LECTURE XXX.

ON THE COMMUNICATION OF MOTION BY COL

LISION.

NATURAL Philofophy is little elfe than the

measuring of fuch motions as are obvious, or accounting for fuch as proceed from an hidden, caufe. I have already explained many of the one;

and described the measures of the other. I have now to confider the laws of communication of motion, by collifion. Little more can be expected than the statement of thefe laws; for philofophy is ftill unable to explain how one body becomes poffeffed of a power of communicating it's motion to another.

The laws of motion I am here going to explain, arise from a principle laid down in the beginning of thefe Mechanical Lectures; namely; that action and re-action are equal, and in contrary directions.

If a body impinges against another body, moving in the direction of á line which joins their centers of gravity, the two bodies mutually act on each other, in any given inftant of their collifion, with equal forces; which equal forces will always have the effect of retarding the ftriking body, and accelerating the body ftruck, if it moves in the fame direction with the ftriking body, and of retarding it if it moves in the contrary direction.

This mutual action and re-action of bodies may be illuftrated by supposing a spring, in a form of an helix (the axis of which coincides with the direction

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direction of the motion), to be interpofed between the two bodies; then in whatever degree the fpring is compreffed, it will exert the fame elaftic force on each of the bodies, (the inertia of the spring not being confidered.) When the spring first begins to be compreffed, the force by which it retards the ftriking body, and accelerates the body ftruck, is the leaft of all; it afterwards will continually increase during each fucceffive inftant, till it's compreffion is the greatest poffible. The intensity of this force may vary according to any imaginable law; but whatever be the variation, it will act equally on both fides.

When the two bodies have acquired a common velocity, the fpring can acquire no further compreffion, and may then begin to reftore itself with various degrees of force, from o to the force by which it was compreffed. When the reftitutive force is equal to that of compreffion, the action of the fpring will be fimilar to that of perfectly elaftic bodies.

Motion cannot be communicated to any body inftantaneously, but must be produced by gradual acceleration; it not being conceivable, that any really exifling body fhould pass from quiefcence into finite motion, or from one degree of finite motion to another, without having poffeffed all the intermediate degrees of velocity.

Suppofe a fpherical body to impinge on another body of the fame form, moving in the fame direction with the line which joins their centers, and let both of them be perfectly non-elastic.

When the furfaces of thefe fpheres are juft in contact, the diftance of their centers will just be half the fum of their diameters; but as the figures are gradually changed by the impact, their centers will become nearer than before. During the time of their approach, the center of the first balk will

move with a greater velocity than that of the ball ftruck, and the refiftance which the fpheres oppofe to the change of their figures, will act equally in both spheres, but in contrary directions; that is, the force by which the ftriking body is refifted, will urge forward the body ftruck; which, therefore, will be gradually accelerated, and the striking ball retarded, until the centers are at their greatest distance, the change of the bodies figures being then the greateft; at which inftant all acceleration of the ball ftruck, and retardation of the ftriking ball, ceafes, and the two centers begin to go on with a common velocity.

This reasoning, concerning collifion of bodies, is equally applicable to the cafe in which both bodies are non-elaftic, as when one is perfectly non-elastic, and the other perfectly hard. It is likewife equally applicable to the collifion of bodies which are elaftic in any degree, fo far as regards the velocity communicated to the body ftruck, during that fmall but finite portion of time in which the figures of the spheres receive their greatest change, their centers then beginning to go on with a common velocity in bodies of every kind of texture.*

OF ELASTICITY,

The action whereby bodies, whofe figures are changed, restore themfelves to their former figure, is termed elasticity. An elaftic body is therefore one whofe figure being changed, it recovers, or has a tendency to recover, it's figure,

There are in nature, as you have already feen, varieties of activities; in fome of which the caufes are rendered manifeft by experimental inquiries; in others, and among these we may reckon clafti

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* See Atwood on Reftilinear Motion,

city,

city, where no caufe at all is discoverable by the fenfes.

A variety of experiments prove the existence of an elaftic force. The feparation of two bodies, after impact, is a proof of clafticity. Metals, femimetals, ftones, gems, foffils, cartilages, most fluids, as air, and even water, exert an influence oppofite to the direction of the force compreffing them, and difcover a tendency to return to their natural state; which tendency is in all of them imperfect, and lefs than the force impreffed; but moft perfect in glass, ivory, hardened fteel, and cartilages.

Elafticity is increased by augmenting the denfity of a body: thus metals are rendered more elaftic by being beaten by a hammer; and their elafticity, which was fcarcely fenfible before, by this procefs becomes very fenfible. Steel is more elaftic when tempered, and it's denfity is increased in the ratio of 7809 to 7738.

Elafticity is fometimes increased by cold: thus the range of a cannon-ball is faid to be greater when the cannon is cold, than when heated; and the ftring of a violin, or a steel lamina, is inflected, and alfo recovers it's fituation, with lefs force in hot than in cold weather.

Metal fibres, and thin fteel laminæ, exhibit no elafticity, unlefs ftretched to a certain degree, and inflected by a certain force; as appears from lax cords, which, if a little ftretched, and removed from their natural ftate, difcover no tendency to, return to it; and when the inflection of a fibre is very great, the influence of elafticity feems to be in fome cafes annihilated; as appears by the fibres of wood, which, inflected to a certain degree, remain quiefcent, and have no tendency to recover their former fituation. The limits, where the claftic power begins, or where it terminates, are unknown.

Motion

Motion is fupposed to be communicated, or diffused, in elaftic bodies, from the point of impact to the remote parts; and this fuppofition is grounded on the following experiments.

Here are two ivory balls fufpended, fo that their centers are in one line. The furface of one of them, B, is fresh painted. By letting them touch each other gently, A has received a fmall point of paint upon it's furface. Now I fhall raise the ball A, fo that it may impinge with fome violence on B, and it is evident that the furface of each ball has been flattened by the blow; for there is on each a circular mark, fhewn by the paint ftruck off, and the other by the paint received; and as the balls retain their spherical figure after the impact, it is clear that the parts of the surface not only loft, but recovered their figure.

Two glafs balls may, with a proper degree of velocity, fo impinge on each other, that the interior parts of the ball will be broken, though the exterior, contiguous to the point of impact, be unbroken.

Sufpend two ivory balls from the fame point, by ftrings of the fame length, and let the fmaller ball, A, impinge upon B, at reft, with a given velocity. A will be reflected always to the fame height, and B will be impelled to the fame height. But if either A or B be hollowed, and lead inserted in the center, or near to the pofterior surface, neither ball, though the weight be the fame, will afcend as high as before the infertion of the lead. The progreffive motion of the parts from the point of impact is ftopped by the infertion of the lead; and, confequently, the force of reftitution, and the change of figure, is lefs than before it was inferted.

The motion diffufed from the point of impact to the remote parts of an elastic body, is continued

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