3. Action is always opposed by reaction; action and reaction are equal, and in directly contrary directions.
We may add to these principles a definition of a force, which is equally and absolutely complete:
Force is that which produces, or tends to produce, motion, or change of motion, in bodies. It is measured statically by the weight that will counterpoise it, or by the pressure which it will produce, and dynamically by the velocity which it will produce, acting in the unit of time on the unit of mass.
The quantitative determinations of dynamic effects of forces are always readily made when it is remembered that the effect of a force equal to its own weight, when the body is free to move, is to produce in one second a velocity of 32.2 feet per second, which quantity is the unit of dynamic measurement.
Work is the product of the resistance met in any instance of the exertion of a force, into the distance through which that force overcomes the resistance.
Energy is the work which a body is capable of doing, by its weight or inertia, under given conditions. The energy of a falling body, or of a flying shot, is about 1∕64 its weight multiplied by the square of its velocity, or, which is the same thing, the product of its weight into the height of fall or height due its velocity. These principles and definitions, with the long-settled definitions of the primary ideas of space and time, were all that were needed to lead the way to that grandest of all physical generalizations, the doctrine of the persistence or conservation of all energy, and to its corollary declaring the equivalence of all forms of energy, and also to the experimental demonstration of the transformability of energy from one mode of existence to another, and its universal existence in the various modes of motion of bodies and of their molecules.
Experimental physical science had hardly become acknowledged as the only and the proper method of acquiring knowledge of natural phenomena at the time of Newton; but it soon became a generally accepted principle. In physics, Gilbert had made valuable investigations before Newton, and Galileo’s experiments at Pisa had been examples of similarly useful research. In chemistry, it was only when, a century later, Lavoisier showed by his splendid example what could be done by the skillful and intelligent use of quantitative measurements, and made the balance the chemist’s most important tool, that a science was formed comprehending all the facts and laws of chemical change and molecular combination. We have already seen how astronomy and mathematics together led philosophers to the creation and the study of what finally became the science of mechanics, when experiment and observation were finally brought to their aid. We can now see how, in all these physical sciences, four primitive ideas are comprehended: matter, force, motion, and space—which latter two terms include all relations of position.
Based on these notions, the science of mechanics comprehends four sections, which are of general application in the study of all physical phenomena. These are:
Statics, which treats of the action and effect of forces.