48. Complementary Branches of Mechanics.
The field of pure or classical mechanics is limited to the above two kinds of energy, work and kinetic energy, though these do not exhaust the manifoldness of the mechanical energies. Accordingly, other branches of mechanics dealing with the corresponding phenomena are added to the classical mechanics described above.
If by mechanical energies we understand all energies in which changes of space are connected with changes of energy, there are as many different forms as there are spacial concepts that seem applicable. Form, Volume, and Surface of bodies in space are especially recognizable as the field of action for energy, which shows different properties or manifoldnesses according to each of these relations.
The energy of form is manifested in bodies (solid or rigid bodies) that maintain a definite shape because every change of shape is connected with work or with the expenditure of some other energy. If the changes are small, the bodies are of such a nature that they return to their former condition of their own accord after the force exerted upon them has ceased to act. This property is called elasticity. However, the theory of elasticity, which has been extensively and rationally developed, is regarded as belonging rather to mathematical physics in general than to mechanics in particular. In greater changes of shape the energy of form, or elastic energy, passes into other forms, and the body does not return to its former shape after the force has been removed.
Other bodies have no energy of form (or only in an infinitesimally slight degree), so that they allow of changes of form without the expenditure of work, but their volume can be changed only by work. These are divided into two classes. First, the liquids, which have a definite volume (corresponding to the definite shape of solids), the changes of which in every sense, both compression and expansion, require work. Secondly, the gases with volume energy in only one sense of the word, in which only the compression of volume requires work, while in expansion a certain amount of work is thrown off. Such bodies can exist only so long as the expenditure of their volume energy by spontaneous expansion is prevented by the presence of a counter energy, as, for example, the elasticity of the walls of a vessel. This tendency is called pressure.
Finally, there are energy qualities at the surfaces between various kinds of bodies which come into play at the change of these surfaces. They always lie in such a direction that the enlargement of the surfaces requires work, and hence, by reason of the law of conservation of energy, cannot proceed by itself. In cases where there has been an inverse kind of energy present, that is, one which diminishes with increasing surface, it also has been active as a rule, thus bringing about the disappearance of the existing boundaries.
Since the seat of this kind of energy is in the surfaces (or superficies), it is called surface-energy. The phenomena depending upon it manifest themselves most clearly at the surface boundaries between liquids and gases. They are called capillary phenomena. This strange name, derived from the word capilla, hair, has its origin in the fact that because of surface-energy liquids rise in tubes which they wet, and the narrower the tube the higher they rise. If the lumen of the tube is as fine as a hair, a considerable rise can be observed. This is the entire connection between the name and the thing.
The mechanics of liquids is called hydromechanics, that of gases, aeromechanics, after the most familiar liquid, water, and the most familiar gas, air. The study of surface-energy under the name of the capillary theory forms part of theoretical physics. While formerly this branch, too, was regarded as a working part, or, rather, as a playing part, of mathematical problems, in more recent times extensive experimental research has made its entry in this province also, and has demonstrated the necessity of passing from the former abstractions or idealizations, which were carried altogether too far, to a better and profounder regard for the actually existing complexities.