432 Pi*of. Thomson on the Mechanical Tfieory of Electrolysis. 



it is ever considerable compared with that which is electrically- 

 conducted ; and the normal law of true electrolytic conduction 

 will therefore be assumed as applicable to the conduction through 

 the electro-chemical apparatus, subject to modification in any 

 case in which the deviations from it can be determined. If, 

 then, we denote by e the electro-chemical equivalent of the 

 particular element referred to for measuring the chemical action, 

 that is, the quantity of it which is electrolysed or combined in a 

 unit of time by the operation of a current of unit strength, since 

 the actual strength of the current is y, we have 



E = 67 (6) 



The deviations from the normal law which may exist in any 

 particular case may be represented by giving e a variable value. 

 I^or instance, if it were true that when the electro-motive inten- 

 sity in an apparatus for the decomposition of water exceeds a 

 certain limit, there is decomposition at a rate precisely propor- 

 tional to the strength of the current; and when the intensity is 

 below that limit, a slight current passes without any decompo- 

 sition * 6 would be a discontinuous function of the intensity, 

 having a constant value when the intensity is above, and being 

 zero when the intensity is below, the limit for decomposition. 



6. According to Joule^s law of the generation of heat in the 

 galvanic cu'cuit, the quantity of heat developed in a unit of time 

 would be rigorously proportional to the square of the strength 

 of the current, if the total resistance were constant in all the 

 circumstances considered ; and therefore we may conveniently 

 assume 



H=K7^; (7) 



but as we are not sure that the whole resistance is independent 

 of the strength of the current when an electrolysed fluid forms 

 part of the circuit, we must not assume that R is constant. In 

 what follows, all that is assumed regarding the value of R is, 

 that it is neither infinitely great nor infinitely small in any of 

 the circumstances considered *. 



* Since the present article was put into the Editor's hands, I have be- 

 come acquainted mth a paper by Mr. Joule " On the Heat evolved during 

 the Electrolysis of Water," published by the Literary and Philosophical 

 Society of Manchester in 1843 (vol. vii. part 3, second series), in which it 

 is shown, that in some cases of electro-chemical action (for instance, when 

 hydrogen is evolved at an electrode or battery-plate of a metal possessing 

 a considerable affinity for oxygen) there is a "resistance to electrolysis 

 without chemical change," producing " a reaction on the intensity of the 

 battery," and causing the evolution of heat to an amount exactly equivalent 

 to the loss of heating power, or of external electro-motive force, which the 

 battery thus suffers. In any electro-chemical apparatus in which this kind 

 of resistance occurs, the quantity of heat developed by a current of strength 

 y will be expressible in the form Ay+By^ where A and B are finite when 



