We can say nothing against a mode of reasoning of that kind. The only fallacy in it was the assumption that heat is a substance. Now, see how well Rumford laid hold of that point, and how he proceeds by experiment to try if possible to satisfy his doubts about it. He says:

'If this were the case, then, according to the modern doctrines of latent Heat, and of caloric, the capacity for Heat of the parts of the metal so reduced to chips, ought not only to be changed, but the change undergone by them should be sufficiently great to account for all the Heat produced.'

Rumford found no difference, so far as his form of experiment enabled him to test it, between the capacity for heat of the abraded metal and the metal before the abrasion had taken place; so that if this experiment had been only a satisfactory one-and Rumford did not see how to make it thoroughly satisfactory-the fact that heat is not matter would have been conclusively established. What Rumford really did want was this: he wanted a process by which to bring the abraded metal and the non-abraded metal, if possible, to the same final state. He tried to do this by throwing them into water-equal quantities of the lumps and of the filings, equally hot, into equal quantities of water at the same lower temperature-to see whether they would produce different changes of temperature, each in its own vessel of water. But then they were not in the same final state. The filings, remember, were in a distorted state; they might have been very considerably compressed, or they might have been distorted in shape by shearing or something of that kind, in virtue of which they might have had a certain quantity of latent heat which he could not discover by this process. The

only legitimate and practicable process which we know of for completely answering that question, which was Rumford's sole difficulty, is a chemical process. Dissolve your lumps and an equal weight of your filings in equal quantities of the same acid. At the end of the operation, of course, there can be no doubt that the chemical substances produced will be precisely the same, whether you begin with lumps or with filings. You will have the same chemical substance; but if there be any mysterious difference as to the capacity for heat in them, that will be shown during the process of solution. In general, in dissolving a metal in an acid, there is a development of heat; but if there were any difference in the quantity of heat which the lumps and an equal weight of filings contained-that is to say, if heat could by any possibility be matter-then there would necessarily have been an escape of heat more in one vessel than the other. If Rumford had tried that one additional experiment, he would have had the sole credit of having established the non-materiality of heat.

The details of Rumford's experiments are given in full, but I shall not describe them to you. I merely mention that they show extraordinary skill and care in experimenting, and wonderful precaution in trying to avoid, as far as possible, the necessary losses in the experiments. When losses were unavoidable and of a large amount, the same skill is shown in making separate side experiments, in order to enable the operator to allow for them in the main experiments. The whole work itself is a model of experimental science. I shall now pass on to the final reasoning, merely mentioning in passing that Rumford actually managed to boil a large quantity of water, though an immense

amount of heat was lost in spite of all his precautions. Still the work of a single horse for two hours and twenty minutes was found sufficient to boil about 19 lbs. of water, besides heating a large casting of the cannon, and all the machinery that was engaged in the process. He says:

'It would be difficult to describe the surprise and astonishment expressed in the countenances of the by-standers, on seeing so large a quantity of cold water heated, and actually made to boil, without any fire.

'Though there was, in fact, nothing that could justly be considered as surprising in this event, yet I acknowledge fairly that it afforded me a degree of childish pleasure which, were I ambitious of the reputation of a grave philosopher, I ought most certainly rather to hide than to discover.'

Here is his final reasoning:

'In reasoning on this subject, we must not forget to consider that most remarkable circumstance, that the source of the Heat generated by friction in these experiments, appeared evidently to be inexhaustible.

'It is hardly necessary to add, that anything which any insulated body or system of bodies can continue to furnish without limitation, cannot possibly be a material substance. It appears to me to be extremely difficult, if not quite impossible, to form any distinct idea of anything capable of being excited and communicated in the manner in which the heat was excited and communicated in these experiments, except it be motion. I am very far from pretending to know how or by what means or mechanical contrivance that particular kind of motion in bodies which has been supposed to constitute Heat is excited, continued, and propagated ;'

and then he proceeds to apologise for the minutia given in his paper.

Now, when we make a calculation from the data furnished by Rumford's paper, we find this: that, supposing heat to be a form of energy, and taking 30,000 foot

pounds per minute as the work of a horse (that is something like an ordinary estimate), the mechanical equivalent of heat is 940 foot-pounds. The meaning of that statement is, that if you were to expend the amount of work designated as 940 foot-pounds in stirring a single pound of water, then that pound of water when brought to rest at the end of the operation would be one degree Fahrenheit hotter than before you commenced. [Rumford throughout uses Fahrenheit's degrees.] We can put it in another form, which is perhaps still more striking. If you had a cascade or waterfall 940 feet high, then, in the fall of the water down that cascade, there would be 940 foot-pounds of work done by gravity upon each pound of water; and therefore if all the energy which the moving water has, as it reaches the bottom of the fall, were spent simply in heating the water, the result would be that the water in the pool at the bottom of the fall would be 1 deg. Fahrenheit hotter than the water at the top of the fall.

I may remind you here, that Rumford's experiments were published in 1798, so that they are of considerably old date; but, like those which I am just going to advert to, they were barely noticed, or noticed only to be laughed at, until somewhere about the year 1840.

Now, in the very year after the experiments of Rumford were published, we had the experiments of Davy. I need not go into minute details about them, because they were not by any means such models of careful experimental work as Rumford's. But, for all that, Davy gave conclusive proof (if he had only at the time seen it himself) that heat is not matter. His proofs were of this kind. He first showed that by rubbing two pieces of ice together-by simply expending work in

the friction of two pieces of ice-you could melt the ice. Now, supposing heat had been matter, this is the sort of argument that a believer in the caloric theory would have used two pieces of ice when rubbed together cannot possibly melt one another, because in order to melt them you will have to furnish heat to them. But the heat can only come from themselves when they are rubbed together; it cannot come from surrounding bodies, and therefore they cannot possibly melt together, because to melt one another, they would have first to part with some of their heat in order to produce the melting. Davy showed, however, that the mere rubbing together of two pieces of ice by proper mechanical processes was sufficient to melt the surface. layer of each. There still was this possible objection, that the heat might have come from some external source, so that his second experiment was of this kind. He rubbed two pieces of metal together, keeping them surrounded by ice, and in the exhausted receiver of an air-pump, so as if possible to avoid radiant heat, heat carried by convection-currents of air, and so on, and to remove every possible disturbing cause, or even source of suspicion, from his experiment; and still he found that these two pieces of metal, when rubbed together thus, constantly produced heat and melted the ice, every precaution having been taken to prevent heat from getting at them from every side. It is curious that his reasoning upon the subject is extremely inconclusive, although his experiments themselves completely settle the question. He says:—

'From this experiment it is evident that ice by friction is converted into water, and according to the supposition its capacity is diminished; but it is a well-known fact that the capacity of water