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except only that the threads, or rifles, are less deflected, making only one turn, or a little more, in the whole length of the piece.
This construction is employed for correcting the irregularity in the flight of balls, from smooth barrels, by imparting to the balls a rotatory motion perpendicular to the line of direction. The same effect has lately been accomplished by an extremely simple and obvious contrivance, and which will, probably, altogether supersede the necessity of rifling the barrel. It consists in cutting a spiral groove in the bullet itself, which, when discharged, is thus acted upon by the air, and the same rotatory motion imparted to it as that produced by the furrows in the barrel. But it is the rotatory motion which steadies the flight of the ball ; and by whichever method this is produced, the theory of its action will be the same. It has been long and generally known, that when the common bullet is discharged from a plane barrel, its flight is extremely irregular and uncertain; it has, for instance, been found, from the experiments of Mr. Robins, that notwithstanding the piece was firmly fixed, and fired with the same weight of powder, the ball was sometimes deflected to the right, sometimes to the left, sometimes above, and at others below the true line of direction. It has also been observed, that the degree of deflection increases in a much greater proportion than the distance of the object fired at. It is not difficult to account for these irregularities; they, doubtless, proceed from the impossibility of fitting a ball so accurately to any plain piece, but that it will rub more against one side of the barrel than another, in its passage through it. Whatever side, therefore, of the muzzle, the ball is last in contact with, on quitting the piece, it will acquire a whirling motion towards that side, and will be found to bend the line of its flight in the same direction, whether it be upwards or downwards, to the right or left; or obliquely, partaking, in some degree, of both; and after quitting the barrel, this deflection, which, though in the first instance, it is but trifling and inconsiderable, is still farther increased by the resistance of the air ; this being greatest on that side where the whirling motion conspires with the progressive one, and least on that side where it is opposed to it. Thus, if the ball, in its passage out, rubs against the left side of the barrel, it will whirl towards that side; and as the right side of the ball will, therefore, turn up against the air during its flight, the resistance of the air will become greatest on the right side, and the ball be forced away to the left, which was the direction it whirled in. It happens, moreover, from various accidental circumstances, that the axis of the ball's rotation frequently changes its position several times during the flight; so that the ball, instead of bending its course uniformly in the same direction, often describes a track variously contorted. From this view of the causes of aberration in the flight of balls, it will be evident, that the only means of correcting it is by preventing the ball from rubbing more against one side of the barrel than another in passing through it; and by giving to the bullet a motion which will counteract every accidental
preserve its direction, by making the resistance of the air upon the forepart continue the same during its whole flight; that is, by giving it a rotatory motion perpendicular to the line of direction. The contrivance for this purpose is called rifling, and consists, as we have above stated, in forming upon the inside of the barrel a number of threads and furrows, either in'a straight or spiral direction, into which the ball is moulded; and hence, when the gun is fired, the indented zone of the bullet follows the sweep of the rifle, and thereby, besides its progressive motion, acquires a considerable one round the axis of the barrel, which motion will be continued to the bullet after its separation from the piece, so that it is constantly made to whirl round an axis coincident with the line of its flight.
Note 15. p. 246. Those who have been in the habit of inspecting the works of the statuary, must frequently have detected the art which he has displayed in imparting stability to his figures, by lowering their centre of gravity. The bronze figure of Achilles, in Hyde Park, affords a very striking illustration of such ingenuity ; it is evident, from the position and height of the figure, that, had not a mass of matter been added to its base, in the form of armour, its stability would have been extremely precarious, since the slightest movement might have thrown its line of direction beyond the base; but the addition of the armour renders such an accident impossible, by lowering its centre of gravity. Other examples of similar contrivance are presented in several celebrated statues, wherein stability is ensured by the judicious distribution of the draperies.
Note 15. p. 273. It has been stated in the text, that the gyrations of the top depend exactly upon the same principle as that which
produces the precession of the equinoxes ; viz., an unequal attractive force exerted upon the revolving mass. In the one case, this is known to arise from the action of the sun and moon on the excess of matter about the equatorial regions of the earth; in the other, from the parts of the top being unequally affected by gravity, while it is spinning in an inclined or oblique position. To those philosophers who have condescended to read the present work, if there be any such, and are thereby induced to pursue the investigation of a subject which has hitherto excited far too little attention, we beg to submit the following remarks :
If a top could be made to revolve on a point without friction, and in a vacuum, in the case of its velocity being infinite, it would continue to revolve for ever, in the same position, without gyration. If the velocity were finite, it would for ever remain unchanged in position, in the event of the centre of gravity being directly over the point of rotation. In any other position (supposing its velocity very great, although not infinite) there would arise a continued uniform gyration. The line which passes through the point of rotation, and the centre of gravity, always making the same angle with the horizon, or describing the same circle round the zenith. But in all artificial experiments the circumstances are very remarkably changed; if, indeed, the centre of gravity happens to be situated perpendicularly over the point of rotation, the top will continue quite steady, or sleeping, as it is termed, till nearly the whole of its velocity of rotation is expended. In any other position the top begins to gyrate, but reclining at all times on the outside of its physical point of gyration, the top is uniformly impelled inwards, and this (when the velocity is considerable, and the point broad) acts with a force sufficient for carrying the top towards its quiescent or sleeping point; but when the velocity is much diminished, this power becomes feeble, the gyrations increase in diameter, and the top ultimately falls.
NOTE 16. p. 310.
A cycloid is a peculiar curve line; and is described by any one point of a circle as it rolls along a plane, and turns round its centre; thus, for instance, the nail on the felly of a cart-wheel traces a cycloid in the air as the wheel proceeds. This curve is distinguished by some remarkable properties, the most important of which is, that any body moving in such a curve, by its own weight, or swing, will pass through all distances of it in exactly the same time; and it is for such a reason that pendulums are made to swing in cyloids, in order that they may move in equal times, whether they go through a long or a short part of the same curve. Where the arc described is small, a portion of the circle will be sufficiently accurate, because it will be seen that such an arc will not deviate much from an equal portion of a cycloidal curve. The cycloid is remarkable as being that path, with the exception of the perpendicular, through which a body will move with the greatest velocity; suppose, for example, a body is to descend from any one point to any other, by, means of some force acting on it, together with its weight; a person unacquainted with mechanics would say at once, that a straight line is the path it must take to effect this