362 Mr. 0. J. Lodge on a Mechanical Illustration 



ing forces are proportional to the elasticities of the several 

 threads, or unless these elasticities are infinite (as they 

 practically are in the case of metals). If an accumulator be 

 charged by means of an electromotive force E continued so 

 long that the p become uniform and constant and equal to 



E 



-~, the last equation may be written, by help of (1), 



°"l2 



<Mi>> ^ 



which proves that there will be no internal charge even in this 

 case if the r are proportional to the k (cf. case 2, § 3). 



After having charged the jar with this long-continued force 

 E , discharge it instantaneously, and then leave it to itself for 

 a time t with S screwed down. The difference of potential 

 between the two coatings, which was at first zero, rises by irre- 

 gular slipping of the buttons; and its value E at the end of 

 any time is given by (24), which we may write 



E / api fli«i V -g* , / a 2 r 2 a 2 /c 2 \.,* g ; , (e> ., 



wr\Wr)~^)r l + {^)-W«)) e " 2 + — (24) 



A quantity of electricity EC can at the same time be got 

 out of the jar; and this is the residual charge. 



Conditions required of the Model in order to he an accurate 

 representation. 



§ 10. The conditions which the model does not naturally 

 satisfy are (1) and (2). Condition (2), however, that the re- 

 storing force shall vary with the displacement, is nearly satis- 

 fied by fig. 1 for small displacements ; and it can be made 

 accurately true by passing each elastic through a smooth fixed 

 ring placed in the line of its mean position at a distance from the 

 fixed pin equal to the natural length of the unstretched elastic. 

 Then (2) is satisfied by the model ; and each button, if pulled 

 aside, would execute a succession of simple harmonic motions 

 about its mean position. 



To satisfy condition (1) is not quite so easy. Electrical 

 resistance is very different from ordinary friction, though they 

 are to some extent analogous. The smallest electromotive 

 force is sufficient to produce some current against any resist- 

 ance however great, and the current increases proportionally 

 to the electromotive force from zero upwards ; but friction is 

 a discontinuous quantity. For small values of force applied 

 to move a body, the friction is exactly equal to the force, and 

 the body does not move ; but as the force increases, at a cer- 

 tain critical point the friction suddenly falls from the value 



