Chapter XX (3)

The third period is that at which the mud was introduced and the animals extirpated, viz. the period of the deluge. It has been already stated, that there is not any alternation of this mud with beds of bone or of stalagmite, such as would have occurred had it been produced by land floods often repeated; _once_, _and once only_, it appears to have been introduced; and we may consider its vehicle to have been the turbid waters of the same inundation that produced universally the diluvial gravel.

The fourth period is that during which the stalagmite was deposited which invests the upper surface of the mud.

In concluding this note, we take the opportunity of recommending all those who feel interested in the researches of geology, to read a work lately published, entitled “THE WONDERS OF GEOLOGY, by Gideon Mantell, LL.D. F.R.S. &c.”

Note 20, p. 137.--THE RIFLE.

Rifle guns are those whose barrels, instead of being smooth on the inside, like our common pieces, are formed with a number of spiral channels, resembling screws; 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 plane 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, though in the first instance 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 one, and 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 before 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. Many familiar examples of the utility and effect of _rifling_ might be here adduced. If the bricklayer, while unroofing a house, be observed, he will be seen to give to the slates which he throws down a whirling motion, at a certain angle, which ensures their falling edgeways on the ground, and thus preserves them from fracture.

In relation to the subject in the text, to which this note refers, may be introduced a notice of the “BOMMERENG,” a missile used by the natives of Australia, and thus described by Major Mitchell in his “_Journal of an expedition to the Rivers Darling and Murray._” “The bommereng, a thin, curved missile, about two feet four inches long, can be thrown by a skilful hand so as to rise upon the wind with a rotatory motion, and in a crooked direction towards any given point with great precision, and to return, after a considerable flight, to within a yard or two of the thrower; or, by striking the ground near him, to bound so as to hit at a great, distance, “_en ricochet_” any object behind a tree. This singular weapon probably originated in the utility of such a missile for the purpose of killing ducks, where they are very numerous, as on the interior rivers and lagoons, and where we accordingly find it much more in use than on the sea coast, and better made, being often covered with good carving.” This instrument may now be purchased in most of the London toy-shops.

Note 21, p. 144.--CENTRE OF PERCUSSION.

If a stick be held at one of its extremities, and allowed to fall on the edge of a table, the farther end will rebound, or the hand will sustain a shock, unless it be struck exactly on the centre of percussion, in which case the stick will fall as a dead weight. The repetition of this simple experiment will readily convey to the young philosopher an idea of the nature of what is termed the _centre of percussion_.

Note 22, p. 150.--SPINNING OF THE TOP.

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 23, p. 161.--THE MECHANICAL POWERS.

The mechanical powers are all founded upon the principle that _the lengths of circles are in proportion to their diameters_; for it is an immediate consequence of this property of the circle, that if a rod of iron, or beam of wood, be placed on a point or pivot, so that it may move round its prop, the two ends will go through parts of circles, each proportioned to that arm of the beam to which it belongs; the two circles will be equal if the pivot is in the centre or middle point of the beam; but if it is nearer one end than the other, say five times, that end will pass through a circular space, or _arc_, five times shorter than the circular space the other end goes through in the same time. If, then, the end of the long beam goes through five times the space, it must move with five times the swiftness of the short end, since both move in the same time; and, therefore, any force applied to the long end must overcome the resistance of five times that force applied at the opposite end, since the two ends move in contrary directions; hence one pound placed at the long end would balance five placed at the short end.

The beam we have been describing constitutes the first of the mechanical powers, and is termed the LEVER. There are, besides, five others, viz. the _wheel and axle_; the _inclined plane_; the _screw_; the _pulley_; and the _wedge_; out of the whole, or a part of which, it will be found that every mechanical engine or piece of machinery is constructed.

THE LEVER being the simplest of all the mechanic powers, is in general considered the first. It is an inflexible rod or bar of any kind, so disposed as to turn on a pivot or prop, which is always called its _fulcrum_. It has the weight or resistance to be overcome attached to some one part of its length, and the power which is to overcome that resistance applied to another; and, since the _power_, _resistance_, and _fulcrum_ admit of various positions with regard to each other, so is the lever divided into three kinds or modifications, distinguished as the first, second, and third kinds of lever. That portion of it which is contained between the fulcrum and the power, is called the acting part or arm of the lever; and that part which is between the fulcrum and resistance, its resisting part or arm.

In the lever of the first kind, the fulcrum is placed between the power and the resistance. A poker, in the act of stirring the fire, well illustrates this subject; the bar is the _fulcrum_, the hand the power, and the coals the resistance to be overcome. Another common application of this kind of lever is the crow-bar, or hand-spike, used for raising a large stone or weight. In all these cases power is gained in proportion as the distance from the fulcrum to the power, or part where the men apply their strength, is greater than the distance from the fulcrum to that end under the stone or weight. A moment’s reflection will show the rationale of this fact; for it is evident that if both the arms of the lever be equal, that is to say, if the fulcrum be midway between the power and weight, no advantage can be gained by it, because they pass over equal spaces in the same time; and, according to the fundamental principle already laid down, _as advantage or power is gained, time must be lost_; but, since no time is lost under such circumstances, there cannot be any power gained. If, now, we suppose the fulcrum to be so removed towards the weight, as to make the acting arm of the lever three times the length of the resisting arm, we shall obtain a lever which gains power in the proportion of three to one, that is, a single pound weight applied at the upper end will balance three pounds suspended at the other. A pair of scissors consists of two levers of this kind, united in one common fulcrum; thus the point at which the two levers are screwed together is the fulcrum; the handles to which the power of the fingers is applied, are the extremities of the acting part of the levers, and the cutting part of the scissors are the resisting parts of the levers; the longer, therefore, the handles, and the shorter the points of the scissors, the more easily you cut with them. A person who has any hard substance to cut, without any knowledge of the theory, diminishes as much as possible the length of the resisting arms, or cutting part of the scissors, by making use of that part of the instrument nearest the screw or rivet. Snuffers are levers of a similar description; so are most kind of pincers, the power of which consists in the resisting arm being very short in comparison with the acting one.

In the lever of the second kind, the resistance or weight is between the fulcrum and the power. Numberless instances of its application daily present themselves to our notice; amongst which may be enumerated the common cutting knife, used by last and patten makers, one end of which is fixed to the work-bench by a swivel-hook. Two men carrying a load between them, by one or more poles, as a sedan chair, or as brewers carrying a cask of beer, in which case either the back or front man may be considered as the fulcrum, and the other as the power. Every door which turns upon its hinges is a lever of this kind; the hinges may be considered as the fulcrum, or centre of motion; the whole door is the weight to be moved, and the power is applied to that side on which the handle is usually fixed. Nut-crackers, oars, rudders of ships, likewise fall under the same division. The boat is the weight to be moved, the water is the fulcrum, and the waterman at the oar is the power. The masts of ships are also levers of the second kind, for the bottom of the vessel is the fulcrum, the ship the weight, and the wind acting against the sail is the moving power. In this kind of lever the power or advantage is gained in proportion as the distance of the power is greater than the distance of the weight from the fulcrum; if, for instance, the weight hang at one inch from the fulcrum, and the power acts at five inches from it, the power gained is five to one; because, in such a case, the power passes over five times as great a space as the weight. It is thus evident why there is considerable difficulty in pushing open a heavy door, if the hand is applied to the part next the hinges, although it may be opened with the greatest ease in the usual method. In the third kind of lever, the fulcrum is again at one of the extremities, the weight or resistance at the other; and it is now the power which is applied between the fulcrum and resistance. As in this case the weight is farther from the centre of motion than the power, such a lever is never used, except in cases of absolute necessity, as in the case of lifting up a ladder perpendicularly, in order to place it against a wall. The man who raises it cannot place his hands on the upper part of the ladder; the power, therefore, is necessarily placed much nearer the fulcrum than the weight; for the hands are the power, the ground the fulcrum, and the upper part of the ladder the weight. The use of the common fire-tongs is another example, but the circumstance that principally gives this lever importance is, that the limbs of men and animals are actuated by it; for the bones are the levers, while the joints are the fulcra, and the muscles which give motion to the limbs, or produce the power, are inserted and act close to the joints, while the action is produced at the extremities; the consequence of such an arrangement is, that although the muscles must necessarily exert an enormous contractile force to produce great action at the extremities, yet a celerity of motion ensues which could not be equally well provided for in any other manner. We may adduce one example in illustration of this fact. In lifting a weight with the hand, the lower part of the arm becomes a lever of the third kind; the elbow is the fulcrum; the muscles of the fleshy part of the arm the power; and as these are nearer to the elbow than the hand, it is necessary that their power should exceed the weight to be raised. The disadvantage, however, with respect to power, is more than compensated by the convenience resulting from this structure of the arm; and it is no doubt that which is best adapted to enable it to perform its various functions. From these observations it must appear, that although this arrangement must be mentioned as a modification of the lever, it cannot, in strictness, be called a mechanical power; since its resisting arm is in all cases, except one, longer than the acting arm, and in that one case is equal to it, on which account it never can gain power, but in most instances must lose it.

THE WHEEL AND AXLE is the next mechanical power to be considered; it must be well known to every reader who has seen a village well; for it is by this power that the bucket is drawn up, although in such cases, instead of a wheel attached to the axle, there is generally only a crooked handle, which answers the purpose of winding the rope round the axle, and thus raising the bucket, as may be seen in the engraving at the head of our third chapter. It is evident, however, that this crooked handle is equivalent to a wheel; for the handle describes a circle as it revolves, while the straight piece which is united to the axle corresponds with the spoke of a wheel. This power may be resolved into a lever; in fact, what is it but a lever moving round an axle? and always retaining the effect gained during every part of the motion, by means of a rope wound round the butt end of the axle; the spoke of the wheel being the long arm of the lever, and the half diameter of the axle its short arm. The axle is not in itself a mechanical power, for it is as impotent as a lever whose fulcrum is in the centre; but add to it the wheel, and we have a power which will increase in proportion as the circumference of the wheel exceeds that of the axle. This arises from the velocity of the circumference being so much greater than that of the axle, as it is farther from the centre of motion; for the wheel describes a great circle in the same space of time that the axle describes a small one; therefore the power is increased in the same proportion as the circumference of the wheel is greater than that of the axle. Those who have ever drawn a bucket from a well by this machine, must have observed, that as the bucket ascended nearer the top the difficulty increased: such an effect must necessarily follow from the views we have just offered; for whenever the rope coils more than once the length of the axle, the difference between its circumference and that of the wheel is necessarily diminished. To the principle of the wheel and axle may be referred the capstan, windlass, and all those numerous kinds of cranes which are to be seen at the different wharfs on the banks of the river Thames. It is scarcely necessary to add that the force of the windmill depends upon a similar power. The _treadmill_ furnishes another striking example. The wheel and axle is sometimes used to multiply motion, instead of to gain power, as in the multiplying wheel of the common jack, to which it is applied when the weight cannot conveniently have a long line of descent; a heavy weight is in this case made to act upon the axle, while the wheel, by its greatest circumference, winds up a much longer quantity of line than the simple descent of the weight could require, and thus the machine is made to go much longer without winding than it otherwise would do.

THE PULLEY is a power of very extensive application. Every one must have seen a pulley; it is a circular and flat piece of wood or metal, with a string which runs in a groove round it. Where, however, this is fixed, it cannot afford any power to raise a weight; for it is evident that, in order to raise it, the power must be greater than the weight, and that if the rope be pulled down one inch, the weight will only ascend the same space; consequently, there cannot be any mechanical advantage from the arrangement. This, however, is not the case where the pulley is not fixed. Suppose one end of the rope be fastened to a hook in the ceiling, and that to the moveable pulley on the rope a cask be attached, is it not evident that the hand applied to the other extremity of the rope will sustain it more easily than if it held the cask suspended to a cord without a pulley? Experience shows that this is the fact, and theory explains it by suggesting that the fixed hook sustains half the weight, and that the hand, therefore, has only the other half to sustain. The hook will also afford the same assistance in raising the weight as in sustaining it; if the hand has but one half the weight to sustain, it will also have only one half the weight to raise; but observe, says Mrs. Marcet, that in raising the weight, the velocity of the hand must be double that of the cask; for, in order to raise the weight one inch, the hand must draw each of the strings one inch; the whole string is therefore shortened two inches, while the weight is raised only one. Pulleys then act on the same principle as the lever, the deficiency of strength of the power being compensated by its superior velocity. It will follow, from these premises, that the greater the number of pulleys connected by a string, the more easily the weight is raised, as the difficulty is divided amongst the number of strings, or rather of parts into which the string is divided by the pulleys. Several pulleys, thus connected, form what is called a system, or tackle of pulleys. They may have been seen suspended from cranes, to raise goods into warehouses, and in ships to draw up the sails.

THE INCLINED PLANE is a mechanic power which is seldom used in the construction of machinery, but applies more particularly to the moving or raising of loads upon slopes or hills, as in rolling a cask up or down a sloping plank into or out of a cart or cellar, or drawing a carriage up a sloping road or hill, all which operations are performed with less exertion than would be required if the same load were lifted perpendicularly. It is a power which cannot be resolved into that of the lever: it is a distinct principle, and those writers who have attempted to simplify the mechanical powers, have been obliged to acknowledge the inclined plane is elementary. The method of estimating the advantage gained by this mechanical power is very easy; for just as much as the length of the plane exceeds its perpendicular height, so much is the advantage gained; if, for instance, its length be three times greater than its height, a weight could be drawn to its summit with a third part of the strength required for lifting it up at the end; but, in accordance with the principle so frequently alluded to, such a power will be at the expense of time, for there will be three times more space to pass over. The reason why horses are eased by taking a zig-zag direction, in ascending or descending a steep hill, will appear from the preceding account of the action of the inclined plane, because in this way the effective length of the inclining surface is increased while its height remains the same.

THE WEDGE is rather a compound, than a distinct mechanical power; since it is composed of two inclined planes, and in action frequently performs the functions of a lever. It is sometimes employed in raising bodies; thus the largest ship may be raised to a small height by driving a wedge below it; but its more common application is that of dividing and cleaving bodies. As an elevator, it resembles exactly the inclined plane; for the action is obviously the very same, whether the wedge be pushed under the load, or the load be drawn under [sic] the wedge. But when the wedge is drawn forward, the percussive tremor excited destroys, for an instant, the adhesion or friction at its sides, and augments prodigiously the effect. From this principle chiefly is derived the power of the wedge in rending wood and other substances. It then acts besides as a lever, insinuating itself into the cleft as fast as the parts are opened by the vibrating concussion. To bring the action of the wedge, therefore, under a strict calculation, would be extremely difficult, if not impossible. Its effects are chiefly discovered by experience. All the various kinds of cutting tools, such as axes, knives, chisels, saws, planes, and files, are only different modifications of the wedge.

THE SCREW is a most efficient mechanic power, and is of great force and general application. It is in reality nothing more than an inclined plane formed round a cylinder, instead of being a continued straight line. Its power is, therefore, estimated by taking its circumference, and dividing this by the distance between any two of its threads; for what is taking the circumference of a screw, but another mode of measuring the length of the inclined plane which wraps round it? and taking the distance between one thread and the next to it, is but measuring the rise of that inclined plane in such length; and from the properties of the inclined plane, it follows, that the closer the threads of a screw are together in proportion to its diameter, the greater will be the power gained by it.

Note 24, p. 165.--THE CYCLOID.

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 mentioned in the text, viz. 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 cycloids, 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 in the shortest possible time, since that is the shortest of all lines that can be drawn between two points. Undoubtedly it is the shortest; notwithstanding which, however, the body would be longer in traversing it, than in moving through a cycloid. If a body were to move through a space of fifty or a hundred yards, by its weight and some other force acting together, the way it must take to do this in the shortest possible time is by moving in a cycloid. It is supposed that birds which build in the rocks possess an instinctive knowledge of this fact, and drop or fly down from height to height in this course. There is certainly a general resemblance between the curved path they describe on such occasions, and the cycloid, but it would be difficult to establish the fact by experiment. Man, however, has founded upon this principle some applications of great value in practical mechanics. In Switzerland, and in several parts of Germany, for example, slides have been constructed along the sides of mountains, by which the timber felled near their summits is conducted with extreme rapidity to the distant valleys.

Note 25, p. 171.--BILLIARDS.

This interesting game is of French origin (_billiard_, of _bile_, and from the Latin, _pila_, a ball). It was hailed as a favourite diversion at the court of Henry III. of France; and was thence communicated to all the courts of modern Europe. To the novice it may appear as a game of accidents and chances, but experience has enabled us to determine the effects of the stroke given to a ball with wonderful precision; and it is quite extraordinary to observe the accuracy with which an accomplished player can effect his object, by measuring with his eye the angle at which he should make the stroke, the position of the ball with respect to the cushion, and the distance of the point of the ball from its centre, at which it should be struck. By such skilful management the ball may be made to take directions which would, at first view, be regarded as contrary to all the known laws of motion, such, for instance, as passing round an object, such as a hat placed on the table, and to strike a ball behind it into a pocket.

Upon this subject the reader should consult a work by M. Mingaud, which has been translated and published by John Thurston, the celebrated billiard-table maker of Catherine Street, Strand. We understand that a still more complete work may be expected from the same source.

Note 26, p. 172.--COLLISION OF BODIES.

In investigating the effects produced upon bodies by collision, it is necessary to distinguish between elastic and non-elastic substances, since their motions after impact are governed by very different laws.

If two bodies, _void of elasticity_, move in one right line, either the same or contrary ways, so that one body may strike directly against another, let the _sum_ of their motions before the stroke, if they move the same way, and the _difference_ of their motions, if contrary ways, be divided into two such parts as are proportional to the quantities of matter in the bodies, and each of those parts will respectively exhibit the motion of each body after the stroke: for example, if the quantities of matter in the bodies be as _two_ to _one_, and their motions before the stroke as _five_ and _four_, then the sum of their motions is _nine_, and the difference is _one_; and therefore, when they move the same way, the motion of that body, which is as _two_, will, after the stroke, be _six_, and the motion of the other, _three_; but, if they move in contrary directions, the motion of the greater body after the stroke will be _two-thirds of one_, and of the lesser body _one-third of one_; for, since the bodies are void of elasticity, they will not separate after the stroke, but move together with one and the same velocity; and, consequently, their motions will be proportional to their quantities of matter; and it follows from the fact of action and reaction being equal, that no motion is either lost or gained by the stroke when the bodies move the same way; because, whatever motion one body imparts to the other, so much must it lose of its own; and, consequently, the _sum_ of their motions before the stroke is neither increased nor diminished by the stroke, but is so divided between the bodies, as that they may move together with one common velocity; that is, it is divided between the bodies in proportion to their quantities of matter: but it is otherwise, where the bodies move in opposite directions, or contrary ways, for then the smaller motion will be destroyed by the stroke, as also an equal quantity of the greater motion, because action and reaction are equal; and the bodies, after the stroke, will move together equally swift, with the _difference_ only of their motions before the stroke; consequently, that difference is, by means of the stroke, divided between them in proportion to their quantities of matter.

The several particular cases, concerning the collision of bodies, may be reduced to four general ones; viz.

1st. It may be, that one body only is in motion at the time of the stroke.

2nd. They may both move one and the same way.

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.”

“The lips do not all point in the same direction, some tending to the south, some to the west, others to the north, and others again to the intermediate points of the compass; _by which it seems as if the makers had been determined in this particular, not by any mystical veneration for one region of the heavens more than another, but by the shape and inclination of the rock, and for the most easy and convenient outlet_.” We must here beg the reader to pause. The above remark is really too valuable to be suffered to pass without some notice. And so the absence of all design and arrangement is adduced as a proof of their artificial origin! What would Dr. Borlase have said, had all these lips been found to point in the same direction? But to proceed:

“The size of rock-basins is as different as their shape; they are formed from six feet to a few inches in diameter. Many uses may suggest themselves to the imaginations of the curious from the description of these new, and hitherto scarce-mentioned monuments; in order, therefore, to obviate some prepossessions, and prevent the mind from resting so far on groundless suppositions as may make it more difficult to embrace the truth, I shall first consider what, in all probability, _cannot_ have been the design of them.”

The doctor then proceeds to show that they could never have been intended for evaporating salt; nor for pounding tin ore, nor for receiving obelisks, or stone deities, nor for altars; and then suggests that they could be no other than vessels most ingeniously contrived for holding holy-water for the rites of washing and purification. “If,” adds the learned antiquary, “fitness can decide the use--and where history is deficient, it is all reason that it should--we shall not long be at a loss. They are mostly placed above the reach of cattle, frequently above the inspection of man; nay, the stones which have these basins on them, do not touch the common ground, but stand on other stones.--Wherefore? but that the water might neither be really defiled by the former, nor incur the imaginary impurity, which touching the ground, according to the druid opinion, gave to every thing that was holy.” We do not know what ideas the druids entertained with respect to the purity of water, but we have seen water in some of these pools so impregnated with the excrement of sea-birds, that we must have been as thirsty as Tantalus, before we could have been induced to cool our tongues with it.

“But,” adds Dr. Borlase, “there are some basins which have no lip or channel; and, therefore, as they could not contribute any of their water to the common store, they _must_ have been appropriated to another use; and since these are found in the same places with the others above-mentioned which have outlets or mouths to them, they must have been subservient to the same system of superstition, though in a different method.”

“These basins are sometimes found near twenty feet high from the common surface; and, therefore, being so withdrawn from vulgar eyes, so elevated from the ground, which was supposed, as I said before, to defile all, they had likely a proportionably greater degree of reverence, and their waters accounted more holy, and more efficacious.”

We shall not trouble the reader with any further quotations from this learned antiquary, except in concluding the history, after the fashion of melo-dramatists, with a splendid scene, in which, with the author’s assistance, we shall bring all the performers on the stage, dressed in appropriate costume, and surrounded by all the pomp of druidical worship.

“From these basins,” says Dr. Borlase, “on solemn occasions the officiating druid, standing on an eminence, sanctified the congregation with a more than ordinarily precious lustration before he expounded to them, or prayed for them, or gave forth his decisions. This water he drank, or purified his hands in, before it touched any other vessel, and was consequently accounted more sacred than the other holy-water. To these more private basins, during the time of libation, the priest might have recourse, and be at liberty to judge by the quantity, colour, motion, and other appearances in the water, of future events, of dubious cases, without danger of contradiction from the people below. This water might serve to mix their mistletoe withal, as a general antidote: for, doubtless, those who would not let it touch the ground, would not mix this their divinity (the mistletoe) with common water. Oak leaves, without which the druid rites did scarce ever proceed, ritually gathered and infused, might make some very medicinal or incantorial potion. Lastly, libations of water were never to be made to their gods, but when they consisted of this purest of all water, as what was immediately come from the heavens, and partly therefore thither to be returned, before it touched any other water or any other vessel whatsoever, placed on the ground.”

“As _logan_, or rocking-stones, were some of the _piæ fraudes_ of the druids, the basins found on them might be used to promote the juggle; by the motion of the stone the water might be so agitated, as to delude the enquirer by a pretended miracle; might make the criminal confess; satisfy the credulous; bring forth the gold of the rich; and make the injured, rich as well as poor, acquiesce in what the druid thought proper.”

Sorry are we to destroy a web which has been so ingeniously woven by its author; but the interests of truth admit not of compromise. Dr. Macculloch, in an interesting paper, published in the Transactions of the Geological Society, on the decomposition of the granite tors of Cornwall, has justly observed, that the true nature of these rock-basins may be easily traced by inspecting the rocks themselves. On examination, they will always be found to contain distinct grains of _quartz_, and fragments of the other constituent parts of the granite. A small force is sufficient to detach from the sides of these cavities additional fragments, showing that a process of decomposition is still going on under favourable circumstances. The principal of these circumstances is the presence of water, or rather the alternate action of air and water. If a drop of water can only make an effectual lodgement on a surface of this granite, a small cavity is sure to be sooner or later produced; this will insensibly enlarge as it becomes capable of holding more water; and the sides, as they continue to waste, will necessarily retain an even and rounded cavity, on account of the uniform texture of the rock. This explanation is sufficiently satisfactory: in addition to which, it may be stated, that these very basins not unfrequently occur on the perpendicular sides of rocks, as may be distinctly seen in the granite of Scilly, and in the gritstone rocks in the park of the late Sir Joseph Banks, in the parish of Ashover, in Derbyshire; a fact which at once excludes the idea of their artificial origin.

The other grotesque and whimsical appearances of rocky masses, such as _rock idols_, _logan stones_, _&c._ are to be explained by the tendency which granite possesses of wearing more rapidly on the angles and edges than on the sides; thus, then, upon simple and philosophical principles, are such appearances to be satisfactorily accounted for, and the _phantasmagoria_ of Borlase vanishes as the light penetrates the theatre so long dedicated to its exhibition.

We shall conclude this note with a few observations upon the celebrated logan, or logging, stone, near the Land’s End, Cornwall, of which we present our readers with a faithful sketch.

The foundation of this part of the coast is a stupendous group of granite rocks, which rise in pyramidal clusters to a great altitude, and overhang the sea. The celebrated _logan stone_ here represented is an immense block weighing above sixty tons. The surface in contact with the under rock is of very small extent, and the whole mass is so nicely balanced, that, notwithstanding its magnitude, the strength of a single man applied to its under edge is sufficient to make it oscillate. It is the nature of granite to disintegrate into rhomboidal and tabular masses, which, by the further operation of air and moisture, gradually lose their solid angles, and approach the spheroidal form. The fact of the upper part of the cliff being more exposed to atmospheric agency than the parts beneath, will sufficiently explain why these rounded masses so frequently rest on blocks which still preserve the tabular form; and since such spheroidal blocks must obviously rest in that position in which their lesser axes are perpendicular to the horizon, it is equally evident that, whenever an adequate force is applied, they must vibrate on their point of support.

Although we are thus led to deny the druidical origin of this stone, for which so many zealous antiquaries have contended, still we by no means intend to deny that the druids employed it as an engine of superstition; it is possible that, having observed so curious a property, they dexterously contrived to make it answer the purposes of an ordeal, and, by regarding it as the _touch-stone_ of truth, acquitted or condemned the accused by its motions. Mason poetically alludes to this supposed property in the following lines:--

“Behold yon huge
And unknown sphere of living adamant,
Which, poised by magic, rests its central weight
On yonder pointed rock; firm as it seems,
Such is its strange and virtuous property,
It moves obsequious to the gentlest touch
Of him whose heart is pure, but to a traitor,
Tho’ e’en a giant’s prowess nerved his arm,
It stands as fixed as Snowdon.”

Note 28, p. 186.--ANIMAL SUCTION.

We are indebted to Sir Everard Home for a description of that peculiar structure by which several species of animals are enabled to sustain their bodies in opposition to the force of gravity. His first paper upon this subject is published in the 106th volume of the Philosophical Transactions, in which he says, he was not aware that any animal, larger than the house-fly, was endowed by nature with such a power, so as to admit of examination, until Sir Joseph Banks mentioned that the _lacerta gecko_, a species of lizard, which is a native of the island of Java, comes out of an evening from the roofs of the houses, and walks down the smooth, hard, and polished chinam walls, in search of the flies which settle upon them, and which are its natural food, and then runs up again to the roof of the house. Sir Joseph, while at Batavia, amused himself with catching this animal, by standing close to the wall, at some distance from the lizard, with a long flattened pole, which being made suddenly to scrape the surface of the wall, knocked the animal down. He presented Sir Everard with a specimen weighing five ounces and three quarters, avoirdupois, which enabled him to ascertain the peculiar mechanism by which the feet of this animal can keep their hold of a smooth, hard, perpendicular wall, and carry up so large a weight as that of its body.