Chapter 32

Note 14, p.99.--Vegetable elasticity.

Impatiens, orTouch me not, affords a good example. The seed-vessel consists of one cell with five divisions; each of these, when the seed is ripe, on being touched, suddenly folds itself into a spiral form, leaps from the stalk, and disperses the seeds to a great distance by its elasticity. The capsule of the geranium and the beard of wild oats are twisted for a similar purpose. (Darwin’sBotanic Garden.) The seed-vessel of Euphorbia is extremely elastic, projecting the seeds with great force. An elastic pouch also serves to scatter the seeds of the Oxalis.

Note 15, p.125.--A simple orrery.

A very instructive toy might be constructed by placing a taper in the centre of a japanned waiter, to represent the sun, and fixing in a watch glass an indian rubber ball, with the parallels of latitude and meridians painted thereon, with the other characters of the globe. During its revolution around the candle, in consequence of the tendency of its centre of gravity to its lowest position, the diurnal and annual motions, and also the parallelism of its axis, will be represented, together with the concomitant phenomena.

Note 16, p.130.--Conic sections.

If a cone, or sugar-loaf, be cut through in certain directions, we shall obtain figures which are termedconic sections; thus, if we cut through the sugar-loaf in a direction parallel to its base, or bottom, the outline or edge of the loaf where it is cut will be acircle. If the cut is made so as to slant, and not be parallel to the base of the loaf, the outline is anellipse, provided the cut goes quite through the sides of the loaf all round; but if it goes slanting, and parallel to the line of the loaf’s side, the outline is aparabola, a conic section, or curve, to which this note more immediately relates. This curve is distinguished by characteristic properties, every point of it bearing a certain fixed relation to a certain point within it, as the circle does to its centre.

Note 17, p.134.--Earthquake of Lisbon.

During the dreadful earthquake of Lisbon, bands of wretches took advantage of the general consternation to commit the most atrocious acts of robbery and murder. In fact, a considerable part of the city was destroyed by incendiaries, who, during the disaster, set fire to the houses, that they might pillage them with greater impunity.

Note 18, p. 134.--Geology applied to agriculture.

Soils consist of a mixture of different finely divided earthy matter, with animal or vegetable substances in a state of decomposition. In order, therefore, to form a just idea of their nature, it is necessary to conceive different rocks decomposed, or ground into parts and powder of different degrees of fineness; some of their soluble parts dissolved by water, and that water adhering to the mass, and the whole mixed with larger or smaller quantities of the remains of vegetables and animals, in different stages of decay. Hence it will follow, that certain rocks will give origin to particular soils; thus poor and hungry soils, such as are produced from the decomposition of granite and sandstone, remain very often for ages with only a thin covering of vegetation; while soils from the decomposition of limestone, chalk, and basalt, are often clothed by nature with the perennial grasses; and afford, when ploughed up, a rich bed of vegetation for every species of cultivatedplant. In adverting to this subject, Dr. Buckland, in his inaugural lecture, very justly observes, that it furnishes an instance of relation between the vegetable and mineral kingdoms, and of the adaptation of one to the other, which always implies design in the surest manner; for had not the surface of the earth been thus prepared for their reception, where would have been the use of all that admirable system of organization bestowed upon vegetables? And it is no small proof of design in the arrangement of the materials that compose the surface of our earth, that whereas the primitive and granitic rocks are least calculated to afford a fertile soil, they are for the most part made to constitute the mountain districts of the world, which, from their elevation and irregularities, would otherwise be but ill adapted for human habitation; whilst the lower and more temperate regions are usually composed of derivative or secondary strata, in which the compound nature of their ingredients qualifies them to be of the greatest utility to mankind by their subserviency to the purposes of luxuriant vegetation.

No doubt, then, can exist as to the important connexion between the geological structure of a country, and its degree of fertility; but the subject has not received the attention which it merits. And in the hope that this note may meet the eye of some zealous geologist, the author suggests the importance of commencing the enquiry in a primitive district; for, as we advance from a primitive to an alluvial district, the relations to which we have alluded become gradually less distinct and apparent, and are ultimately lost in the confused complication of the soil itself, and in that general obscurity which necessarily envelopes every object in a state of decomposition: we can, therefore, only hope to succeed in such an investigation, by a patient and laborious examination of a primitive country, after which we may be enabled to extend our enquiries with advantage through those districts which are more completely covered with soil, and obscured by luxuriant vegetation; as the eye, gazing upon a beautiful statue, traces the outline of the limbs, and the swelling contour of its form, through the flowing draperies which invest it.

Note 19, p.135.--Buckland’s researches.

The geological researches of Dr. Buckland have been long directed by a desire to accumulate facts to prove thatthere must have been an universal inundation of the earth; and, in his inaugural lecture, he has presented us with a summary of such facts, which, to use his own expression, whether considered collectively or separately, present such a conformity of proofs, tending to establish the universality of a recent inundation of the earth, as no difficulties or objections that have hitherto arisen are in any way sufficient to overrule.

In the year 1822, Dr. Buckland read a memoir before the Royal Society, announcing the discovery of a singular cave at Kirkdale in Yorkshire, containing an assemblage of fossil teeth and bones of the elephant, rhinoceros, hippopotamus, bear, tiger, and hyæna, and sixteen other animals; with a comparative view of five similar caverns in various parts of England, and others on the continent. For this important paper the society awarded to its author their Copley medal; and it constitutes the basis of a later and much more extended work, entitled “Reliquiæ Diluvianæ; or Observations on the Organic Remains contained in Caves, Fissures, and Diluvial Gravel; and on other Geological Phenomena, attesting the Action of an Universal Deluge. By the Rev.W. Buckland, B.D. F.R.S. &c.”

Let us explore the interior of this cavern. It was not till the summer of 1821, that the existence of any animal remains, or of the cavern containing them, was suspected. At this time, in continuing the operations of a large quarry, the workmen accidentally intersected the mouth of a long hole, closed externally with rubbish, and overgrown with grass and bushes. As this rubbish was removed before any competent person had examined it, it is not certain whether it was composed of diluvial gravel and rolled pebbles, or was simply the debris that had fallen from the softer portions of the strata that lay above it: the workman, however, who removed it, and some gentlemen who saw it, assured Dr. Buckland that it was composed of gravel and sand. In the interior of the cavern, our indefatigable geologist could not find a single rolled pebble, nor has he ever seen one bone, or fragment of bone, that bore the slightest mark of having been rolled by the action of water.

The original entrance is said to have been very small, and, having been filled up as above described, there could not have been any admission of external air through it to the interior of the cavern. Nearly 30 feet of its outer extremityhave now been removed, and the present entrance is a hole in the perpendicular face of the quarry, about three feet high and five feet broad, which it is only possible for a man to enter on his hands and knees, and which expands and contracts itself irregularly from two to seven feet in breadth, and two to fourteen feet in height. It is unnecessary to enter into farther details; the reader, if he wishes more minute information, may consult Dr. Buckland’s work.

On entering the cave, the first thing observed was a sediment of soft mud or loam, covering entirely its whole bottom to the average depth of about a foot, and concealing the subjacent rock, or actual floor of the cavern. Not a particle of mud was found attached either to the sides or roof; nor was there a trace of it adhering to the sides or upper portions of the transverse fissures, or any thing to suggest the idea that it had entered through them. The mud was covered by astalagmiticcrust, which had been formed by the dripping of water impregnated with calcareous matter, as is common in all the cavities of limestone; but it is important to remark, that there was not any alternation of mud with any repeated beds ofstalagmite, but simply a partial deposit of the latter on the floor beneath; so that the mud was encased, like meat in a pie, with an upper and under crust. It was chiefly in the lower part of the earthy sediment, and in the calcareous matter beneath it, that the animal remains were found.

In the whole extent of the cave, only a very few large bones have been discovered that are tolerably perfect; most of them are broken into small angular fragments and chips, the greater part of which lay separately in the mud, whilst others were wholly or partially invested with stalagmite, and others again mixed with masses of still smaller fragments. In some few places, where the mud was shallow, and the heaps of teeth and bones considerable, parts of the latter were elevated some inches above the surface of the mud and its calcareous crust; and the upper ends of the bones thus projecting, like the legs of pigeons through a pie crust, into the void space above, have become thinly covered with calcareous drippings, whilst their lower extremities have no such incrustation, and have simply adhering to them the mud in which they have been imbedded.

The effect of the loam and stalagmite in preserving thebones from decomposition, by protecting them from all access of atmospheric air, has been very remarkable.

The workmen, in first discovering the bones at Kirkdale, supposed them to have belonged to cattle that died by a murrain in this district a few years ago, and they were for some time neglected, and thrown on the roads with the common limestone; they were, at length, noticed by Mr. Harrison, a medical gentleman in the neighbourhood, and have since been collected and deposited in various private and public museums. The teeth and bones which have been discovered in this cave appear to have belonged to thehyæna, tiger, bear, wolf, fox, weasel, elephant, rhinoceros, hippopotamus, horse, ox, deer, hare, rabbit, water-rat, mouse, raven, pigeon, lark, snipe, and a small species ofduck.

The bottom of the cave, on first removing the mud, was found to be strewed all over like a dog-kennel, from one end to the other, with hundreds of teeth and bones, or rather broken and splintered fragments of bones, of all the animals above enumerated; scarcely a single bone has escaped fracture, with the exception of some of the more solid and hard bones of the foot; on some of these bones marks may be traced, which, on applying one to the other, appear exactly to fit the form of the canine teeth of the hyæna that occur in the cave. The hyæna’s bones have been broken, and apparently gnawed equally with those of the other animals. Heaps of small splinters, and highly comminuted, yet angular fragments of bone, mixed with teeth of all the varieties of animals above enumerated, lay in the bottom of the den, occasionally adhering together by calcareous cement. Not one skull is to be found entire; and it is so rare to find a large bone of any kind that has not been more or less broken, that there is no hope of obtaining materials for the construction of a single limb, and still less of an entire skeleton. The jaw-bones, also, even of the hyænas, are broken to pieces like the rest.

It must already appear probable, from the facts above described, particularly from the comminuted and gnawed condition of the bones, that the cave at Kirkdale was, during a long succession of years, inhabited as a den by hyænas, and that they dragged into its recesses the other animals, whose remains are found indiscriminately mixed with their own: an hypothesis which is certainly strengthened by Dr. Buckland having found the excrement of theanimal in the same cave. Should it be asked why we do not find, at least, the entire skeleton of the one or more hyænas that died last, and left no survivors to devour them; we find a sufficient reply to this question, in the circumstance of the probable destruction of the last individuals by the waters of the deluge. On the rise of these, had there been any hyænas in the den, they would have rushed out, and fled for safety to the hills; and if absent, they could not by any possibility have returned to it from the higher levels; that they were extirpated by the catastrophe is obvious, from the discovery of their bones in the diluvial gravel both of England and Germany.

The accumulation of these bones, then, appears to have been a process of years, whilst all the animals in question were natives of this country. The general dispersion of bones of the same animals through the diluvial gravel of high latitudes, over a great part of the northern hemisphere, shows that the period in which they inhabited these regions was that immediately preceding the formation of this gravel, and that they perished by the same waters which produced it. M. Cuvier has, moreover, ascertained that the fossil elephant, rhinoceros, hippopotamus, and hyæna, belong to species now unknown; and as there is no evidence that they have at any time, subsequent to the formation of the diluvium, existed in these regions, we may conclude that the period at which the bones of these extinct species were introduced into the cave at Kirkdale was before the deluge.

Thus the phenomena of this cave seem referable to a period immediately antecedent to the general deluge, and in which the world was inhabited by land animals, almost all bearing a generic, and many a specific resemblance to those which now exist; but so completely has the violence of that tremendous convulsion destroyed and remodelled the form of the antediluvian surface, that it is only in caverns that have been protected from its ravages, that we may hope to find undisturbed evidence of events in the period immediately preceding it. The bones already described, and the calcareous matter formed before the introduction of the diluvial mud, are what Dr. Buckland considers to be the products of the period in question. It was indeed probable, before the discovery of this cave, from the abundance in which the remains of similar speciesoccur in superficial gravel beds, which cannot be referred to any other than a diluvial origin, that such animals were the antediluvian inhabitants not only of this country, but generally of all those northern latitudes in which their remains are found, (but the proof was imperfect, as it was possible they might have been drifted or floated hither by the waters from the warmer regions of the earth,) but the facts developed in this charnel-house of the antediluvian forests of Yorkshire demonstrate that there was a long succession of years, in which the elephant, rhinoceros, and hippopotamus had been the prey of the hyænas, which, like themselves, inhabited England in the period immediately preceding the formation of the diluvial gravel. Having thus far described the principal facts to be observed in the interior of this cave, Dr. Buckland proceeds to point out the chronological inferences that may be derived from the state of the bones, and of the mud and stalagmite that accompany them, and to extract the following detail of events that have been going on successively within this curious cave:--

First, There appears to have been a period (and, if we may form an estimate from the small quantity of stalagmite now found on the actual floor of the cave, a very short one,) during which this aperture in the rock existed in its present state, but was not tenanted by the hyænas.

The second period was that during which the cave was inhabited by the hyænas, and the stalactite and stalagmite were still forming.

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 calledrifling, 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 ofriflingmight 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 theRivers 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 thecentre 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 theprecession 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 beinginfinite, it would continue to revolve for ever, in the same position, without gyration. If the velocity werefinite, 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, orsleeping, 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 orsleepingpoint; 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 thatthe 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, orarc, 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; henceone 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 theLEVER. There are, besides, five others, viz. thewheel and axle; theinclined plane; thescrew; thepulley; and thewedge; out of the whole, or a part of which, it will be found that every mechanical engine or piece of machinery is constructed.

The Leverbeing 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 itsfulcrum. 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 thepower,resistance, andfulcrumadmit 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 thefulcrum, 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 resistingarm, 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 fromthe 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 Axleis 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 windmilldepends upon a similar power. Thetreadmillfurnishes 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 Pulleyis 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 difficultyis 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 Planeis 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 Wedgeis 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 exciteddestroys, 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 Screwis 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.

Acycloidis 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 theexception 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.

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