We may now briefly consider the chief theories of the various forms of energy which have been advanced of late times. All of them assume at the outset forces of attraction or repulsion between particles, or else a highly elastic fluid, or rattier solid, if we may so call it, in which the particles of matter float, or are imbedded. 'We have already considered the difficulties attending the latter supposition; but it is the only one which does not refer force back to force, thus apparently leaving the question where it found it. We may dismiss it with the remark, that a fluid or quasi-solid absolutely continuous and alike in every part is difficult to conceive; and it is hard to understand how motion can be propagated through it. If it be not continuous, forces must be supposed to be exerted by its parts on each other, else the motion of one part would not affect the others. There is one way in which the latter difficulty has been attacked, which seems plausible enough; and that is, that the particles of this fluid are in a state of rapid motion, and continually impinging on each other and on the particles of matter, no forces being exerted except those of pressure at the impact. This is the notion of Le Sage. But, unless these particles be supposed elastic, their motion would be lessened at every impact, and destroyed completely if the impact were direct. This objection seems to be a very strong one. The first-mentioned theory, that of Epinus and lilosotti, assumes that material particles float in a general atmosphere of ether, that the particles of each repel one another, but that a particle of matter attracts one of ether. From these suppositions, and an hypothetical pressure with density in such an ether, Mosotti has deduced gravitation and the molecular forces; but to apply the hypothesis to the other physical energies, other suppositions are necessary. These have been supplied by Clausius and Redtcnbacher, who, with the assumptions of particles of matter and of ether as before, imagine those of mutter to attract each other, and also those of ether, but the latter to be mutually repulsive. Light and radiant heat, accord ing to this theory, are vibrations of the ether which fills all space between the particles of matter, or rather, between the atmospheres of ether which, by the foregoing assump tions, the particles of matter will collect about them. Heat consists of vibrations of the molecules of matter, or of the groups of atoms (see ATOMIC THEORY) of which the molecule of a compound body is built up, together with their atmospheres. Electric-• ity, magnetism, etc., are explained to be rotations in the atmospheres. Redtenbaeher and Clausius are not quite agreed as to the physical energies corresponding to each of these forms of motion, but the above sketch will give a general idea of the nature of their speculations.
. But the most startling of all the reflections on force, and its ultimate nature,• which have perhaps ever been made, are those of Faraday. 'Without calling in question in ordinary cases the truth of the conservation of energy, has endeavored, by experi ment (the only genuine test in a question so novel and so profound), to prove what may he called the conservation of force. Here we understand force itself, and not energy. He argues thus: Two masses, according to the undisputed law of gravitation, attract with four times their mutual force if their 'distance be diminished to half; and with only one fourth of the same, if their distance be doubled. He asks whence comes the additional force in the former, and what becomes of the lost force in the latter case? • Now, it is evident that this is a new question, totally distinct from any we have yet considered. To answer it, we must know what force is. Would gravitation have any existence if there were but one'partiele of matter in the universe, or does it suddenly come into existence when a second particle appears? Is it an attribute of matter, or is it due to something between the particles of -matter? Faraday has tried several experi ments of an exceedingly delicate kind, in order to get at some answer to his question.
A slight sketch of one of them must suffice. A pound-weight is not so heavy at the ceiling of a room as it is 'when on the floor; for, in the former case, it is more distant from the mass of the earth than in the latter. The difference for a height of 30 ft. is (roughly) about of a pound. Now, if a mass of metal be dropped through such a space, an additional force, of its weight; is called into play, and the object of the experiment was to detect whether electrical effects accompanied this apparent creation of force. The mass, therefore, was a long copper wire, whose coils were insulated (see ELECTRICITY) from each other, and whose extremities were connected with those of the coil of a delicate galvanometer (q.v.). Had any trace of an electric current been produced, the needle of the galvanometer would have: been deflected, but, when all causes were avoided, no such deflection was detected. Other experi ments with a view to the detection of other physical energies, were also tried, but, like the first, with negative results only.
We must not hastily conclude that there is such a thing as force, though we are in the constant habit of speaking about it. Our sensations are all more or less misleading until we can interpret them. The pain produced by a blow is quite a different tiling from the energy of motion of a cudgel; and when our muscular sense impresses on sus the idea that we arc exerting force, we must be cautious in our conclusions. For it is certain that force is merely the rate per unit of length at which energy is transferred or transformed.
There are, in mechanics, several other quantities which retain a fixed value under certain circumstances. We may briefly consider a few of them.
Conservation of Areas. -Invariabl Plane:—We have seen (CENTRAL FORCES) that if a particle move about a center of force, its motion is confined to a plane, and its radius vector traces out equal areas in equal times. Similar theorems hold in any system of particles acted on only by their mutual attractions. If in such a system we suppose the positions of the respective particles to be continually projected (orthogonally, see PROJECTION) on any fixed plane, and radii vectores to be drawn from any point in that plane to the projections—the sum of the areas swept out by all those radii vectores will be equal in equal times. Also, this true of all planes, there is one for which this sum is a maximum, and this plane is foxed space. It is thence called the invariable plane of the system. Similar propositions hold for a system of bodies each of finite size, their several axial rotations being taken into account; hence what is called the invariable plane (q.v.) of the solar system.
Conservation of two masses' attract or impinge, the forces they exert on each other are evidently equal and opposite. Now, the measure of a force is the momentum it produces; hence equal and opposite momenta, in addition to their original quantities, will be communicated to the masses, and therefore the sum of the momenta of the two, resolved in any direction, will be unaltered; hence, the suns of the momenta, of any number of bodies will be unaltered by mutual actions either of the nature of attraction or impact.
Conservation of the Motion of the Center of Gravity.—Again, in such a system, the momentum of the whole collected at its center of inertia. resolved in any assigned direction, is the sum of the momenta of the separate bodies in that direction; hence, the center of inertia of a system, subject to none but the mutual actions of its components, either remains at rest, or moves uniformly in a straight line.
For a simple, and as far as possible non-technical, discussion of the subjects so briefly noticed above, the reader may be referred to Tait's ilecent Advances in Physical Science (second edition).