114 STATIC ELECTRICITY 



potential and is then insulated, the fall of potential in a given time 

 is proportional to the initial potential, and, further, that if at any 

 instant the jar is discharged, the instantaneous discharge is pro- 

 portional to the potential just before the discharge was made. 

 Kohlrausch formed a theory of the action going on which 

 apparently involved the idea of conduction, though he did not 

 express it in that form. But he pointed out the resemblance of 

 the residual phenomena to those of "elastic after-action" in 

 strained wires, which gives a very valuable analogy. If a wire is 

 twisted for instance, if a glass fibre is fixed vertically in a clam}) 

 at its upper end, and if the lower end is twisted and held, it will 

 return on release towards its original position, but not the whole 

 way. If it is now held in its new position for a time and is then 

 released, it will return another portion towards its original position, 

 and so on. We may explain this after-action, as it is termed, by 

 supposing that some parts of the glass retain strain energy as long 

 as the strain is retained, while in other parts, though the sh 

 remains, the energy is dissipated, or the diminishes. 



Imagine, for instance, that the outer shell of the fibre is " tnu " in 

 its elasticity, i>e. that the stress is always proportion*] to tin- 

 strain, but that the inner core gradually lo>e> its "train ^'ix-Tgy, 

 even though its strain is maintained. Now twist the compound 

 fibre. If it is instantly released before the energy in the core has 

 had time to become dissipated it will return to the original position. 

 But if the fibre is held twisted for a time the stress in the core 

 gradually decreases and the effective strain <1< \\lnn tin 



fibre is released the effective strain in the core will be entirely 

 removed before the fibre is entirely untwisted. But some stress 

 still remains in the outer shell when this point is reached, and the 

 outer shell still tends to untwist, and will continue to untwist till 

 the core is strained in the opposite direction so much that the 

 negative stress in it just balances the positm itNH -till mi mining 

 in the shell On again holding the fibre this negative stress 

 decreases, and on release the outer shell will be able to impart 

 some more negative strain to the core, and so on. Gradually the 

 fibre will return to its original position if the outer shell is 

 perfectly "true" in its elasticity. But if it too exhibits some 

 dissipation of energy the return will not be complete. 



The most probable explanation of residual effects is analc 

 to this, and was given by Maxwell* somewhat in the following 

 form. It takes account of effects which must certainly exist, and 

 so far it must be a true explanation, though it may not be com])! 

 In it the dielectric is regarded as heterogeneous, of which \>; 

 are slightly conducting, while other parts remain completely insu- 

 lating. We may imagine, as in Chapter IV, that the strain" in the 



* Electricity and Magnetism, vol. i. chap. x. An account of Maxwell's theory 

 on somewhat simpler lines is given in the P/til. Mag., Series V. vol. xxi. (1886), 

 p. 419. 



