Kinetic energy that has disappeared = work that has arisen.

Thus, while work can be called a substance only in a limited sense, since its conservation is limited only to perfect machines, we may call energy a substance unqualifiedly, since in every instance of which we know the principle has been maintained that a quantity of any energy never disappears unless an equivalent quantity of another energy arises. Accordingly, this law of the conservation of energy must be taken as a fundamental law of the physical sciences. But not only do all the phenomena of physics, including chemistry, occur within the limits of the law of conservation, but until the contrary is proved the law of conservation must also be regarded as operative in all the later sciences, that is, in all the activities of organisms, so that all the phenomena of life must also take place within the limits of the law of conservation. This corresponds to the general fact, which I have emphasized a number of times, that all the laws of a former science find application in all the following sciences, since the latter can only contain concepts which by specialization, that is, by the addition of further characteristics, have sprung from the concepts of the former or more general sciences.

45. Mass and Matter.

It has been noted above that kinetic energy depends upon another magnitude beside velocity. A conception of its nature can be obtained when we try to put different bodies in motion. In doing so the muscles of the arm perform certain quantities of work, and we feel whether the quantities are greater or smaller. In this way we obtain a clear consciousness of the fact that different bodies require quite different quantities of work for the same velocity. The property which comes into play here is called mass, and mass is proportional to the work which the various bodies require to attain the same velocity. Since the work and the velocity can be measured very accurately by appropriate means, mass also lends itself to a correspondingly accurate measurement.

All known ponderable bodies have mass. That means there is a regular connection between the property which makes a body tend to the earth with a certain definite force (called weight) and the property by virtue of which a body assumes certain velocities under the influences of motive causes. We can readily conceive that it is possible for us to learn only of such bodies as are heavy, that is, bodies which are held by the earth, since the others, if they exist at all, would naturally have left the earth long ago. That all these bodies also have mass is to be explained in a similar way. For a body of mass zero would at each impulse assume infinitely great velocity, and could therefore never be the object of our observation. Consequently, by reason of the physical conditions obtaining on the earth's surface, the bodies known to us must combine both properties, mass and weight.

The name given to this concept of the combined presence of mass and weight in space is matter. Experience shows that there is a law of conservation for these magnitudes also, according to which whatever changes we may produce in bodies possessing weight and mass, no change will occur in the sum of their weight and mass. According to the nomenclature previously introduced we must therefore call weight and mass substances, since they remain the same as to quantity, no matter what changes they may undergo. However, it is usual to apply the name substance to the concept of matter composed of mass and weight. In fact, scientists often go so far as to limit the name to this single instance of the various laws of conservation, and to take substance to mean exclusively the combination of mass and weight. This is connected with the conception which we are about to discuss, that all natural phenomena can ultimately be conceived as the motion of matter. Through the greater part of the nineteenth century this conception, called scientific materialism, was accepted almost without opposition. At present it is being more and more recognized that it was only an unproved assumption, which the development of science daily proves to be more untenable.

46. Energetic Mechanics.

In the light of our previous observations the branch of science traditionally known as mechanics appears as the science of work and of kinetic energy. Furthermore, statics is shown to be the science of work, while dynamics, besides treating of kinetic energy in itself, also treats of the phenomena of the change of work into kinetic energy, and vice versa. We shall find the same relation again later, only in more manifold forms. Every branch of physics proves to be the science of a special kind of energy, and to the knowledge of each kind of energy must be added the knowledge of the relations by which it changes to the other forms of energy and vice versa. It is true that in the traditional division of physics this system has not been strictly carried out, since an additional and very influential motive for classification has been the regard paid to the various human sense organs.

Nevertheless this ground does not lie in the field of physics, but in that of physiology, and must, therefore, be abandoned in the interest of strict systematization.