116 STATIC ELECTRICITY 



and CD remains, and the potential difference between AB and CD 

 becomes positive again. Let us suppose that AB remains insulated 

 till the strain between it and EF has decreased from 8 to 4. 

 There will then be charge + 12 on EF. On connecting AB and 

 CD the two charges 4 and 8 will be equally shared, which 

 implies a discharge of 2 from CD to AB, equivalent to a 

 discharge of + 2 from AB. There will then be 6 on each of AB 

 and CD, with the corresponding -f-12 on EF. Again insulate AB 

 till the strain 6 between EF and AB has fallen to 3. On 

 connecting AB and CD there will be a passage of 1'5 from 

 CD equivalent to +1*5 from AB, and 9 remains on EF. If we 

 suppose the strain between AB and EF to be halved in this way 

 each time, the successive discharges from the first will be 



24, 2, 1-5, 1*125, &c. 



Evidently discharges will be obtained till the space bet\\e-n 

 EF and CD is completely free from strain that is, until all the 

 charge on CD is gone, Hence, if we have a completely inflating 

 layer, the sum of all the discharges must equal the original charge. 

 If, however, the layer between EF and CD is not completely 

 insulating, but is a worse conductor than the upper layer, though 

 we shall have residual discharges their sum will bo less than Un- 

 original charge, owing to the decay of strain terminating on CD. 



It is obvious that if the dielectric is homqfleneoua and .slightly 

 conducting throughout there will be no residual phenomena accord- 

 ing to this theory. For the strain will break down .simultaneously 

 from plate to plate, and the first discharge will be complete, as 

 there will be no charges left within the medium as we have supposed 

 those left on EF in the above explanation. 



We may note here how this explanation differs from that of 

 Faraday. He appears to have thought of the charge from AB as 

 gradually moving towards EF, the first links of the chain, as it 

 were, breaking down first. Then after discharge he thought of the 

 charge as gradually moving back again towards AB. It is evident, 

 however, that Faraday had the essential features of the prt- 

 theory. 



If a jar is charged, allowed to rest, discharged, and then 

 charged in the opposite direction to a less extent than at first, it is 

 found that it may ultimately show a residual charge of the same 

 sign as the first charge. The theory gives an explanation of this 

 phenomenon. For suppose that after the first discharge in the 

 case we have considered, where 8 is the strain in the upper half 

 and + 8 is that in the lower, we give a negative charge 4 on AB 

 and + 4 on CD, we shall begin with strain 12 in the upper 

 half and + 4 in the lower, or with AB at lower potential than 

 CD. But if we leave the jar long enough the strain in the upper 

 half will decay to less than 4, and the potential of AB will then 



