Now this theorem of pure mechanics was found wanting every time friction took place--that is to say, in all really observable cases. The more perceptible the friction, the more considerable the difference; but, in addition, a new phenomenon always appeared and heat was produced. By experiments which are now classic, it became established that the quantity of heat thus created independently of the nature of the bodies is always (provided no other phenomena intervene) proportional to the energy which has disappeared. Reciprocally, also, heat may disappear, and we always find a constant relation between the quantities of heat and work which mutually replace each other. It is quite clear that such experiments do not prove that heat is work. We might just as well say that work is heat. It is making a gratuitous hypothesis to admit this reduction of heat to mechanism; but this hypothesis was so seductive, and so much in conformity with the desire of nearly all physicists to arrive at some sort of unity in nature, that they made it with eagerness and became unreservedly convinced that heat was an active internal force. Their error was not in admitting this hypothesis; it was a legitimate one since it has proved very fruitful. But some of them committed the fault of forgetting that it was an hypothesis, and considered it a demonstrated truth. Moreover, they were thus brought to see in phenomena nothing but these two particular forms of energy which in their minds were easily identified with each other. From the outset, however, it became manifest that the principle is applicable to cases where heat plays only a parasitical part. There were thus discovered, by translating the principle of equivalence, numerical relations between the magnitudes of electricity, for instance, and the magnitudes of mechanics. Heat was a sort of variable intermediary convenient for calculation, but introduced in a roundabout way and destined to disappear in the final result. Verdet, who, in lectures which have rightly remained celebrated, defined with remarkable clearness the new theories, said, in 1862: "Electrical phenomena are always accompanied by calorific manifestations, of which the study belongs to the mechanical theory of heat. This study, moreover, will not only have the effect of making known to us interesting facts in electricity, but will throw some light on the phenomena of electricity themselves."