49. The Theory of Heat.
The various forms of energies the aggregate of which is comprehended in physics, have very different special characters. A systematic investigation has not yet been made of the characters of manifoldness by which, for example, work is distinguished from heat, electrical energy from kinetic energy, etc., nor of what are the essential properties peculiar to each individual energy. We feel certain that differences do exist, for otherwise the energies could not be distinguished, and we feel certain that these differences are very important, for doubt seldom arises as to the kind of energy to which a certain phenomenon is to be assigned. But just as we have no systematic table of the elementary concepts, so we are still without a systematic natural history of the forms of energy in which the peculiarities of every species are characterized, and in which the entire material is so arranged according to these characteristics that we can take a general survey of it.
As regards heat energy, its foremost and most striking characteristic is its physiological effect. In our skin there are organs for the perception of heat as well as of cold, that is, for temperatures above and below the temperature of the skin. However, the temperature that these organs can bear without injury to themselves is of a very small range, beyond which physical apparatuses of all kinds must be used, such as "thermometers."
Heat is the simplest kind of energy from the point of view of manifoldness. Every heat quantity is marked by a temperature, just as a kinetic energy is marked by velocity. But while a velocity is determined in space so that velocities of equal magnitude have in addition a threefold infinite manifoldness in reference to direction, a temperature is characterized completely and unambiguously by a simple number, the degree of temperature. Two temperatures of equal degree can in no wise be distinguished, since temperature possesses no other possible manifoldness than degree.
The same property is found in heat energy itself. In heat energy we measure the quantity of energy itself and call it the heat quantity, while in some of the other kinds of energy, only the factors into which they can be divided are measured, and no habitual conception of the energy itself is developed. A heat quantity is likewise fully indicated by its measure number.
That heat is an energy, that is, that it is developed in equal quantities from other kinds of energy, and can change back again into them, is a discovery which, despite its fundamental and general character, was not made before the forties of the nineteenth century. As often happens in cases of important scientific advances, the same idea came simultaneously to a number of investigators. The first to grasp and fully comprehend this idea was Julius Robert Mayer of Heilbronn, who published his results in 1842. Mayer not only showed that the imperfect machines ([p. 134]), which limit the validity of the law of the conservation of work, owe this peculiarity to the fact that they transform a part of the work into heat, and that when we take account of this part, the law of conservation holds perfectly good, but he also calculated, with extraordinary acumen, the mechanical equivalent of heat from the then existing data of physics. That is to say, he determined how many units of heat (in the measure then in use) correspond to a unit of work (in its specific measure) in the change from one to the other, and back. And this fundamental knowledge of the existence of a quantitatively unchangeable substance, arising from work, and capable of being transformed into it, Mayer did not limit in its application merely to heat. He was the first to construct a table, which he made as complete as possible, of all the forms of energy then known, and to assert and prove the possibility of their reciprocal change into each other.
In view of this relation of the quantitative equivalent of the various forms of energy when transformed into one another, an attempt is being made at present to measure them all with the same unit. That is, some easily obtained quantity of energy is arbitrarily chosen as a unit and it is determined that in every other form of energy the unit shall be equal to the quantity obtained from that unit on its transformation into the energy in question. For formal reasons the kinetic energy of a mass of two grams which moves with the velocity of one centimeter in a second has been chosen as the unit. It is called erg, an abbreviation of energy. The amount is very small, and for technical reasons 1010 times greater unit is used. To raise the temperature of a gram of water one degree a quantity of energy equal to 41,830,000 ergs is required.