496 



Mr. J. Hopkinson on the 



[Jan. 18, 



II. Residual Charge of the Ley den Jar.~II. Dielectric Properties 

 of various Glasses .^^ By J. Hopkinson, M.A., D.Sc. Com- 

 municated by Prof. Sir William Thomson, P. U.S. Received 

 November 30, 1876. 



(Abstract.) 



I. The two following propositions are included under the law that 

 the effects of simultaneous electromotive forces are superposable. 



(a) If two jars be made of the same glass but of different thicknesses, 

 if they be charged to the same potential for equal times, discharged for 

 equal times, and then insulated, the residual charge will after equal times 

 have the same potential in each. 



(6) Residual charge is proportional to exciting charge. 



These propositions are verified experimentally within the limits of 

 errors of observation. 



II. Electric displacement through a dielectric may be supposed to 

 depend not only on the electromotive force at the instant, but also in 

 part on the electromotive forces at all previous times. If we assume 

 that the effect of the electromotive force at any previous time decreases 

 according to some law as the time elapsed increases, and that these effects 

 are superposable, we may write 



where ^< is the electromotive force at time ^, and yt is the surface integral 

 of electric displacement divided by the instantaneous capacity of the jar. 



If -v/r (w) is determined for all values of w, the properties of the glass as 

 regards conduction and residual charge are completely expressed. 



^ {co) is equal to the reciprocal of the specific resistance of the 

 material multiplied by 47r and divided by the specific inductive capacity. 

 During insulation yt is constant ; hence 



This is the fundamental equation of the following experiments. 

 Two methods of finding values of i^ (w) present themselves. 

 1st. Let be constant = X for a time T ; insulate for time t. 



if t be small. 



dx,_ _X;f/(^ + T)-J^ ^^^l^wd(o 



dt —TV.-/ . 



^^^=»X^(T), 



and the value of may be observed with more or less accuracy, 

 dt 



