On a particular differential Equation. 211 



times proportional to the measure of the chemical forces em- 

 ployed. The battery was on one occasion kept in continuous 

 action for two hours, and, by a little contrivance, the potassium 

 was in each cell simultaneously raised from its membrane into 

 the supernatant naphtha, and remained there in a quiescent 

 state until the following evening, when it was again used with 

 facility; no loss having occurred of any consequence, except 

 in the giving way of three membranes. It was found that, for 

 delicate experiments with one pair, goldbeaters' skin or turkey's 

 craw is considerably more efficient than bladder : decomposi- 

 tion of water is scarcely perceptible when the latter is employed. 



XXXI. Remarks on a Paper by the Rev. Brice Bronwin, 

 On the Solution of a particular differential Equation. 



To the Editors of the Philosophical Magazine and Journal. 



Gentlemen, 

 T^HERE is a single explanation which, after reading Mr. 

 -■■ Bronwin's remarks published in the last Number of your 

 Journal, I deem it right to make. 



Mr. Bronwin observes that I have in various papers made 

 assertions without alleging any proof, or entering into any 

 sufficient explanation, and that he was led to conclude from 

 this, that I held it to be always lawful to reject the supernu- 

 merary constants of the solution of a differential equation. 



I think it probable that in the instances to which Mr. Bron- 

 win refers, sufficient detail was not given. Having clearly 

 stated in one paper the general principles which decide whether 

 the elements in question are to be rejected or determined, I 

 have in subsequent applications of the same method, contented 

 myself with simply referring to the original paper, and, in one 

 instance, with applying the principle without reference. Mr. 

 Bronwin will find upon examination that the results are in 

 each instance correct, and that the cases are mutually analo- 

 gous, — the real point of analogy being the relative position of 

 the direct and the inverse factors of operation. But inasmuch 

 as there may really have been a deficiency of needful expla- 

 nation, I feel it just to make the present acknowledgement; 

 and had the same view of the case presented itself to me be- 

 fore, I would have made it sooner. 



I am, Gentlemen, 



Your obedient Servant, 



August 4, 1848. GEOttGE BoOLE. 



