Friction acts as a retarding influence in the action of all mechanical contrivances, and a due allowance must in every case be made for it. In many instances it destroys more than a half of the power employed, and seldon destroys less than a third. However small it may be, it sooner or later causes the wearing down and destruction of mechanism, and therefore forms an insurmountable obstacie to the lasting duration of bodies and the perpetuity of motion. Friction is found to depend on the following circumstances:-1st, The degree of roughness of the surfaces. 2d, The weight of the body to be moved. 3d, The extent of surfaces in certain bodies presented to the action of rubbing. 4th, The nature of the bodies. 5th, The degree of velocity of the motion. 6th, The manner of the motion. Roughness. It is of the utmost importance to smooth the surfaces. An apparently insignificant piece of matter, or even particles of dust, will greatly retard the motion of a body. But there is a limit beyond which it would be imprudent to smooth the surfaces of bodies having a close texture. If the surfaces be highly polished and levelled, the bodies will adhere by the effect of attraction of cohesion, even when the atmospheric air is not entirely expelled from between them, and more forcibly when the air is completely expelled. Practically, roads, railways, and similar bodies, cannot be made too smooth. Weight.-Friction from weight differs in different bodies, and depends on concurring circumstances, as nature of surface, and so forth. Friction always increases in exact proportion as the weight increases, when all other circumstances remain the same. The parts of machinery, therefore, should be made as light as possible, consistent with strength and durability. Extent of surfaces.-Rough bodies are more easily drawn along when their surface of contact is narrow than when they are broad. For example, it is easier to draw two narrow brushes across each other, than two broad ones of the same weight. Friction may, therefore, be diminished in rough bodies by lessening the extent of surfaces in contact. But there is a limit to this diminution. If the moving surface be very thin, and the other soft, the thin surface will plough a groove in the soft one, and thus the friction will be increased, and the machine injured. Nature of Bodies. It is a remarkable truth that two bodies which are of the same nature, or homogeneous, produce greater friction in movement than bodies which are different in their nature, or heterogeneous. Thus, iron working against iron, steel against steel, or brass against brass, causes in each case greater friction and wearing of parts, than when iron or steel is made to work against brass. This circumstance is always attended to in the construction of machinery. Frequently, a small piece of leather is adjusted round an axle, to prevent the metals from coming in contact. Degree of Velocity. Friction is a uniformly retarding force, except in the case of small velocities, when it is greater in proportion. The reason for it being greater in small velocities is, that in these cases time is allowed for the prominences of the moving body to sink deeply into the hollows of the surface on which it is moving, which has a retarding effect. Manner of the Motion. The least advantageous manner in which one body can be moved upon another, is to cause it to slide or drag. The most advantageous manner is to cause it to roll or turn. The causing of a body to roll instead of to slide, is one of the chief means of diminishing friction. The opposition presented by inequalities of surface to a rolling wheel, is overcome with ease, in proportion to the extent of On a perfectly horizontal plane, the friction of wheels on the plane is very inconsiderable; the chief seat of friction in such cases being diameter of the wheel. in the axles working in their sockets. Friction is greatly diminished by lubricating the rubbing surfaces with an oily or greasy substance, which substance forms a medium of small soft particles betwixt the bodies, and so prevents the tendency to grind or wear down the surfaces. Water or any similar fluid will also act as a medium to prevent friction, but the effects are only temporary, and would frequently be injurious, as the substance speedily evaporates, and would corrode metals. I'ractically, fine pure oil is found to be the best unguent for machinery. One of the first considerations on the part of contrivers of mechanism, should be how to provide for and diminish the effects of friction in their machines. For want of forethought on this important point, thousands of ingenious schemes, which seemed perfect in the form of models and drawings on paper, have been completely frustrated when attempted to be brought into use. Whatever may be the retarding and frequently inconvenient effects of friction, in reference to the action of mechanism, it is certain that friction is indispensable in the economy of both nature and art, and serves as an essential auxiliary to gravitation. It is a property which is frequently necessary, in order to allow one kind of matter to possess a hold upon another, without actual cohesion. We walk and maintain our erect posture by means of gravitation and action and reactionin other words, we are held to the earth by gravitation, and our pressure with our feet exemplifies action and reaction; but if there was no such property as friction, we should either stick to the earth by attraction of cohesion, or slide along it as upon the smoothest ice. In order to keep our feet from sliding when on ice, if we received any impulse, we either tie rough substances on our shoes, or scatter ashes in our path; and thus we receive the benefit of friction. It is by friction that rains wear down hills, and that rivers wear away their banks, by which ceaseless process the external configu ration of the globe is constantly undergoing a change. The operations in art, of washing, cleaning, scouring, sharpening, polishing, cutting, bruising, beating, and so forth, are all effected less or more by friction. The hold which one fibrous substance has on another, or mutual friction, permits the operations of weaving cloth, twisting ropes and threads, and the tying of one body to another. Thus, friction is of universal service; and the only known instances in nature in which it is not required, and therefore not present, are the movements of the heavenly bodies, which revolve in a vacuum, and are consequently not impeded in their motions. RESISTANCE OF AIR AND WATER. Atmospheric air and water are fluids of different densities, and both present an obstacle to the motion of solid bodies through them. There is a rule in respect to the resistance presented in moderate velocities, which applies both to air and water. It is, that the resistance is proportional to the square of the velocity. For example, a velocity of twenty niles an hour causes a resistance four times greater than a velocity of ten miles an hour, for the square of twenty (which is 20 times 20, or 400) is four times the square of ten (which is 10 times 10, or 100). Thus, by increasing the velocity of bodies through the air or water, we must increase the power in a greater proportion, in order to compensate the loss caused by resistance. Although the above rule is nearly correct for mode. rate velocities, it deviates considerably from what is observable in the case of great velocities, such as that of a cannon-ball. When the velocity is upwards of 1000 feet per second through the air, the quick passage of the body is believed to cause a partial vacuum behind it, which causes a retardation of its motion. Resistance to motion in fluids is greatly modified, also, by the form of the moving body. The form that gives least resistance is nearly that of a parabola, or a form somewhat resembling the breast of a duck, the head of a fish, or the rounded bow of a vessel, sharpened to cleave the fluid through which the body passes. Printed and published by W. and R. CHAMBERS, Edinburgh. Sold also by W. S. Orr & Co., London. NUMBER 53. CONDUCTED BY WILLIAM AND ROBERT CHAMBERS, EDITORS OF CHAMBERS'S NEW AND IMPROVED SERIES. PRICE lad. HYDROSTATICS-HYDRAULICS-PNEUMATICS. GENERAL DEFINITIONS. MATTER exists in three principal forms-solid, liquid, and gaseous or aëriform. These forms respectively, and the various modifications of them, are the immediate result of certain principles of attraction and repulsion operating on the atoms or particles of which matter is composed. The solid, liquid, and aëriform varieties of matter, assume a position on our globe corresponding to their heaviness or density in a given volume. The solid sinks lowest, and composes the chief mass of the earth; above the solid lies the liquid variety, in the form of the ocean, rivers, and lakes; and above all is the atmosphere, consisting of an expanse of aëriform matter, which wraps the whole earth round to an elevation of from fortyfive to fifty miles above the highest mountains. In this great ocean of air, loaded less or more with particles of moisture from the liquids beneath, we live, breathe, and move, and plants grow and receive an appropriate nourishment. Though differing both in substance and appearance, the liquid and aeriform varieties of matter resemble each other in many of their properties and tendencies, and constitute the class of bodies termed fluids. Fluids siguify bodies which will flow, or whose component particles are easily moved among each other. Some fluids are so thick and viscous, or sticky, that they can scarcely flow, as tar, honey, and some metals in a state of fusion; others flow with ease, as water and distilled spirits; while others are so light and volatile, as to be impalpable to the touch and invisible to the eye, as pure atmospheric air and various gases. It is common to divide fluids into two kinds-nonelastic fluids and elastic fluids; that is, fluids which cannot be compressed into a smaller bulk, and those which are susceptible of compression. The non-elastic fluids are water and all other varieties of liquid bodies; but recent experiments prove that the term is not strictly applicable to them. It has been found that water may be compressed in a confined vessel, to a small extent, by means of a very great pressure, and it is certain that water at a considerable depth in the ocean is more dense or compressed than at the surface; water, consequently, is an elastic substance; but as it can be compressed only with very great difficulty, the term non-elastic fluid is not altogether inappro priate. Atmospheric air and all gases are elastic. They can with little difficulty be compressed into a much smaller volume than they ordinarily possess; and when the pressure is removed, they return to their original bulk. Some gases may be compressed to such an extent as to assume the form of liquids and solids; in other words, from the condition of being perfectly invisible to the eye, they can be made to appear as a piece of solid matter, which may be touched and handled. In treating the subject of fluids, it is convenient to refer in the first place to those which are of the liquid form, and afterwards to those which are elastic or aëriform. Pure water, at an ordinary temperature, furnishes the most suitable example of liquid bodies. Water also gives the name of the department of science which includes the laws of liquids. Thus, Hydrostatics, from two Greek words signifying water and to stand, treats of the weight, pressure, and equilibrium of liquids in a state of rest; and Hydraulics, from two Greek words signifying water and a pipe, treats of liquids in motion, and the artificial means of conducting liquids in pipes, or raising them by pumps. mmmmm HYDROSTATICS. In ancient times water was believed to be an element or simple substance in nature. It is now ascertained by experiment that water is not an elementary body, but is a substance composed chiefly of two gases in a state of chemical union, and into these gases it can be resolved by an artificial process. The investigation of this subject belongs to Chemistry. As a liquid, water consists of exceedingly small particles or atoms of matter in mechanical combination. The exact nature and form of the atoms composing water are not satisfactorily known, in consequence of their exceeding smallness. They may be compared to very small particles of sand, cohering slightly, and easily slipping or sliding over each other. Whatever may be the nature and form of these exquisitely fine atoms, it is certain that they can adhere firmly together so as to assume the form of a solid, as in the case of ice, and be made to separate from each other, and disperse through the thinner fluid of the atmosphere, in the forms of steam, clouds, or mist. Thus, imperfect cohesion of atoms or particles is a property common to all fluids. The atoms composing water, being in closer union than those of air, are observable as a mass, and palpable to the touch. When the hand is dipped into them, and then withdrawn, a certain quantity of the atoms is brought away on the surface of the skin; and this adhesion of the particles of water (caused by attraction of cohesion) is what we in ordinary language call wetness. Certain substances, as is well known, absorb water to a great extent; in such cases, the minute particles of the water merely penetrate and fill up the crevices in the substance. Solid bodies, as a stone, or piece of metal, or wood, have a natural tendency to press only in one direction, that is downwards, or in the direction of the earth's centre, in obedience to the law of terrestrial attraction. Water has a similar natural tendency to press downwards, and from the same cause; as, for example, when a jug of water is spilled, the water is seen to fall in a Pressure equally in all directions may be considered as the first or great leading law in reference to water, and generally all fluids, liquid and gaseous. The pressure equally in all directions is a result of the exceeding smallness of the individual particles, and of the perfect ease with which they glide over or amongst each other. To exemplify equal pressure, fill a leathern bag with water, and then sow up the mouth of the bag so closely that none of the water can escape. Now, squeeze or press upon the bag so as almost to make it burst. The pressure so applied does not merely act upon the water immediately under the point of pressure, but acts equally upon every particle of water in the mass-the particles at the centre being as much pressed upon as those at the outside; and it will be observed that the water will squirt out with equal impetuosity at whatever part you make a hole in the surface. E tapering to a narrow base CD. The dotted enclosure Fig. 1. A If we take a vessel of the same capacity, but with a broad base, as in fig. 2, the pressure on the bottom is very different. In this case, the base EF sustains a pressure equal to the weight of a column whose base is EF, and height equal to AC; for the water in the central ABCD presses laterally E or sidewise, with the same force as it does on the part on which it stands; and thus an uniformity of pressure is established over every part of the bottom. column Fig. 2. In this, as in all similar cases, there is a transmission of pressure throughout the mass. Each particle presses on those next it; and so, by the force communicating from particle to particle, the whole are equally affected. In the case of water lying at repose in an open vessel, the tendency to press equally in all directions is not observed to act upward, because the gravity of the mass From these two cases combined, the reason is evident keeps the water down; but on pressing upon the sur- why fluids contained in the several parts of vessels face of the liquid, we observe that it rises against the remain every where at the same height; for the lowest compression, or tries to escape in any way it can. To part where they communicate may be regarded as the take another example-if we plunge our hand into a common base; and the fluids which rest thereon are in vessel of water, we displace so much liquid, and cause equilibrio then only, when their heights are equal, howit to rise higher up the sides of the vessel. In this case ever their quantities may vary. the water is observed to rise without any reluctance; it as readily presses upward as downward. Although it is a property in fluids to press equally in all directions, the degree of intensity of pressure in any mass of fluid is estimated by the vertical height of the mass, and its area at the base. Pressure of water in proportion to its vertical height, and its area at the base, is therefore a second leading feature in the laws of water. In other words, the pressure of a column of water does not depend on the width or thickness of the column, but on its height and the extent of its base or lower part. The whole of any fluid mass may be imagined to consist of a number of columns of an inconsiderable thickness, which stand perpendicularly on the horizontal base of the containing vessel, and press the base of the vessel with their respective weights. The pressure, then, if the height of the fluid be the same throughout, is as the number of columns, and this number is according to the area of the base. Consequently, in vessels whose bases differ as to area, and which contain fluids of the same density, but different heights, the pressure will be in the compound ratio of the bases and heights. If the columns of which a fluid mass was supposed to consist, were formed of particles lying in perpendicular lines, the pressure of the fluid would be exerted on the bottom of the vessel only; but as they are situated in every irregular position, there must of consequence be a pressure exerted in every direction, which pressure must be equal at equal depths. For if any part of the whole mass were not equally pressed on all sides, it would not move towards the side on which the pressure was least, and would not become quiescent till such equal pressure was obtained. The quiescence of the parts of fluids is therefore a proof that they are equally pressed on all sides. Several interesting experiments may be made to prove that the pressure of water is in proportion to its height and width of base. Figure 1 represents a vessel with a broad top EE, various ways. The K We may prove the truth of these propositions in Let ABCD, fig. 3, represent a cylindri cal vessel, to the inside of which is fitted the cover G, which, by means of leather at the edge, will easily slide up and down in the internal cavity, without permitting any water to pass between it and the surface of the cylinder. In the cover is inserted the small tube EF, open at top, and communicating with the inside of the cylinder below the cover at G. cylinder is filled with water, and the cover put on. Then if the cover be loaded with the weight, suppose of a pound, it will be depressed, the water will rise in the tube to E, and the weight will be sustained. In A other words, a very small quantity of water in this narrow tube will press with a force as great as if the C vessel were of the dimensions KLCD, instead of ABCD. By filling the tube to F, a force will be gained sufficient to balance additional pound weights on the cover G, and as great as could be conferred by a vessel of equal breadth all the way up Fig. 3. B to F. Water, in its pressure equally in all directions, presses upwards as well as downwards. This is seen in the above experiments. Take fig. 3 as an example. The water in the vessel ABCD, when the tube is filled, presses, as has been said, with a force equal to that of a column of water of equal breadth all the way up to F. This can only be in consequence of the water in the vessel ABCD pressing violently upwards against the cover G, which violence causes a corresponding reac tion on the bottom of the vessel. This reaction, then, is equivalent to vertical height. To use a figure of speech, the water in the vessel is in the condition of a man pressing equally upwards with his shoulders and downwards with his feet at the same time; and the more he is acted upon by weight above, the more ed enla powerfully does he exert his pressure in both direc- | pressure on the sides. We next find the weight per tions. A An instrument called the hydrostatic bellows has been constructed to exemplify the effect produced by the pressure of a small column of water. As represented in fig. 4, it consists of two circular stout boards connected together with leather, in the form of a pair of strong bellows. A tube A communicates with the interior between the boards. Supposing the instrument to be strong enough, a person standing on the upper board may raise himself by pouring water into the tube, and filling it along with the bellows. It is usual to estimate the pressure by means of weights, W. If the tube hold an ounce of water, and has an area equal to a thousandth cubic foot, which is reckoned to be 1000 ounces; then 11,520, multiplied by 1000, gives 11,520,000 ounces, which is the pressure of the water on the sides. In consequence of the pressure of liquids being as the vertical height and area of the base, it may happen that the lateral pressure on the sides of a containing vessel is greater than the whole weight of the liquid; this will be the case when the surface of the sides in contact with the liquid exceeds the ratio of double the magnitude of the bottom-at double the magnitude, both lateral and perpendicular pressures are alike, and each is equal to the weight of the liquid. The circumstance of pressure increasing in proportion to depth, suggests the valuable practical lesson of greatly increasing the breadth of embankments for dams and canals from the top downwards, so as to give B much greater strength to the base than the summit also of increasing the strength of the lower hoops of large vats, to prevent their bursting. It likewise demonstrates the propriety of making dams, ponds, canals, and vessels for liquids generally, as shallow as is consistent with convenience or their required purpose. In each case, it is important to recollect that the degree of pressure on the sides is irrespective of shape or size of the contents, and depends exclusively on the height of the liquid from its upper surface to its base. Fig. 4. part of the area of the top of the bellows, one ounce of water in the tube will balance a thousand ounces placed on the bellows. This remarkable property in liquids, which is called the hydrostatic parador, is analogous in principle to that which in mechanics is called the Law of Virtual Velocities. According to this fundamental rule, a small weight descending a long way, in any given length of time, is equal in effect to a great weight descending a proportionally shorter way in the same space of time. The rule, as applied to liquids, may be stated thus:A small quantity of water descending in a long column is equal in effect to a proportionately great pressure exerted by a large volume of water in a short column. The law of pressure in proportion to height of column is shown in the annexed representation, fig. 5, of a vessel with an uniformly level base, and full of water. Divid- 1ing the depth into 10 equal 3 sections, to represent feet, as marked from 1 to 10, it is found, that, at the depth of 1, there is a pressure of one foot of water, 10 at 2, two feet, and so on to 10 2 4. 64 9 Fig. 5. at the bottom, where there is a pressure of ten vertical feet of water. The average pressure of the whole is at the middle, at 5. These degrees of intensity of pressure have no reference to the horizontal breadth or length of the mass. The same pressure is sustained, whether the vessel be a foot or a mile in breadth. As in this example, whatever deficiency of pressure there is upon the perpendicular sides of a vessel of water above the middle or point of average pressure, is compensated by a corresponding excess of pressure beneath the middle; consequently, the entire pressure diffused over the sides is equal to that at the middle or point of average pressure. A perpendicular side of a cubical vessel, according to this statement, sustains a lateral pressure precisely equal to the half of that which is endured by the bottom. We may calculate the degree of lateral pressure in vessels having perpendicular sides and flat horizontal bottoms, by first finding the number of square feet in the sides below the surface of the liquid; then multiplying that by the number of feet in half the depth of the liquid; by which calculation, the product will express the number of solid feet of the liquid, whose weight is equal to the lateral pressure. We may find the number of square feet in the sides, by multiplying the number of feet in the circumference of the bottom by the number of feet in the depth of the liquid. Example-To find the degree of pressure on the perpendicular sides of a vat 24 feet deep from the surface of the liquid, and 40 feet in circumference.-Multiply the 24 by 40, and the product 960 gives the area of the sides; then multiply the 960 by half the height, that is 12, and the product is 11,520 cubic feet of water, or the volume of liquid whose weight is equal to the That pressure in water is not according to the volume, but the height above the point of pressure, is obvious from many facts both in nature and art. Whether we plunge an object a foot deep in the ocean or in a jar of water, the pressure upon it is the same. The mere extent of the volume of liquid is of no consequence. Therefore, a precipitous shore pressed upon by the sea to the height of any given number of feet, suffers no more pressure (supposing the sea to be at rest) than the side of a canal of the same number of feet in height. If the law of pressure of fluids were otherwise than that now stated, no species of embankment, no strength of shore, could withstand the pressure of the ocean, particularly in a high state of the tide. In consequence of the law of pressure being simply as the vertical height, we are enabled by artificial means to stem the volume of a far-spreading ocean, and to secure the dry land from its invasion. A knowledge of this important law might induce the attempt to secure many thousand acres of land which are now covered by the tide. B If a vessel, as for instance a barrel, be filled with water, and three apertures be made in its side at different heights, as in fig. 6, the liquid will pour out with an impetuosity corresponding to the depth of the aperture from the top. The jet A nearest the top of the barrel, having little pressure above it, will be projected but a short way; the jet B, having a greater pressure, will perhaps go to double the distance; and the jet C, having the greatest pressure of all, will go to a greater distance still. Jets of this kind obey the laws which govern solid projectiles in their flight; they describe a curvilinear motion, the width of curve being proportional to the impressed force. Fig. 6. C Practically, the discharge of liquids from apertures is partly affected by the shape and width of the aperture; for water is retarded by friction, and by its own impetuosity or cross currents in a small channel. It is reckoned that the pressure of water on any body plunged into it, or on the bottom or sides of the containing vessel, is about one pound on the square inch for every two feet of the depth. Pieces of wood sunk to great depths in the ocean become so saturated with water by the pressure of the superincumbent mass, that they lose their buoyancy, and remain at rest at the bottom. The depth to which divers can descend is limited by the increased pressure they experience in their descent. If a bottle be firmly corked and sealed, and sunk to a great depth in the ocean, the cork will either be forced in or the bottle broken by the pressure. An air-bell rising from a depth, expands as it approaches the surface. At the depth of a thousand fathoms, water is estimated to be about a twentieth part more dense in the bulk than at the surface. The great effects which may take place by the action of a small but high column of water, are sometimes exemplified in the rending of mountains. In fig. 7, a mountain or high rocky knoll is represented, with a small vertical crevice A reaching from the summit to an internal reservoir of water near the base. If there be no means of outlet to the liquid, and if rain continue to keep the crevice and its terminating reservoir full, the lateral force exerted by the upright column will be very considerable. Supposing the crevice to be an B Fig. 7. water necessarily possesses the same surface level in all its parts; one portion cannot stand higher than another; all portions, great and small, are only distributed parts of a single mass. The tendency which water has to stand at the same surface level in all parts of its mass, is usually referred to by the phrase "water finding its level." It is this inherent tendency in water to find its level that produces the various phenomena of the trickling down of rain and moisture into the ground, the flowing of all kinds of streams, from the small brook to the mighty river, and the shooting of rapids and cataracts over precipices. In each case, the water, in obedience to the natural law or tendency which governs it, is only trying to find its level. In pursuit of this object, the water, by the rubbing force which it exercises, wears down all the solid objects which present an obstacle to it in its course. Thus, the substances of which hills and plains are composed, are carried away by streams into the ocean--the ground of continents and islands dimi nishes in bulk-new land rises in the sea; and so, by the effects of a simple natural cause, great alterations are produced in the external features of the globe. There are two kinds of levels--the true level and the natural level. The true level is a perfectly horizontal plane, as for instance an even line, thus or a perfectly even surface of a floor. The natural level is a surface, every point of which is at the same distance from the centre of the earth. The surface level of water is always the natural level. The character of a natural level is understood by a reference to the spherical shape of the earth and the pressure of gravitation. The globe is a ball, and any piece of water which lies upon it, lies in the form of a plaster round the ball. Water, therefore, cannot possibly have a true surface level; its level partakes of the sphericity of the ball. Every piece of water, in a state of entire or partial repose, is in this manner convex in its surface. inch in diameter, and 200 feet deep, the pressure would be equal to nearly half a ton on every square inch; such a force continually acting on the sides of the mountain (laying out of view the great additional force The degree of convexity of the earth is, as nearly as given by expansion of the liquid in freezing during it can be stated in figures, 7 inches and 9-10ths of an winter) would probably in time overcome the cohesive-inch, or nearly 8 inches, in each mile. The convexity, ness of the mass, and burst the whole asunder. In however, is somewhat less towards the north and south this property in water, therefore, we see one of the poles, because the earth is a spheroid, or a sphere flatmany provisions of nature for producing changes cn tened at the ends. the surface of the earth. Effects of a similar character, but on a less scale, are observable in the bursting of walls behind which earth has been piled, and in which no proper outlets for water have been provided; also in the bursting upwards of drains upon a declivity, when they become choked. The easy motion of the particles among each other causes them to accommodate themselves to the shape of any vessel. The force of gravity also causes them to seek the lowest level for repose-each particle tries to get as low as it can. The result of this general tendency throughout the mass is a perfect levelness of surface-the top of the water is smooth. An uniform levelness of surface takes place in every connected mass of water, whatever be its magnitude or its shape. This forms the third leading feature in the laws of water, and is the cause of many of the phenomena in nature. One of the most familiar examples of the equal height and levelness of surface of water, is that observable in a common teapot. In the representation of a teapot, fig. 8, the surface of the liquid in the pot is seen to be at A, and also at the very same height at B in the spout. A straight dotted line is drawn from the one to the other, to show that both surfaces are of the same level. It is customary to say that the small column of water in the spout balances the large mass of water in the pot; but, in reality, there is no balancing in the case. The B Fig. 8. Fig. 9 represents a segment of the earth's surface, with the appearance of a true and natural level marked с Fig. 9. upon it. The curve ES is the earth's surface. PC is a perpendicular line pointing to the centre of the earth. At right angles from this line, a line TL is drawn, representing the true level. Supposing that the line TL is a mile in length, if we draw a line from L to the centre at C, it will cut across the surface of the earth at a point a mile distant from the line at T, which point will be 7 inches and 9-10ths depressed below the part at L. The convexity of the earth's surface is not observ. able in small quantities of water. The surface of a glass of water is not a true level, but the degree of convexity is so small that it cannot be practically estimated or measured. It is only when a sheet of water is * In mathematics, the term apparent level is used instead of true level, and the term dead level instead of natural level. |