By giving more precision to the conceptions of Rankine, the physicists of the end of the nineteenth century were brought to consider that in all physical phenomena there occur apparitions and disappearances which are balanced by various energies.  It is natural, however, to suppose that these equivalent apparitions and disappearances correspond to transformations and not to simultaneous creations and destructions.  We thus represent energy to ourselves as taking different forms—­mechanical, electrical, calorific, and chemical—­ capable of changing one into the other, but in such a way that the quantitative value always remains the same.  In like manner a bank draft may be represented by notes, gold, silver, or bullion.  The earliest known form of energy, i.e. work, will serve as the standard as gold serves as the monetary standard, and energy in all its forms will be estimated by the corresponding work.  In each particular case we can strictly define and measure, by the correct application of the principle of the conservation of energy, the quantity of energy evolved under a given form.

We can thus arrange a machine comprising a body capable of evolving this energy; then we can force all the organs of this machine to complete an entirely closed cycle, with the exception of the body itself, which, however, has to return to such a state that all the variables from which this state depends resume their initial values except the particular variable to which the evolution of the energy under consideration is linked.  The difference between the work thus accomplished and that which would have been obtained if this variable also had returned to its original value, is the measure of the energy evolved.

In the same way that, in the minds of mechanicians, all forces of whatever origin, which are capable of compounding with each other and of balancing each other, belong to the same category of beings, so for many physicists energy is a sort of entity which we find under various aspects.  There thus exists for them a world, which comes in some way to superpose itself upon the world of matter—­that is to say, the world of energy, dominated in its turn by a fundamental law similar to that of Lavoisier.[5] This conception, as we have already seen, passes the limit of experience; but others go further still.  Absorbed in the contemplation of this new world, they succeed in persuading themselves that the old world of matter has no real existence and that energy is sufficient by itself to give us a complete comprehension of the Universe and of all the phenomena produced in it.  They point out that all our sensations correspond to changes of energy, and that everything apparent to our senses is, in truth, energy.  The famous experiment of the blows with a stick by which it was demonstrated to a sceptical philosopher that an outer world existed, only proves, in reality, the existence of energy, and not that of matter.  The stick in itself is inoffensive, as Professor Ostwald remarks, and it is its vis viva, its kinetic energy, which is painful to us; while if we possessed a speed equal to its own, moving in the same direction, it would no longer exist so far as our sense of touch is concerned.