But

capable of giving an almost exact result. Mayer by chance, then, in the middle of his à priori speculations, lit upon a method-although he got it from a false principle—which Joule afterwards proved to be a good one, and used as one of his modes of obtaining the value of the dynamical equivalent of heat. Still, we must give Mayer no credit for that, for although he laid down his law quite generally, air was the only substance he had data for, and he chose it on that account. even with this, his data were so bad that he got a result as far from the truth as the one obtained by Séguin. Only Séguin has this great credit, to which Mayer has no claim, that, seeing that if heat be not matter, some of it must disappear in the working of an engine, he tried to measure the quantity of heat coming to the condenser, in order to show that it was less than that which left the boiler.

I find that I have now exhausted my time, and therefore I shall merely mention that, in my next lecture, I shall take up the history of the theory of energy, as it was developed by the sound methods of Colding and Joule in papers published about 1843; and I shall then endeavour, with the facilities which this room affords me, to illustrate my explanation by a few experiments.

[Note to Third Edition. The last three or four pages have been left in their original form, as expressing what was well known in 1874. But, of late, attention has been called to the services of Mohr, whose date is prior to that of Séguin, and still more so to that of Mayer. In the next lecture, a notice of these services will be inserted.]

LECTURE III.

ESTABLISHMENT OF THE CONSERVATION OF ENERGY.

Further inquiry into the asserted claims of Mayer. Opinions of Colding and Joule on Mayer's first paper. [Insertion (1884) on the prior claims of Mohr.] Colding's Experiments. Joule's Experiments. Numerical value of the Dynamical Equivalent of Heat. Helmholtz's argument from the Perpetual Motion. Transformation and Dissipation of Energy. Illustrative experiments.

IN my last lecture I showed you in what state Newton left the grand question of conservation of energy, what an enormous step he took, and what was the sole great difficulty remaining in his way. Then I showed you how, in regard to the particular branch of it which we call the dynamical theory of heat, Rumford and Davy had, at the very end of last century, almost completely settled the question that heat is not matter. A little was wanting in the work of each. Rumford wanted only one small chemical experiment in addition to his grand physical experiments. Davy wanted a little more conclusive reasoning than he showed at the time. Had one or other of these been furnished before the end of the last century, it would have been to the last century that we should have been indebted entirely for the dynamical theory of heat. It was not, however, until 1812 that Davy applied correct reasoning to his experiments, and obtained the correct deductions from them; and then he stated in a distinct form the important

propositions that heat is motion, and that the laws of its communication are precisely the same as the laws of communication of motion. Then I showed you that Séguin, although he was altogether wrong in his à priori idea, had a true sense of what was really wanted to this question, and that he made a correct, but unhappily unsuccessful, experimental attempt to supply it. Then we came to Mayer, a man who has, especially of late, been persistently held up as the discoverer, not merely of the dynamical theory of heat, but of the whole subject of conservation of energy. Of him, I may remark -because the question is one of importance-though at the present day we are hardly perhaps far enough advanced in time calmly and dispassionately to consider the relative claims of these authors; still, I may remark that a great deal of the eulogy which has been bestowed upon Mayer is altogether undeserved, and that Joule has even yet received far too little credit for the enormous advances he made. In the first place, Mayer was altogether wrong in his à priori idea. On that Sir William Thomson and I made, in 1862, the following remarks, which no one has ventured directly to challenge in the slightest particular :

'Mayer's method is founded on the supposition that diminution of the volume of a body implies an evolution or generation of heat; and it involves essentially a false analogy between the natural fall of a body to the earth, and the condensation produced in an elastic fluid by the application of external force. The hypothesis on which he thus grounds a definite numerical estimate of the relation between the agencies here involved, is that the heat evolved when an elastic fluid is compressed and kept cool, is simply the dynamical equivalent of the work employed in compressing it. The experimental investigations of subsequent naturalists have shown that this hypothesis is altogether false for the generality of fluids, espe

cially liquids, and is at best only approximately true for air; whereas Mayer's statements imply its indiscriminate application to all bodies in nature, whether gaseous, liquid, or solid, and show no reason for choosing air for the application of the supposed principle to calculation ; but that at the time he wrote, air was the only body for which the requisite numerical data were known with any approximation to accuracy.'

reasons.

Then, in addition to these two absolute errors which are mentioned in this passage, I may call attention to the preposterous à priori principles upon which he There are two of them; the one is causa æquat effectum, to which I have never been able to attach any meaning, and the other ex nihilo nihil fit. These may be a basis for scholastic disquisitions, such as the celebrated old question of the number of angels that can simultaneously dance on the point of a needle, but they are altogether unfit for introduction in any shape whatever into physical reasoning. Then, again, Mayer's work was altogether destitute of experiment. He suggests, no doubt, the carrying out, on a larger scale, an experiment which he says he tried, namely, shaking a little phial of water for a considerable time, to find it at the end of the time warmer than it was at the commencement :-merely, I may say in passing, a bad substitute for a hint due to Rumford, that the churning of water would be a good experimental method. I daresay most of you will see that such an experiment as Mayer's, unless proper precautions were taken to prevent conduction of heat from the hand to the bottle of water, would very probably have resulted in the heating of the water considerably, even without the shaking: so that, in order to prove that the heat was due to the shaking, we should have required at all events a statement on Mayer's part of the precautions he had taken to

prevent one known source of heat from affecting the water.1

But, in addition to this, Mayer did not even believe that heat depends on motion; and this is perhaps the most wonderful comment that can be made upon the consistency of those who, while constantly speaking of heat as a 'mode of motion,' call him the discoverer of the modern theory of heat. To effect this must surely have involved (to use the vigorous and expressive language of one of the most prominent popularisers of science) the necessity of 'wrangling resolutely with the facts!' Mayer himself says, in his very earliest paper, and he never afterwards to my knowledge modified this statement (I translate freely), 'We might much rather assert the opposite, that motion, whether it be a simple one or a vibratory one-like light, like radiant heat, and so on-must, in order to become heat, cease to be motion.' He actually says it must cease to be motion in order to become heat! Then he makes another and a very curious statement, the absolute erroneousness of which you will see in the course of another lecture. He says, sneeringly: 'Let any one try to melt ice by pressure, however enormous.' I shall show you that, as a consequence of the second law of thermo-dynamics, the melting of ice by pressure was predicted beforehand, and was verified afterwards by actual experiment.

It is time, then, I say, that Mayer, even with our as yet imperfect means of judging, should be ranged, so far as we can, in his true place. He has been injudiciously praised, and he has been an unfortunate man,

1 Even this experiment, but carried out with something like philosophical precautions, was long before described by Reade in Nicholson's Journal, 1808, p. 113.