Here we have a smooth plane and a weight held upon it by means of a power P, as in the figure. Now, if we overbalance P by a single grain, we shall bring the weight w from the bottom to the top of the plane. But when this has taken place, it is evident that P has fallen through a vertical distance equal to the length of the plane, while on the other hand w has only risen through a vertical distance equal to the height. Hence, in order that the principle of virtual velocities shall hold, we must have P multiplied into its fall equal to w multiplied into its rise, that is to say, PX Length of plane w x Height of plane, 46. The two examples now given are quite sufficient to enable our readers to see the true function of a machine, and they are now doubtless disposed to acknowledge tha no machine will give back more energy than is spent upon it. It is not, however, equally clear that it will not give back less; indeed, it is a well-known fact that it constantly does so. For we have supposed our machine to be without friction-but no machine is without friction-and the consequence is that the available out-come of the machine is more or less diminished by this drawback. Now, unless we are able to see clearly what part friction really plays, we cannot prove the conservation of energy. We see clearly enough that energy cannot be created, but we are not equally sure that it cannot be destroyed; indeed, we may say we have apparent grounds for believing that it is destroyedthat is our present position. Now, if the theory of the conservation of energy be true-that is to say, if energy is in any sense indestructible-friction will prove itself to be, not the destroyer of energy, but merely the converter of it into some less apparent and perhaps less useful form. 47. We must, therefore, prepare ourselves to study what friction really does, and also to recognize energy in a form remote from that possessed by a body in visible motion, or by a head of water. To friction we may add percussion, as a process by which energy is apparently destroyed; and as we have (Art. 39) considered the case of a kilogramme shot vertically upwards, demonstrating that it will ultimately reach the ground with an energy equal to that with which it was shot upwards, we may pursue the experiment one step further, and ask what becomes of its energy after it has struck We may vary the ground and come to rest? tion by asking what becomes of the energy of the smith's blow after his hammer has struck the anvil, or what of the energy of the cannon ball after it has struck the target, or what of that of the railway train after it has been stopped by friction at the break-wheel? All these are cases in which percussion or friction appears at first sight to have destroyed visible energy; but before pro- . nouncing upon this seeming destruction, it clearly behoves us to ask if anything else makes its appearance at the moment when the visible energy is apparently destroyed. For, after all, energy may be like the Eastern magicians, of whom we read that they had the power of changing themselves into a variety of forms, but were nevertheless very careful not to disappear altogether. When Motion is destroyed, Heat appears. 48. Now, in reply to the question we have put, it may be confidently asserted that whenever visible energy is apparently destroyed by percussion or friction, something else makes its appearance, and that something is heat. Thus, a piece of lead placed upon an anvil may be greatly heated by successive blows of a blacksmith's hammer. The collision of flint and steel will produce heat, and a rapidly-moving cannon ball, when striking against an iron target, may even be heated to redness. Again, with regard to friction, we know that on a dark night sparks are seen to issue from the break-wheel which is stopping a railway train, and we know, also, that the axles of railway carriages get alarmingly hot, if they are not well supplied with grease. Finally, the schoolboy will tell us that he is in the habit of rubbing a brass button upon the desk, and applying it to the back of his neighbour's hand, and that when his own hand has been treated in this way, he has found the button unmistakeably hot. Heat a species of Motion. 49. For a long time this appearance of heat by friction or percussion was regarded as inexplicable, because it was believed that heat was a kind of matter, and it was difficult to understand where all this heat came from. The partisans of the material hypothesis, no doubt, ventured to suggest that in such processes heat might be drawn from the neighbouring bodies, so that the Caloric (which was the name given to the imaginary substance of heat) was squeezed or rubbed out of them, according as the process was percussion or friction. But this was regarded by many as no explanation, even before Sir Humphry Davy, about the end of last century, clearly showed it to be untenable. 50. Davy's experiments consisted in rubbing together two pieces of ice until it was found that both were nearly melted, and he varied the conditions of his experiments in such a manner as to show that the heat produced in this case could not be abstracted from the neighbouring bodies. 51. Let us pause to consider the alternatives to which we are driven by this experiment. If we still choose to regard heat as a substance, since this has not been taken from the surrounding bodies, it must necessarily have been created in the process of friction. But if we choose to regard heat as a species of motion, we have a simpler alternative, for, inasmuch as the energy of visible motion has disappeared in the process of friction, we may suppose that it has been transformed into a species of molecular motion, which we call heat; and this was the conclusion to which Davy came. 52. About the same time another philosopher was occupied with a similar experiment. Count Rumford was superintending the boring of cannon at the arsenal at Munich, and was forcibly struck with the very great amount of heat caused by this process. The source of this heat appeared to him to be absolutely inexhaustible, and, being unwilling to regard it as the creation of a species of matter, he was led like Davy to attribute it to motion. 53. Assuming, therefore, that heat is a species of motion, the next point is to endeavour to comprehend what kind of motion it is, and in what respects it is different from ordinary visible motion. To do this, let us imagine a railway carriage, full of passengers, to be whirling along at a great speed, its occupants quietly at ease, because, although they are in rapid motion, they are all moving at the same rate and in the same direction. Now, suppose that the train meets with a sudden check;-a disaster is the consequence, and the quiet placidity of the occupants of the carriage is instantly at an end. Even if we suppose that the carriage is not broken up and its occupants killed, yet they are all in a violent |