3rd. They may move in direct opposition to each other, and that with equal quantities of motion.
4th. They may be carried with unequal motions in directions contrary to each other.
As the bodies may be either equal or unequal, each of these four general cases may be considered as consisting of two branches.
As to the first, if a body in motion strikes another equal body at rest, they will, according to the proposition, move together each of them with one half of the motion that the body had which was in motion before the stroke; and since the quantity of motion in any body is as the product arising from the multiplication of its quantity of matter into its velocity, the common velocity of the two bodies will be but one half of the velocity of the moving body before the stroke.
As to the second general case, where both the bodies are in motion before the stroke, and move one and the same way. In order to find their common velocity after impact, let the sum of their motions before the stroke be divided by the sum of the bodies, and the quotient will express the common velocity.
As to the third general case, where the bodies move in direct opposition to each other, if they have equal quantities of motion, they will upon the stroke lose all their motion, and continue at rest; for, by the proposition, the bodies after impact will be carried with the difference of their motions before the stroke; which difference, in such a case, is nothing.
When two bodies meet with unequal quantities of motion, if the difference of their motions be divided by the sum of the bodies, the quotient will express their common velocity after the stroke; for, by the proposition, the difference of their motions before the stroke is equal to the sum of their motions after the stroke; consequently, that difference divided by the sum of the bodies must give the velocity.
Such are the principal laws which govern the collision of bodies devoid of elasticity. The motions of elastic bodies are determined by different rules: for when they are perfectly elastic, the velocity gained by the body struck, and the velocity lost by the striking body, will be twice as great as if the bodies were perfectly inelastic. In estimating, therefore, the motions of such bodies, we may first consider what they would have been after impact, had they been inelastic, and thence deduce the desired conclusion. See Helsham’s Lectures, a work in which the subject appears to be very clearly treated.
Note 27, p. [181].--Druidical remains.
Karn-brêh hill rises a little to the south-west of Redruth in Cornwall, to an elevation of 697 feet. Its principal interest is derived from the speculations of the antiquary, Doctor Borlase, who regarded it as having been once the grand centre of druidical worship; and he asserts, in his Antiquities of Cornwall, that, at this very time, the remains of those monuments which were peculiar to that priesthood may be discovered, such as rock-basins, circles, rock-idols, cromlechs, karns, caves, religious enclosures, logan stones, a gorseddau, or place of elevation, whence the druids pronounced their decrees, and the traces of a grove of oaks. This is all very ingenious and imposing, and may be easily believed by those who have either not visited the spot, or, having visited it, not viewed the objects with geological eyes. There is no ground whatever for considering the druidical monuments of Dr. Borlase as the works of man: on the contrary, they are evidently the results of the operation of time and the elements, the usual agents employed by Nature in the decomposition of mountain masses: but the age of antiquarian illusion is past; the light of geological science has dispelled the phantoms created by the wizard Fancy, just as the rising sun dissolves the mystic forms which the most common object assumes in twilight, when viewed through the medium of credulity and superstition. The “rock-basins” of antiquaries are rounded cavities on the surface of rocks, and are occasionally as spheroidal internally as if they had been actually formed by a turning-lathe. It was this artificial appearance which first suggested the hypothesis concerning their origin, and induced the antiquary to regard them as pools of lustration. It may, however, be remarked, in the first place, that, supposing them to have been the works of the druids, these priests must have been indefatigable artists, for there is scarcely a block of granite on which one or more of such pools are not visible, although some are, undoubtedly, much more complete and imposing than others. We shall introduce to the reader an account of these rock-basins in the words of their great defender, and we think that he will be amused with the ingenuity and confidence with which the antiquary dwells upon every appearance, and bends the facts to suit his favourite theory. “Since no author has mentioned, and attempted to explain these monuments, let us see what light and assistance their shape and structure, exposition, number, and place, considered together with the customs and known rites of antiquity, may afford us in this untrodden path. Of these basins there are two sorts; some have lips or channels to them, others have none; and therefore, as those lips are manifestly the works of design, not of accident, those that have so material a difference must needs have been intended for a different use, and yet both these sorts seem to be the works of the same people, for there is a multitude of these basins which have no lips or outlets, as well as those which have, to be seen on Karn-brêh hill, and elsewhere, on contiguous rocks. Their shape is not uniform; some are quite irregular, some oval, and some are exactly circular. Their openings do not converge in the top as a jar or hogshead, but rather spread and widen, as if to expose the hollow as much as possible to the skies. Some have little falls into a larger basin, which receives their tribute, and detains it, having no outlet. Other large ones intermixed with little ones have passages from one to another, and, by successive falls uniting, transmit what they receive into one common basin, which has a drain to it, that serves itself and all the basins above it.”