Newton's Principia : $b The mathematical principles of natural philosophyNewton, Isaac
General
Newton's Principia : $b The mathematical principles of natural philosophy
Newton, Isaac
Celestial mechanics -- Early works to 1800; Mechanics -- Early works to 1800
But to prevent an objection that may perhaps be alledged against the
rule, for the proof of which this experiment was made, as if this
rule did suppose that the bodies were either absolutely hard, or at
least perfectly elastic (whereas no such bodies are to be found in
nature), I must add, that the experiments we have been describing, by
no means depending upon that quality of hardness, do succeed as well
in soft as in hard bodies. For if the rule is to be tried in bodies
not perfectly hard, we are only to diminish the reflexion in such a
certain proportion as the quantity of the elastic force requires. By
the theory of Wren and Huygens, bodies absolutely hard return one from
another with the same velocity with which they meet. But this may be
affirmed with more certainty of bodies perfectly elastic. In bodies
imperfectly elastic the velocity of the return is to be diminished
together with the elastic force; because that force (except when the
parts of bodies are bruised by their congress, or suffer some such
extension as happens under the strokes of a hammer) is (as far as I can
perceive) certain and determined, and makes the bodies to return one
from the other with a relative velocity, which is in a given ratio to
that relative velocity with which they met. This I tried in balls of
wool, made up tightly, and strongly compressed. For, first, by letting
go the pendulous bodies, and measuring their reflexion, I determined
the quantity of their elastic force; and then, according to this
force, estimated the reflexions that ought to happen in other cases of
congress. And with this computation other experiments made afterwards
did accordingly agree; the balls always receding one from the other
with a relative velocity, which was to the relative velocity with which
they met as about 5 to 9. Balls of steel returned with almost the same
velocity: those of cork with a velocity something less; but in balls
of glass the proportion was as about 15 to 16. And thus the third Law,
so far as it regards percussions and reflexions, is proved by a theory
exactly agreeing with experience.
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