Volume 1
A course of lectures on natural philosophy and the mechanical arts / by Thomas Young.
- Thomas Young
- Date:
- 1845
Licence: Public Domain Mark
Credit: A course of lectures on natural philosophy and the mechanical arts / by Thomas Young. Source: Wellcome Collection.
Provider: This material has been provided by King’s College London. The original may be consulted at King’s College London.
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![instance a second, if there were no other motions than undisturbed or uniform motions; but tiie velocity may vary very considerably within the second, and we must therefore have some other measure of it than tlie space actually described in any finite interval of time. If, however, the times be supposed infinitely short, the elements of space described may be considered as the true measures of velocities. These elements, although smaller than any assignable quantity, may yet be accurately compared with each other; and the reason that they afford a true criterion of the velo- city is this, that the change produced in the velocity during so short an interval of time, must be absolutely inconsiderable, in comparison with the whole velocity, and the element of space becomes a true measure of the temporary velocity, in the same manner as any larger portion of space may be the measure of a uniform velocity. Wlien the increase or diminution of the velocity of a moving body is uniform, its cause is called a unifonn force; the sjjaces which would be described in any given time with the actual velocity uniformly continued, being always equally increased or diminished by the action of such a force. For example, if the velocities at the beginning of any two separate seconds be such that the body would describe one foot and ten feet in the respective seconds, if undisturbed, and the spaces actually described become two feet and eleven feet, each being increased one foot, the accele- rating force must be denominated uniform. The power of gravitation, acting at or near the earth’s surface, may, without sensible error, be considered as such a force. Thus, if a body begins to fall fi’om a state of rest, it describes about 16 feet, or more cor- rectly 16-Pr in the first second ; if it begins a second with a velocity of 32 feet, it describes 32 and 16, or 48 feet in this second. The decrease of the force of gravitation, in proportion to the squares of the distances from the earth’s centre, is barely perceptible, at any heights within our reach, by the nicest tests tliat we can employ. The velocity produced by any uniformly accelerating force, is propor- tional to the magnitude of the force and the time of its operation con- jointly.* When the forces are the same, a little consideration will convince us that, since every equal portion of time adds equally to the velocity, the whole velocity pi'oduced or destroyed must be in proportion to the whole time; and when the forces differ, the velocities differ in the same ratio ; for the forces are only measured by the velocities which they generate. Tims a double force, in a double time, produces a quadruple velocity. That a force producing a double velocity is ])roperly called a douljle force, may be shown from the laws of the composition of motion ; for when the equal sides of a parallelogram representing two separate forces or motions, approach to each other, and at last coincide in direction, the diagonal of the parallelogram, representing their joint effect, becomes equal to the sum of the sides. (Plate I. Fig. 10.) t The machine invented by Mr. Atwood J (Plate I. Fig. 11) furnishes us * Galileo, Dialogues on Motion, Dial. III. Dcf. t Halley, Ph. Tr.xvi. 9 (1G86). + On the Rectilinear Motion, and the Rotation of Bodies, Camb. 180-1, p. 291.](https://iiif.wellcomecollection.org/image/b21301840_0001_0057.jp2/full/800%2C/0/default.jpg)
