The Principles of Science

readers as are well acquainted with the syllogistic logic to pronounce upon the comparative simplicity and power of the new and old systems. For other acute objections brought forward by Mr. Robertson, I must refer the reader to the article in question.

One point in my last chapter, that on the Results and Limits of Scientific Method, has been criticised by Professor W. K. Clifford in his lecture1 on The First and the Last Catastrophe." In vol. ii. p. 438 of the first edition (p. 744 of this edition) I referred to certain inferences drawn by eminent physicists as to a limit to the antiquity of the present order of things. "According to Sir W. Thomson's deductions from Fourier's theory of heat, we can trace down the dissipation of heat by conduction and radiation to an infinitely distant time when all things will be uniformly cold. But we cannot similarly trace the Heat-history of the Universe to an infinite distance in the past. For a certain negative value of the time, the formulæ give impossible values, indicating that there was some initial distribution of heat which could not have resulted, according to known laws of nature, from any previous distribution."

Now according to Professor Clifford I have here misstated Thomson's results. "It is not according to the known laws of nature, it is according to the known laws of conduction of heat, that Sir William Thomson is speaking. . . . All these physical writers, knowing what they were writing about, simply drew such conclusions from the facts which were before them as could be reasonably drawn. They say, here is a state of things which could not have been produced by the circumstances we are at present investigating Then your speculator comes, he reads a sentence and says, 'Here is an opportunity for me to have my fling.' And he has his fling, and makes a purely baseless theory about the necessary origin of the

1 Fortnightly Review, New Series, April 1875, p. 480. Lecture reprinted by the Sunday Lecture Society, p. 24.

present order of nature at some definite point of time, which might be calculated."

Professor Clifford proceeds to explain that Thomson's formulæ only give a limit to the heat history of, say, the earth's crust in the solid state. We are led back to the time when it became solidified from the fluid condition. There is discontinuity in the history of the solid matter, but still discontinuity which is within our comprehension. Still further back we should come to discontinuity again, when the liquid was formed by the condensation of heated gaseous matter. Beyond that event, however, there is no need to suppose further discontinuity of law, for the gaseous matter might consist of molecules which had been falling together from different parts of space through infinite past time. As Professor Clifford says (p. 481) of the bodies of the universe, "What they have actually done is to fall together and get solid. If we should reverse the process we should see them separating and getting cool, and as a limit to that, we should find that all these bodies would be resolved into melecules, and all these would be flying away from each other. There would be no limit to that process, and we could trace it as far back as ever we liked to trace it."

Assuming that I have erred, I should like to point out that I have erred in the best company, or more strictly, being a speculator, I have been led into error by the best physical writers. Professor Tait, in his Sketch of Thermodynamics, speaking of the laws discovered by Fourier for the motion of heat in a solid, says, "Their mathematical expressions point also to the fact that a uniform distribution of heat, or a distribution tending to become uniform, must have arisen from some primitive distribution of heat of a kind not capable of being produced by known laws from any previous distribution." In the latter words it will be seen that there is no limitation to the laws of conduction, and, although I had carefully referred to Sir W. Thomson's original paper, it is not unnatural

that I should take Professor Tait's interpretion of its meaning.1

In his new work On some Recent Advances in Physical Science, Professor Tait has recurred to the subject as follows: "A profound lesson may be learned from one of the earliest little papers of Sir W. Thomson, published while he was an undergraduate at Cambridge, where he shows that Fourier's magnificent treatment of the conduction of heat [in a solid body] leads to formulæ for its distribution which are intelligible (and of course capable of being fully verified by experiment) for all time future, but which, except in particular cases, when extended to time past, remain intelligible for a finite period only, and then indicate a state of things which could not have resulted under known laws from any conceivable previous distribution [of heat in the body]. So far as heat is concerned, modern investigations have shown that a previous distribution of the matter involved may, by its potential energy, be capable of producing such a state of things at the moment of its aggregation; but the example is now adduced not for its bearing on heat alone, but as a simple illustration of the fact that all portions of our Science, especially that beautiful one, the Dissipation of Energy, point unanimously to a beginning, to a state of things incapable of being derived by present laws [of tangible matter and its energy] from any conceivable previous arrangement." As this was published nearly a year after Professor Clifford's lecture, it may be inferred

1 Sir W. Thomson's words are as follows (Cambridge Mathematical Journal, Nov. 1842, vol. iii. p. 174). "When is negative, the state represented cannot be the result of any possible distribution of temperature which has previously existed." There is no limitation in the sentence to the laws of conduction, but, as the whole paper treats of the results of conduction in a solid, it may no doubt be understood that there is a tacit limitation. See also a second paper on the subject in the same journal for February, 1844, vol. iv. p. 67, where again there is no expressed limitation.

Pp. 25-26. The parentheses are in the original, and show Professor Tait's corrections in the verbatim reports of his lectures. The subject is treated again on pp. 168-9.

that Professor Tait adheres to his original opinion that the theory of heat does give evidence of "a beginning."

I may add that Professor Clerk Maxwell's words seem to countenance the same view, for he says, "This is only one of the cases in which a consideration of the dissipation of energy leads to the determination of a superior limit to the antiquity of the observed order of things." The expression "observed order of things" is open to much ambiguity, but in the absence of qualification I should take it to include the aggregate of the laws of nature known to us. I should interpret Professor Maxwell as meaning that the theory of heat indicates the occurrence of some event of which our science cannot give any further explanation. The physical writers thus seem not to be so clear about the matter as Professor Clifford assumes.

So far as I may venture to form an independent opinion on the subject, it is to the effect that Professor Clifford is right, and that the known laws of nature do not enable us to assign a "beginning." Science leads us. backwards into infinite past duration. But that Professor Clifford is right on this point, is no reason why we should suppose him to be right in his other opinions, some of which I am sure are wrong. Nor is it a reason why other parts of my last chapter should be wrong. The question only affects the single paragraph on pp. 744-5 of this book, which might, I believe, be struck out without necessitating any alteration in the rest of the text. is always to be remembered that the failure of an argument in favour of a proposition does not, generally speaking, add much, if any, probability to the contradictory proposition. I cannot conclude without expressing my acknowledgments to Professor Clifford for his kind expressions regarding my work as a whole.

1 Theory of Heat, 1871, p. 245.

2, THE CHESTNUTS,

WEST HEATH,

August 15, 1877.

HAMPSTEAD, N.W.

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The Principles of Science: A Treatise on Logic and Scientific Method