Force. As employed in physical science, the term force means any cause which changes the direction or speed of the motion of a portion of matter. It is therefore correctly applied to a push or pull, to the weight of a body, the attraction exerted by a magnet on a piece of iron or by an electrified body on a pith-ball, &c. This is expressly laid down in the first of Newton's Laws of Motion—to wit:
Every body perseveres in its state of rest, or of uniform motion in a straight line, except in so far as it is compelled by forces to change that state.
Now, we find that we can, by conscious muscular exertion, set a piece of matter in motion, and also change its motion both in speed and in direction. Hence we figure to ourselves that we are exerting force upon it. But here great caution is requisite, as the direct impressions of sense are, in many cases, notoriously misleading. Until we know what Matter (q.v.) is, it is practically useless to speculate as to the precise nature of force, if indeed there be such a thing at all. Even Newton's language has an anthropomorphic character which it would be difficult to avoid without coining words for the purpose. Of course in Newton's system the force is assigned in direction and magnitude by the change of motion (i.e. of Momentum, q.v.) said to be produced by it in a given time. This is the essence of the second law of motion.
And the third law greatly extends our view of the subject, for it points out that force is always dual:
To every action there is always an equal and contrary reaction, or the mutual actions between two bodies are always equal and oppositely directed.
But, as the results of the action and reaction alike are mere changes of momentum, and as neither can present itself without the other, all that we are logically entitled to say is that no change of motion takes place unaccompanied by an equal and opposite change. The introduction of the action and reaction may thus be merely an attempt to explain this observed interchange of momentum by the help of the sense-suggested notion of force.
There is no doubt that the introduction of the idea of force has been very useful, if only in enabling us to express the fundamental laws of dynamics in a particularly concise and easily intelligible form. But there is equally little doubt that everything yet known on the subject can be perfectly well expressed without the use of the term force, or of the idea which it embodies.
The dynamical expression for which the term force has been introduced as a substitute presents itself in two forms, different in name and conception, but intrinsically the same—viz. the time-rate at which momentum (see MOTION, LAWS OF) changes, or the space-rate at which Energy (q.v.) is transformed or transferred. Thus, when a stone is let fall, the momentum which it acquires is proportional to the time of falling, so that after seconds its amount is, say, ; and in falling through a space of feet it loses in potential energy, while it gains in kinetic energy, an amount proportional to the height fallen through, say, . Experimental measurement shows us that A and B are one and the same quantity, and we say it represents the weight of the stone—i.e. the force under which we figure to ourselves that the fall takes place. It is very convenient to do so. But, except the indications of our muscular sense, we have no proof whatever that there is any reason for the fall of the stone other than the observed fact that energy has the property of preferring the kinetic to the potential form. And the statement that a stone of given mass has potential energy to a given amount, depending directly on its elevation above the earth, is sufficient (without even mention of weight, or of force in any form) to enable us to calculate all the circumstances of its fall. Though we have confined ourselves to an exceedingly simple example, a similar but of course more general statement as to energy enables us to make the calculation requisite for determining the motion in all cases, however complex.
Newton's definition of force has sometimes been amended (?) into 'Any cause which changes, or tends to change, the motion of a body.' But this is entirely foreign to his system. For his second law expressly says, 'Change of momentum is proportional to force, and takes place in the direction of the force.' Hence, from Newton's point of view, there is no balancing of forces, though there may be balancing of the effects of forces.
The Resultant of two forces which act on the same particle of matter is defined as the single force which could produce in that particle the same change of momentum as would the two given forces if they acted jointly on it for the same period of time. As it follows at once from Newton's second law that different forces, acting for equal times on the same particle, produce velocities in their own directions and proportional to their magnitudes, the question of compounding these forces is the same as that of compounding the corresponding velocities. Hence we have at once the only correct basis for the proof of that Parallelogram of Forces, or Triangle of Forces, on which (from the so-called statical point of view) as much absolutely useless thought has been expended as upon Euclid's celebrated twelfth axiom and its consequences.
The true measure of a force is, of course, the amount of momentum which it produces in a given time. Hence, if our fundamental units of mass, length, and time be the pound, foot, and second, unit force is that which gives in one second a speed of one foot per second to a mass of one pound. This is the British absolute unit of force. As gravity produces a speed of about 32 feet per second during each second of the motion of a falling body, the unit force is (speaking very roughly) about d part of the weight of a pound—i.e. about the weight of half an ounce. If we adopt the so-called C.G.S. system, in which the units are the centimètre, gramme, and second, the unit force (called a dyne) is that which in one second produces a speed of one centimètre per second in a mass of one gramme. Compared with the British absolute unit, the dyne is very small, being little more than th part of it.
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, he has endeavoured, by experiment (the only genuine test in a question so novel and so profound), to prove what may be 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 particle 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 experiments 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 feet is (roughly) about th of its weight. Now, if a mass of metal be dropped through such a space, an additional force, th 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 disturbing causes were avoided, no such deflection was detected. Other experiments with a view to the detection of other physical energies were also tried, but, like the first, with negative results only.
From what has been said above it is clear that 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 thing from the energy of motion of a cudgel; and, when our muscular sense impresses on us the idea that we are 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.