Iquili- rium. ~)rigin of
- he idea
.if force. Stress. Tension and pressure force may have different origins, but it is always one and the same ; and it produces, in any body to which it is applied, a change of momentum in its own direction, and in amount proportional to its magnitude and to the time during which it acts. 287. Thus, from Newton s point of view, equilibrium is not a balancing of forces, but a balancing of the effects of forces. When a mass rests on a table, gravity produces in it a vertically downward velocity which is continually neutral ized by the equal upward velocity produced by the reaction of the table ; and these forces, whose origins and places of application are alike so widely different, are (as forces), in every respect except direction, similar and equal. And they are so because they produce, in equal times, equal and opposite quantities of motion. 288. The idea of "force" was undoubtedly suggested by the " muscular sense ; and there can be no question as to the vividness of the sensation of effort we experience when we try to lift a heavy weight or to open a massive gate. In this, as in other cases, it is the business of science to find what objective fact corresponds to the subjective data of sensation. It is very difficult to realize the fact, certain as it is, that light (in the sense of brightness} is a mere sensation or subjective impression, and has no objective existence. Yet we know that, beside those radiations which give us the sensation of light, there are others, in endless series both higher and lower in their refrangibility, to which our eyes are absolutely blind. And the only difference between these and the former is one of mere wave-length or of period of vibration. Similarly, it is very hard to realize the fact that sound (in the sense of noise) is only a sensation ; and that outside us there is merely a series of alternate compressions and dilatations of the air, the great majority of which produce no sensible effect upon our ears. Thus because we know that we should seek in vain for brightness or noise in the external world, familiar as our senses have rendered us with these conceptions, we are driven to inquire whether the idea of force may not also be a mere suggestion of sense, corre sponding (no doubt) to some process going on outside us, but quite as different from the sensation which suggests it as is a periodic shearing of the ether from brightness, or a periodic change of density of air from noise. 289. So far, we have treated of force as acting on a body without inquiring whence or why ; we have referred to the first and second laws of motion only, and have thus seen only one half of the phenomenon. As soon, however, as we turn to the third law, we find a new light cast on the question. Force is always dual. To every action there is always an equal and contrary reaction. Thus the weight which we lift or try to lift, and the massive gate which we open or try to open, both as truly exert force upon our hands as we do upon them. This looking to the other side of the account, as it were, puts matters in .a very different aspect. " Do you mean to tell me," said a medical man of the old school, "that, if I pull a subject by the hand, it will pull me with an equal and opposite force 1 ?" When he was convinced of the truth of this state ment, he gave up the objectivity of force at once. 290. The third law, in modern phraseology, is merely this : Every action between two bodies is a stress. When we pull one end of a string, the other end being fixed, we produce what is called tension in the string. When we push one end of a beam, of which the other end is fixed, we produce what is called jiressure throughout the beam. Leaving out of account, for the moment, the effects of gravity, this merely amounts to saying that there is stress across every transverse section of the string or beam. But, in the case of the string, the part of the stress which every 747 portion exerts on the adjoining portion is a pull ; in the case of the beam it is a push. And all this distribution of stress, though exerted across every one of the infinitely numerous cross sections of the string or beam, disappears the moment we let go the end. We can thus, by a touch, call into action at will an infinite number of stresses, and put them out of existence again as easily. This, of itself, is a very strong argument against the supposition that force, in. any form, can have objective reality. 291. We must now say a word or two on the question Objective of the objective realities in the physical world. If we phy. si 5 al inquire carefully into the grounds we have for believing reallties - that matter (whatever it may be) has objective existence, we find that by far the most convincing of them is what may be called the " conservation of matter." This means that, do what we will, we cannot alter the mass or quantity of a portion of matter. We may change its form, dimen sions, state of aggregation, &c., or (by chemical processes) we may entirely alter its appearance and properties, but its quantity remains unchanged. It is this experimental result which has led, by the aid of the balance, to the immense developments of modern chemistry. If we receive this as evidence of the objective reality of matter, we must allow objective jeality to anything else which we find to be conserved in the same sense as matter is conserved. Now there is no such thing as negative mass ; mass is, in mathematical language, a signless quantity. Hence the conservation of matter does not contemplate the simul taneous production of equal quantities of positive and negative mass, thus leaving the (algebraic) sum un changed. But this is the nature of conservation of momentum ( 1G5) and of moment of momentum. The only other known thing in the physical universe, which is conserved in the same sense as matter is conserved, is energy. Hence we naturally consider energy as the other objective reality in the physical universe, and look to it for information as to the true nature of what we call force. 292. When we do so, the answer is easily obtained, True and in a completely satisfactory form. We give only a very nature of simple instance. When a stone, whose mass is M and force> weight W, has fallen through a space h towards the earth, it has acquired a speed ?, which ( 28) is given by the equation ph; 2 = m. This is a particular case of the conservation of energy, but the terms in which it is expressed are those suggested by Newton s laws of motion, and are therefore based on the recognition of "force." The first member of the equation represents the kinetic energy acquired ; the second the potential energy lost, or the work done by gravity upon the stone during its fall. Both members therefore express real things, having objective existence. But the "force" (so-called) which is said to have pro- duced the motion, has the value i.e., it is the rate per unit of length, at which potential energy is converted into kinetic energy during the fall. In other words, it is merely an expression for the space-rate at which energy is transformed. 293. Another mode of presenting the case will make this still more clear. The average speed with which the stone falls is ( 28) v/2. Divide both sides of the equation above by this quantity, remembering that %h/v is the time of falling, which we call t. We have thus, as another perfectly legitimate deduction from our premises, t-tf r It W-M/- _ Here the (so-called) force appears in a new light. _ It is now the time-rate at which momentum is generated in the falling stone. Space- transfer- mation of e Time- TflL6 OI change of momen-
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