Electric Residue in the Leyden Jar. 477 



through the au-, so that at the time t it amounts only to Q^, then 

 the ideal state of equilibrium towards which the glass strives at 

 the time t will no longer necessitate the residue joQg, but merely 

 juQ^. If an actual concealed residue r^ has been formed during 

 this time, then the distance from the state of equilibrium is 



P^t-'-f .... 



Now this distance will continually decrease; whence its dif- 

 ferential must be made negative, and the velocity of its change, 

 or 



d[pQi-rt) 

 Jt ' 

 is evidently greater the greater the distance which still exists ; 

 hence it might be set propoi-tional to some function of the same. 

 If, by way of trial, we write 



we find by integration that the constants, among which j) (as 

 may easily be seen from the observations) has not a very exten- 

 sive field of variation, cannot be determined so as sufficiently to 

 satisfy the observations. 



The velocity in the change of the distance from the state of 

 equilibrium, however, is not in reality merely a function of this 

 distance, as may be seen fi'om the following fact, the mention of 

 which has been hitherto purposely postponed. 



If the residue r be generated by a strong charge in a very 

 short time, and afterwards the same residue r be generated by a 

 weak charge in a longer time, the distances from the state of 

 equilibrium on discharging the jar will still in both cases be 

 equal. Notwithstanding this, the former residue sooner converts 

 itself into disposable charge than the latter. Thus we see that 

 the said velocity in the change does not depend solely upon the 

 magnitude of the distance from the state of equilibrium, but 

 also upon the time during which the strain has continued. Owing 

 to the secondary action, similar phsenomena would probably be 

 observed in elasticity if suitable bodies could be investigated. If 

 a piece of wood were considerably bent for a short time, or only 

 bent a little but for a long time, it may easily be conceived that, 

 when released, an equal departure from the original form might 

 be manifested in both cases, whilst the times which would be 

 required completely to regain that form might be very diSerent*. 



* It should here be mentioned, that W. Weber, in bis rcseareh on the 

 elastic force of a silken thread, has ol)tained an eciuation for the curve of 

 ehistic secondar.v action which is exactly analogous to the above, and does 

 not contain a particular function of the time. That which we have calletl 



