that "Professor Young involves himself in a palpable inconsistency when he arrives at the fact of the ellipse question admitting multiple solutions, by an examination of the original analytical conditions, and at the same time alleges that the analytical result is quite incompetent to supply that information." The mathematical readers of this Journal will however readily perceive, that what is here charged as "palpable inconsistency" is in perfect accordance with the strictest analytical accuracy; and that the "inconsistency" would have been, in inferring the multiple solutions from the analytical result, without reference to the original conditions, as Mr. Woolhouse has done, thus assuming (what is not true) that the converse of a certain proposition holds merely because the proposition itself is known to be true. Mr. Horner in the present volume of this Journal (p. 43.) has brought forward whole cluster of instances, in each of which, as he clearly shows, "the analytical result is quite incompetent to supply the information" even as to whether the question admits of a single solution, much less as to whether it admits of multiple solutions: the information sought must be obtained in all these cases, as I have obtained it in the ellipse question, viz. by a direct appeal to "the original analytical conditions." Without such an appeal how are we to know whether the analytical result to which the condition

will supply values competent to satisfy that condition? The presumption is that it will supply such values; upon trial however we find them to fail: and yet these values will satisfy the immediately antecedent equation, but this is not sufficient; every anterior step must be satisfied, up to the original equation inclusively; and the error committed in overlooking this would be precisely similar to that which Mr. Woolhouse appears to me to have committed, in inferring the multiple solutions to the ellipse question, merely because these solutions satisfy the final result*. The same mistaken view of the "theory of

It is but justice to Mr. Woolhouse to state, however, that he admits (p. 399) that" the nature of the problem, as originally presented, is the proper source of rejective information," although he maintains that the original analytical conditions do not furnish the proper source of information, as to whether, in certain hypotheses, one of those conditions becomes destroyed, or two or more of them become dependent; but, on the contrary, that the result is a sufficient indication that one or other of these circumstances must take place. (See III. p. 394.) I have endeavoured to show, however, that this result is not competent to furnish any information on the subject.

analytical results" accompanies his animadversions at page 398-9 in the last number of this Journal; he appears to think it sufficient that the antecedent equation should be satisfied, for he remarks, "The corresponding antecedent equation to the result x = , when cleared of fractions, is ox = 0, or 0 = 0, an equation that is obviously satisfied without any limitation to the value of x, and that cannot fail therefore to be compatible with the other equations or conditions." The statement, in connexion with this remark, viz. that "O can never be the symbol of absurdity," has a little surprised me, because the contrary is a fact so generally known to analysts. To occupy these pages by examples of this would be quite superfluous, as they abound in most of the Continental books on algebra. In the comprehensive work of Bourdon there is an ample supply of such examples, and from which he deduces the ordinary conclusion, viz. that "le symbol est tantôt un caractère d'indétermination, tantôt un caractère d'absurdité."

From what has now been said of the symbol, it appears that, when it is not the indication of absurdity, or of incompatible conditions, it may arise from either of these two causes: viz.

P

from taking the ultimate, or limiting, value of the general Q'

result of an analytical process; or, without regard to this extreme limit, it may arise from the destruction of one or more of the conditional equations. One or other of these circumstances must take place in connexion with the occurrence of

whenever this symbol is at all interpretable. I say whenever the symbol is interpretable, for cases may arise in which this symbol is indicative of neither multiple solutions, nor of limiting values, nor of incompatible conditions. In such cases therefore other modes of solution must be sought. The instances to which I now allude are among those in which the vanishing of the numerator is not necessarily accompanied by the vanishing of the denominator; but where each vanishes independently, in virtue of distinct hypotheses introduced among the arbitrary quantities in each. With the exception of these unintelligible results, the occurrence of is always traceable to one or other of the circumstances before mentioned; which circumstances, although having no necessary connexion, may nevertheless, as in the case of the ellipse question, both exist simultaneously.

When therefore takes the place of

P

Q'

in any hypothesis,

will always

P we may be assured that the limiting values of Q

subsist with the original analytical conditions, however they may be modified under the proposed hypothesis; but we can neither deny, nor affirm, that other values may also subsist with these conditions; for "this is information which the analytical result is quite incompetent to supply," and which must be derived solely from ascertaining the effect of the proposed hypothesis upon the original analytical restrictions; and that this is a fair and legitimate deduction from the foregoing examination, I think no person who enters into it with unbiassed judgement, will be disposed to deny.

Belfast, May 7th, 1836.

LXXXIX. On the History of the Condensation of the Gases, in reply to Dr. Davy, introduced by some Remarks on that of Electro-magnetic Rotation. By MICHAEL FARADAY, Esq., D.C.L. F.R.S., &c., in a Letter to Richard Phillips, Esq., F.R.S. L. & E., &c.

MY DEAR SIR,

Royal Institution, May 10, 1836.

I HAVE just concluded looking over Dr. Davy's Life of his brother Sir Humphry Davy. In it, between pages 160 and 164 of the second volume, the author links together some account, with observations, of the discovery of electro-magnetic rotation, and that of the condensation of the gases, concluding at page 164 with these words: "I am surprised that Mr. Faraday has not come forward to do him [Sir Humphry Davy] justice. As I view the matter, it appears hardly less necessary to his own honest fame than his acknowledgement to Dr. Wollaston, on the subject of the first idea of the rotary magnetic motion."

I regret that Dr. Davy by saying this has made that necessary which I did not before think so; but I feel that I cannot after his observation indulge my earnest desire to be silent on the matter without incurring the risk of being charged with something opposed to an honest character. This I dare not risk; but in answering for myself, I trust it will be understood that I have been driven unwillingly into utterance.

Dr. Davy speaks of electro-magnetic rotation, and so also must I, for the purpose of showing certain coincidences in dates, &c. between the latter part of that affair and the condensation of chlorine and the gases, &c. Oersted's experiments were publised in Thomson's Annals of Philosophy for October 1820, and from this, I believe, was derived the first knowledge of them which we had in this country. At all events it was the first intimation Sir Humphry Davy and I had of them, for he brought down the Number into the laboratory on the morning of its appearance (October 1st) and we re

peated the experiments together. I may remark that this is a proof that Dr. Davy, in the Life* as well as elsewheret, does not always understand the meaning of his brother's words, and I think that he would never have written the lines which have driven me to the present and a former reply‡ if he had.

Immediately upon Oersted's great discovery, the subject was pursued earnestly, and various papers were written, amongst which is one by Sir Humphry Davy, Phil. Trans. 1821, page 7, read before the Royal Society Nov. 16, 1820, in which, at page 17, he describes the rolling of certain wires upon knifeedges, being attracted when the north pole of the magnet was presented under certain conditions of current, and repelled under certain other conditions of current, &c.

Another paper was a brief statement by the Editor of the Quarterly Journal of Science, (Mr. Brande,) in which he announces distinctly and clearly Dr. Wollaston's view of the nature of the electro-magnetic force, and its circumferential character. It is in the tenth volume, p. 363, and may be dated according to the number of the Journal, 1st January 1821.

Then there are my historical sketches in the Annals of Philosophy, N.S., vols. ii. and iii. written in July, August, and September 1821, and the paper describing my discovery of the electro-magnetic rotation dated 11th September 1821§, and others; but we will pass on to that of Sir Humphry Davy, read 6th March 1823||, which with its consequents is synchronous with the affair of the condensation of gases. This is the paper which Dr. Davy says "he (Sir H. D.,) concludes by an act of justice to Dr. Wollaston, pointing out how the discovery of the rotations of the electro-magnetic wire round its axis by the approach of a magnet, realized by the ingenuity of Mr. Faraday had been anticipated, and even attempted by Dr. Wollaston in the laboratory of the Royal Institution ¶".

I have elsewhere** done full justice to Dr. Wollaston on the point of electro-magnetic rotation, and have no desire to lessen the force of anything I have said, but would rather exalt it. But as Dr. Davy has connected it with the condensation of the gases, I must show the continual tendency to error which has occurred in both these matters. Dr. Davy, then, is in error when he says I realized Dr. Wollaston's expectation; nor does Sir Humphry Davy say what his brother imputes to him. I did not realize the rotations of the electro-magnetic wire

* Vol. ii. p. 143. ↑ Lond. and Edinb. Phil. Mag., 1835, vol. vii. p. 340. + Ibid. p. 337. § Quarterly Journal of Science, vol. xii. p. 74. Phil. Trans. 1823, p. 153. Life, vol. ii. p. 160. Quarterly Journal, vol. xv. p. 288.

round its axis; that fact was discovered by M. Ampère, at a later date; and even after I had discovered the rotation of the wire round the magnet as a centre, and that of the magnet round the wire, I could not succeed in causing the wire to revolve on its own axis*. The result which Wollaston very philosophically and beautifully deduced from his principles, and which he tried to obtain in the laboratory, was, that wires could be caused to roll, not by attraction and repulsion as had been effected by Davyt, but by a tangential action, according to the principles which had been already made known to the public as his (Dr. W.'s) by Mr. Brande‡.

What Sir Humphry Davy says in his printed paper § is this: "I cannot with propriety conclude without mentioning a circumstance in the history of the progress of electro-magnetism which, though well known to many Fellows of this Society, has, I believe, never been made public, namely, that we owe to the sagacity of Dr. Wollaston the first idea of the possibility of the rotations of the electro-magnetic wire round its axis by the approach of a magnet; and I witnessed early in 1821 an unsuccessful experiment which he made to produce the effect in the laboratory of the Royal Institution." This paper being read on the 6th of March 1823, was reported on the first of the following month in the Annals of Philosophy, N.S., vol. v. p. 304; the reporter giving altogether a different sense to what is conveyed by Sir Humphry Davy's printed paper, and saying that had not an experiment on the subject made by Dr. W. in the laboratory of the Royal Institution, and witnessed by Sir Humphry failed, merely through an accident which happened to the apparatus, he would have been the discoverer of that phenomenon ||."

I have an impression that this report of the paper was first made known to me by Sir Humphry Davy himself, but a friend's recollection makes me doubtful on this point: however, Sir Humphry, when first he adverted to the subject, told me it was inaccurate and very unjust; and advised me to draw up a contradiction which the Editor should insert the next month. I drew up a short note, and submitting it to Sir Humphry he altered it and made it what it appears in the May Number of the Annals of Philosophy, N.S. vol. v. page 391, as from the Editor, all the parts from "but writing only" to the end being Sir Humphry's; and I have the manuscript in his hand-writing inserted as an illustration into my copy of Paris's Life of Davy.

* Quart. Journ. of Science, vol. xii. p. 79. + Phil. Trans. 1821, p.17. ‡ Quart. Journ., vol. x. p. 363. § Phil. Trans. 1823, p. 158. In justice to the reporter, I have sought carefully at the Royal Society's for the original manuscript, being the paper which he heard read; but it cannot be found in its place.