Prof, Thomson on Transient Electric Currents. 401 



charger consequent on the successive sparks*. Thus, if the 

 general law of electro-chemical decomposition be applicable to 

 currents of such very short duration as that of each alternation 

 in such an oscillatory discharge as may take place in these cir- 

 cumstances, there will be decomposed altogether as much water 

 as is electro-chemically equivalent to the sum of the quantities 

 of electricity that pass in all the successive currents in the two 

 directions, while the quantities of oxygen and hydrogen which 

 appear at the two electrodes will differ by the quantities arising 

 from the decomposition of a quantity of water electro-chemically 

 equivalent to only the quantity of electricity initially contained 

 by the principal conductor. The formulae investigated above 

 will be applicable to this case if the end of the discharging train 

 next the machine be placed in metallic communication with an 

 insulated conductor, satisfying the conditions laid down with 

 reference to the ^' principal conductor " at the commencement of 

 this paper, and if this conductor be successively electrified by 

 sparks from the machine. The whole quantity of water decom- 

 posed will therefore be the electro-chemical equivalent of the 

 sum of the absolute values of the quantities of electricity flowing 

 out of and into the principal conductor during the successive 

 alternations of the current, that is, according to the preceding 

 formulae, the electro-chemical equivalent of the quantity, 



_ kir 

 kTT 2k7r 1 -l-e 2A*' 



Q(l+2e-SA^'-f-26-^A^' + &c.), or Q _ ^^ , 



1 — e 2Aa' 



of electricity. This quantity will be the greater the more nearly 



_k'ir 

 6 2A«' 



^ . 4A 



or the greater is j-^ . Hence the greater the electro-dynamic 



capacity of the discharger, the less its resistance, and the less 



«' approaches to unity,tnat IS the greater IS ~~ir~^^\Tr^—'^ } t 



* This explanation occurred to me about a year and a half ago, in con- 

 sequence of the conclusions regarding the oscillatory nature of the discharge 

 in certain circumstances drawn from the mathematical investigation. I 

 afterwards found that it had been suggested, as a conjecture by Helmholtz, 

 in his Erhaltung der Kraft (Berlin 1847), in the following terms : — 



*' ** It is easy to explain this law if we assume that the discharge of a 

 battery is not a simple motion of the electricity in one direction, but a back- 

 ward and forward motion between the coatings, in oscillations which become 

 continually smaller until the entire vis viva is destroyed by the sum of the 

 resistances. The notion that the current of discharge consists of alter- 

 nately opposed currents is favoured by the alternately opposed magnetic 

 actions of the same ; and secondly, by the phaenomena observed by Wol- 

 laston while attempting to decompose water by electric shocks, that both 

 descriptions of gases are exhibited at both electrodes." [Quoted from the 

 translation in Taylor's New Scientific Memoirs, Part II.] 



