV <DD', one root is positive and the other negative, and ultimately the 

 charges augment in proportion to e*' if p be the positive root. 



