Life and death

by A. Dastre

Force in general is the cause of motion. Hence force exists only in so far as there is motion. There would be no force without action. This is Newton’s point of view. It did not prevail, and was not the point of view of his successors. The name of force has been given not only to the cause which produces or modifies motion, but to the cause which resists and prevents it. And then not only have forces in action been considered (dynamics), but forces at rest (statics). Now, to Newton there was no statics. Forces do not continue to exist when they produce no motion; they are not in equilibrium, they are destroyed.

The idea of force therefore is a metaphysical idea which contains the idea of cause. But it becomes experimental immediately it is looked upon as resisting motion, according to the point of view of Newton’s opponents. Its foundations lie in the muscular activity of man.

Man can support a burden without bending or moving. This burden is a weight—that is to say, a mass acted on by the force of weight. Man resists this force so as to prevent its effect. If it were not annihilated by man’s effort, this effect would be the motion or the fall of the heavy body. The effort and the force are thus in equilibrium, and the effort is equal and opposite to the force. It gives to the man who exercises it the conscious idea of force. Thus we know of force through effort. Every clear idea that we can have of force springs from the observation of our muscular effort.

The notion of force is thus an anthropomorphic notion. When an effect is produced in nature outside human intervention, we say that it is by something analogous to what in man is effort, and we give to this something a name which is also analogous, namely force. To give a name to effort and to compare efforts in magnitude, we need not know all about them, nor need we know in what they essentially consist, of what series of physical, chemical, and physiological actions they are the consequence. And so it is with force. It is a resistance to motion or the cause of motion. This cause of motion may be an anterior motion (kinetic force). It may be an anterior physical energy (physical and chemical forces).

Forces are measured in the C.G.S. system by comparing them with the unit called the Dyne.[7] In practice they are compared with a much larger unit—the gramme, which is the weight, the force acting on a unit of mass of one centimetre of distilled water at a temperature of 4° C.

Work.—The muscular activity of man may be brought into play in yet another manner. When we employ workmen, as Carnot said in his Essai sur l’équilibre et le mouvement, it is not a question of “knowing the burdens that they can carry without moving from their position,” but rather the burdens that they can carry from one point to another. For instance, a workman may have to lift the water from the bottom of a well to a given height, and the case is the same for the animals we employ. “This is what we understand by force when we say that the force of a horse is equal to the force of seven men. We do not mean that if seven men were pulling in one direction and the horse in another that there would be equilibrium, but that in a piece of work the horse alone would lift, for example, as much water from the bottom of a well to a given height as the seven men together would do in the same time.”[8]

Here, then, we have to do with the second form of muscular activity, which is called in mechanics, “work”—at least, if in the preceding quotation we attach no particular importance to the words “in the same time,” and retain the employment of muscular activity only “under constant conditions.” Mechanical work is compared with the elevation of a certain weight to a certain height. It is measured by the product of the force (understood in the sense in which it was used just now—that is to say, as causing or resisting motion) and the displacement due to this motion. The unit is the Kilogrammetre—that is to say, the work necessary to lift a weight of one kilogramme to the height of one metre.

It will be remarked that the idea of time does not intervene in our estimation of work. The notion of work is independent of the ideas of velocity and time. “The greater or less time that we take to do a piece of work is of no more assistance in measuring its magnitude than the number of years that a man may have taken to grow rich or to ruin himself can help to estimate the present amount of his fortune.”

Going back to Carnot’s comparison, an employer who employed his workmen only on piece-work,—that is to say, who would only care about the amount of work done, and would be indifferent to the time that they took over it,—would be at the same point of view as the advocates of the mechanical theory. M. Bouasse, whom we follow here, has remarked that this idea of mechanical work may be traced back to Descartes. His predecessors, and Galileo in particular, had quite a different idea of the way in which mechanical activity should be measured; and so, among the mathematicians of the eighteenth century, Leibniz and, later, John Bernoulli were almost alone in looking at it from this point of view.

Energy.—Work thus understood is mechanical energy. It represents the lasting and objective effect of the mechanical activity independent of all the circumstances under which it was carried out. The same work may be done under very different conditions of time, velocity, force, and displacement. It is therefore the permanent element in the variety of mechanical aspects. Work, for example, in the collision of bodies when the motion of a body appears to be destroyed on impact with another, reappears as indestructible vis viva. This, then, is exactly what we call energy; and if we agree to give it this name, we may say that the conservation of energy is invariable throughout all mechanical transformations.