Lectures de Potentia Restitutiva, or of Spring

Their motion possesses such a velocity original: "Velocity"; speed of motion impressed from the ambient original: "Ambient"; the surrounding medium or environment on the two extreme particles 1 and 8. First, if by any external power acting on the two extremes 1 and 8, they are moved further apart, such as to the points C and D, then all the vibrating particles original: "Vibrative Particles" shall be proportionately extended. Consequently, the number of vibrations—and therefore the number of collisions original: "occurſions"; the striking together of particles—will be reciprocally diminished. Because of this, their effort to move back toward each other will also be reciprocally diminished.

For example, suppose this second dimension of length is to the first as 3 is to 2; the length of the vibrations will increase, and the frequency of collisions will be reciprocally diminished. Whereas I previously supposed there were 1,000,000 vibrations in a second, in this state there can be only 666,666. Consequently, the spring original: "Spring"; the elastic force or tension pulling inward must be proportional to the extension original: "Extenſion"; the act of stretching beyond its natural length.

Secondly, if by any external force the extreme particles are moved a third part closer together (assuming the external natural force remains the same in this instance as in the former, acting as the balance to the particles in their natural state), the length of the vibrations shall be proportionately diminished. The number of vibrations, and consequently the number of collisions, will be reciprocally increased; instead of 1,000,000, there shall be 1,500,000.