Lectures de Potentia Restitutiva, or of Spring

Because the particles of air are exceedingly small, their motion—in order to maintain a balance with other earthly bodies—is exceedingly swift. Furthermore, their vibrative spaces The distance or range over which a particle moves or oscillates. are exceedingly large compared to the vibrative spaces of other terrestrial bodies. I suppose that the vibrative space of the air near the Earth in its natural state may be 8,000 times greater than that of steel, and above a thousand times greater than that of common water. Proportionally, I suppose that its motion must be eight thousand times swifter than the former, and above a thousand times swifter than the latter.

If, therefore, a quantity of this air is enclosed by a solid body, and that body is designed to compress the air into less room, the motion of the air (assuming the heat remains the same) will continue the same. Consequently, the vibrations and occursions original: "Occursions"; refers to the collisions or "runnings-into" one another of particles. will be increased in reciprocal proportion. That is, if it is condensed into half the space, the vibrations and collisions will be double in number; if into a quarter of the space, the vibrations and collisions will be quadruple, and so on.

Again, if the containing vessel is designed to leave the air more space, the length of the vibrations will be proportionally enlarged, and the number of vibrations and collisions will be reciprocally diminished. That is, if it is allowed to extend to twice its former dimensions, its vibrations will be twice as long, and the number of its vibrations and collisions will be fewer by half; consequently, its outward endeavors The pressure or force exerted by the air against the walls of its container. will also be weaker by half.

These explanations will serve, with the necessary changes being made original: "mutatis mutandis", for explaining the spring The "spring" refers to elasticity or the force of tension and compression. of any other body whatsoever.

It now remains for me to show how—given that the constitutions of springy bodies are as described—the vibrations of a spring, or a body moved by a spring, shall be of equal duration whether they are greater or less, provided the motion is equal and uniform.