of California, FROM THi: I.IUKAKV t >F DR. FRANCIS LIEBER, or of History and Law in Columbia C'']K"_'<\ N<-\v York T^E GIFT OF MICHAEL REESE, Of SUM Franciscd. 1 S 7 3 . THE CABINET OF NATURAL PHILOSOPHY. CONDUCTED BY THE REV. DIONYSIUS LARDNER, LL.D. F.R.S. L.&E. M.R.I.A. P.R.Ast.S. F.L.S. F.Z.S. Hon. F.C.P.S. &c. &c. ASSISTED BT EMINENT SCIENTIFIC MEN. HYDROSTATICS AND PNEUMATICS. BY THE REV. DIONYSIUS LARDNER. WITH NOTES BY THE AMERICAN EDITOR. PHILADELPHIA ". CAREY AND LEA CHESTNUT STREET. 1832. TREATISE ON HYDROSTATICS AND PNEUMATIC S . BY THE REV. DIONYSIUS LARDNER, LL.D. F.R.S JFfvst Shnerfcan, from t$e Jffrst Hontroti 35faftfon. WITH NOTES, BY BENJAMIN F. JOSLIN, M. D PROFESSOR OF NATURAL PHILOSOPHY IN U1UON COLLEGE. CAREY AND LEA CHESTNUT STREET. CONTENTS. HYDROSTATICS. CHAP. I INTRODUCTION. Division of the physical Forms of Matter. The solid and liquid States. Cohe- sion. Repulsion. Heat. Subject of Hydrostatics Page 1 CHAP. II. PRESSURE OF LIQUIDS. Pressure transmitted equally in all Directions. Experimental Proof of this. A Liquid is a Machine. Hydrostatic Paradox. Bramah's Hydrostatic Press. Hydrostatic Bellows. Various useful Applications of this Property. Means of transmuting Signals. Dr. Arnott's Suggestion of its Application in surgical Cases Illustrations from the Animal Economy. Circulation of the Blood. . 3 CHAP. Ill OF THE PRESSURE PRODUCED BY THE WEIGHT OF A LIQ.UID. Pressure proportional to the Depth. Pressure on the horizontal Bottom and per- pendicular Sides of a Vessel. Experimental Proofs of the Property. Total Pressure on the perpendicular Sides of a Vessel computed. Embankments, Dams, and Floodgates. Method of computing the total Pressure on the Surface of a Vessel of any Shape. Examples. Globe. Cube. Various Effects pro- duced by the Pressure of Liquids at great Depths. Cork forced into a Bottle. Water forced into the Pores of Wood. Liquids not absolutely incompressible. Experiment to prove this 17 CHAP. IV. LIQUIDS MAINTAIN THEIK LEVEL. Experimental Proofs. Vessels connected with communicating Tube. Several Vessels between which there is a free Communication. Hydrostatic Paradox explained by this Principle. Surface of a Liquid level. Why the Quality does not extend to Solids. Surface of the Land. Surface of the Sea. Curious optical Deception in Waves. Similar Property in revolving Screw. Ornamen- tal Fountain Clocks. Phenomena of Rivers, Springs, Wells, Cataracts, explain- ed. Canals, Looks. Method of supplying Water to Towns. Exact Sense of the word Level. Common Surface of two Liquids in the same Vessel. Level- ing Instruments. Spirit Level 37 Vl CONTENTS. CHAP. V. OF THE IMMERSION OF SOLIDS IN LIQUID! To determine the exact Magnitude of an irregular Solid. When soluble in the Liquid. When porous. Effect on the apparent Weight of the Liquid. Effect on the apparent Weight of the Solid. The real Weight of the Solid and Liquid not changed by Immersion. Cause of the apparent Change. When a Body is suspended. Floating Bodies. These Properties deduced from the fundamental Principles of Hydrostatics. The same Solid sinks in some Liquids and rises in others. Buoyancy. Its Effects in submarine Operations. Its Effects perceiv- able in Bathing. Boats may be formed of any Material, however heavy. An. Iron Boat which cannot sink. Method of preventing Ships from foundering. Effects of the Cargo. Ball Cock, and other floating Regulators. Means of raising Weights from the Bottom of the Sea. Method of lifting Vessels over Shoals. Life Preservers. Swimming. Water Fowl. Fish. Why a drowned Body floats. Philosophical Toy. Why Ice floats. Rocks raised to the Sur- face by Ice , , ..,,,,. 53 I CHAP. VI. OF DIFFERENT LIQUIDS IN COMMUNICATING VESSELS. Lighter Liquids float to the Top. Oil, Water, and Mercury. Cream of Milk. Ingredients of the Blood. Oil and Spirits, Proof Spirits. Water and Wine. Water in the Depths of a frozen Sea less cold than at the Surface. A Liquid may boil at the Surface, while the lower Parts are cold. Method of applying Heat to boil a Liquid. Method of applying Ice to cool Wine. Different Liquids in a bent Tube. Method of raising Water by impregnating it with Air. .. 83 CHAP. VII. EQUILIBRIUM OF FLOATING BODIES. Conditions of Equilibrium. Cases of Stable, Instable, and Neutral Equilibrium. Experimental Proof. Feat of walking on the Water Life Preserver Stabil- ity of Ships. Position of Cargo. Ballast. Danger of standing up in a Boat. Inclination of a sailing Vessel. How avoided in Steam Vessels 91 CHAP. VIII. SPECIFIC GRAVITIES. Different Senses of the Terms Heavy and Light. Weight absolute and relative. Specific Gravity. Standard of Comparison for Solids and Liquids. For Gases. Density. The Immersion of Solids in Liquids gives their Specific Gravities. Methods of ascertaining Specific Gravities. Hydrostatic Balance. Sikes's Hydrometer. Nicholson's Hydrometer. De Parcieux's Hydrometer. Method of determining the Constituent Parts of Compound Bodies. Alloys of Metal. Spirits. Adulteration of Milk and other domestic Liquids. Hiero's Crown. Penetration of Dimensions 109 CONTENTS. VII CHAP. IX. HYDRAULICS. Velocity of Efflux from an Aperture in a Vessel. Proportional to the Depth of the Aperture. Equal to the Velocity acquired in falling through that Depth. Effect of atmospheric Resistance. Vena Contracta. Rate at which the Level of the Water in the Vessel falls. Lateral Communication of Motion by a Liquid. River flowing through a Lake. Currents and Eddies. Effects of the Shape of the Bed and Banks of a River. Force of a Liquid striking a Solid, or vice versfr. Effect of an Oar. Wings of a Bird. Direction of the resisting Sur- face. Effect of the Velocity of the striking Body. Solid of least Resistance. Shape of Fishes and Birds. Speed of Boats and Ships limited. Comparative Advantages of Railroads and Canals , . 130 CHAP. X. OF HYDRAULIC MACHINES. Water Wheels. Overshot. Undershot. Breast. Barker's Mill. Archiraedei' Screw. Sluica Governor. Chain Pump , , , , , 150 PNEUMATICS CHAP. I. INTRODUCTION. Form of Bodies. How affected by Heat Aeriform State Elasticity. Division of mechanical Science Compressibility and Incompressibility. Permanently elastic Fluids. Vapor Steam. Atmospheric Air * .... 169 CHAP. II! PROPERTIES OF ATMOSPHERIC AIR. Atmospheric Air is material. Its Color. Cause of the blue Sky. Cause of the green Sea. Air has Weight. Experimental Proofs. Air has Inertia. Exam- ples of its Resistance. It acquires moving Force. Examples of its Impact. Air is impenetrable. Experimental Proofs 174 CHAP. III. ELASTICITY OF AIR. Elastic and compressing Forces equal. Limited Height of the Atmosphere. Elasticity proportional to the Density. Experimental Proofs. Internal and external Pressure on close Vessels containing Air 181 Vlll CONTENTS. CHAP. IV. V.'EIOHT OF AIF. Maxim of the Ancients. Abhorrence of a Vacuum, Suction. Galileo's Investi- gations. Torricelli discovers the atmospheric Pressure. The Barometer. Pascal's Experiment. Requisites for a good Barometer. Means of securing thenu Diagonal Barometer. Wheel Barometer. Vernier. Uses of the Ba- rometer. Variation of atmospheric Pressure. Weather Glass. Rules in com- mon Use absurd. Correct Rules. Measurement of Heights. Pressure on Bodies. Why not apparent. Effect of a Leather Sucker. How Flies adhere to Ceilings, and Fishes to Rocks. Breathing. Common Bellows. Forge Bellows. Vent-Peg. Tea-Pot. Kettle. Ink-Bottles. Pneumatic Trough. Gpggling Noise in decanting Wine 188 CHAP. V RAREFACTION AND CONDENSATION OF AIR. Exhausting Syringe. Rate of Exhaustion. Impossible to produce a perfect Vacuum. Mechanical Defects. The Air Pump. Barometer Gauge. Siphon Gauge. Various Forms of Air Pump. Pump without Suction Valve. Exper- iments with Air Pump. Bladder burst by atmospheric Pressure. Bladder burst by Elasticity of Air. Dried Fruit inflated by fixed Air. Flaccid Bladder swells by Expansion. Water raised by elastic Force. A Pump cannot act in the Absence of atmospheric Pressure. Suction ceases when this Pressure is remov- ed. The Magdeburg Hemisphere. Guinea and Feather Experiment. Cupping. Effervescing Liquors. Sparkling of Champagne, &c. Presence of Air necessary for the Transmission of Sound. -The Condensing Syringe. The Con- denser , .214 CHAP. VI. MACHINES FOR RAISING WATER* The Lifting Pump. Pump without Friction. The Suction Pump. The Forcing Pump. The same with Air Vessel. The same with a solid Plunger. Double Forcing Pump. The Fire Engine. Siphon. The Wurtemburg Siphon. . .238 CHAP. VII THX AIR GUN, AIR BALLOON, AND DIVING BELL. Tha Air Gun. First Attempts at Balloons. Lana's Balloon of rarefied Air. Fire Balloons. Montgolfier's Balloon. First Ascent. Balloons inflated with Hydrogen. Parachute. Blanchard's Experiment. Causes of the Efficacy of the Parachute. Ascent of Gay-Lussac and Biot. Appearances in the higher Regions of the Atmosphere. The Diving Bell 257 A TREATISE ON HYDROSTATICS- CHAP, i. INTRODUCTION. DIVISION OF THE PHYSICAL FORMS OF MATTER. THE SOLID AND LIQUID STATES. COHESION. REPULSION. HEAT. SUBJECT OF HYDROSTATICS. (].) To investigate and explain the phenomena of nature, and to exhibit with clearness and perspicuity the laws which prevail among them, it is necessary to group the objects and appearances which are under consideration in classes distin- guished by definite lines of separation. This system ought, however, to be regarded as artificial, and adopted as an aid to the limited powers of the human mind, rather than as corre- sponding to the actual state of the natural world. Material substances, and the various relations which are developed by their mutual agency, exist separately and individually ; science arranges them in .classes, according to certain similitudes and analogies which are observed among them ; but this classifica- tion is often to a great extent arbitrary, and the individuals of one class are by imperceptible degrees shaded off into those of another, like the languages, manners, and habits of adjacent countries 'between Avhich no natural boundary is placed. It must be admitted that, under such circumstances, classification does a violence to nature ; but yet the aids which it affords to the investigation of her laws, and the impulse which it gives to the general progress of discovery, are advantages which outweigh the objections which lie against it. The division of bodies, or rather of the physical states in which bodies are found, into solid and fluid, suggests these reflections. Two opposite influences are observed to pervade % A TREATISE ON HYDROSTATICS. CHAP. 1. the material world. The cohesive principle is one, in virtue of which the component particles of all bodies have a tendency to collect and consolidate themselves into hard and dense masses. This principle is opposed by one of a contrary nature, which generally seems to be connected, if not identical, with that of heat. By virtue of this latter, the elementary molecules of the body which it pervades have a disposition to separate, fly asunder, or repel each other. In different bodies these two opposing forces have different relations, upon which the physical state of the body depends. If the cohesive influence predom- inate over the repulsive in any considerable degree, the par- ticles of the body are held together in a solid concrete mass, not separable by any force less in amount than that by which the cohesive attraction which binds the particles together exceeds the repulsive force which tends to separate them. If, on the contrary, these two principles have an opposite relation, and the repulsive force which gives the particles a disposition to fly asunder prevail over the cohesive force, then the ele- mentary parts of the body will separate indefinitely, and dilate and spread themselves through any vacant space to which they have free access. Such is the case with atmospheric air, and all other bodies existing under the gaseous form. Between these two opposite states there are an infinite variety of others, corresponding to all the possible relations which can subsist between the cohesive and repulsive forces. Nevertheless there is but one intermediate state which is distinctly recognized in mechanical science, to explain which it will be necessary to take into consideration another force, viz. the gravity of the component particles. A body is said to be solid when the cohesive force by which its particles are held together is not only sufficiently powerful to neutralize the repulsive force which may tend to separate them, but also to resist the tendency which they have to fall asunder, like the grains of a mass of sand, by their own weight. If this be the case, the body, placed upon a level plane, or enclosed in a vessel sufficiently large to contain it, will maintain its figure ; nor will its projecting corners or protuberant angles drop off in obedience to their gravity, but will be held firm in their relative positions. If, however, the cohesive force, though sufficient to prevent the separation of the constituent particles of a body by reason of the repulsive force which depends on the presence of heat or any other cause, yet be unable to prevent their falling asunder by their own weight, then the mass of the body, if it were placed upon a plane, would be scattered over the surface by the unresisted tendency which the particles have to fall asunder by their gravity ; and if the body were placed in a vessel which by its sides would restrain the particles, they would then fall into CHAP. II. TRANS-MISSION OP PRESSURE. 3 every cavity of the vessel, and, all the lower parts being filled, the upper part of the mass would settle itself into a level sur- face. Such is the case of water, and all other bodies in the liquid form. There are, however, various states between this of decided liquidity, and that already described of decided solidity. The gradual transition of glue from the solid state to the soft and viscid, and finally to the perfect liquid, will eluci- date these observations. The division of mechanical science, on which we are now about to enter, is confined to the con- sideration of bodies in a perfectly liquid state ; and, as water has been assumed as the type of all other liquids, this division of the science has been called HYDROSTATICS.* CHAP. II. PRESSURE OF LIQUIDS. PRESSURE TRANSMITTED EQUALLY IN ALL DIRECTIONS. EXPERI- ~MENTAL PROOF OF THIS. A LIQUID IS A MACHINE. HYDROSTATIC PARADOX. BRAMAH'S HYDROSTATIC PRESS. HYDROSTATIC BEL- LOWS. VARIOUS USEFUL APPLICATIONS OF THIS PROPERTY. MEANS OF TRANSMITTING SIGNALS. DR. ARNOTT ; S SUGGESTION OK ITS APPLICATION IN SURGICAL CASES. ILLUSTRATIONS FROM THE ANIMAL ECONOMY. CIRCULATION OF THE BLOOD. (2.) THE most striking of those qualities of bodies which depend on the fluid state, and that, indeed, by which this state is mainly distinguished from the solid, is the power to transmit pressure equally in every direction. In mathematical treatises, this property is usually taken as the definition of fluidity, and as the basis of the reasoning by which the whole superstructure of the science is raised. Fig. I. * The terms hydrodynamics and hydraulics are used to express certain division! of the science, "it will be convenient, however, in the present case, to embrace the whole under the titlo Hydrostatics. A TREATISE ON HYDROSTATICS. CHAP H the ' every part of thV n PrGSSUre w be transmitted to and a force tending to burst the vessel wiU be produced thP total amount of which will be as many pounds^ ^ there are square inches in the inner surface of the vessel. If the whole mner surface of the vessel amounted to 10,000 square inches then a pressure of one pound on the piston would produce a to be Fig. 2. the vesfi! e apeUreS ' ' and erer y P^rt of CHAP. II. TRANSMISSION OF PRESSURE. 5 a pound. Now suppose the piston P' to press upon the surface of the water with a force greater than a pound, then the piston P 7 will descend in the cylinder, and the piston P will rise. Thus it appears that the force of one pound acting at P trans- mits to P' a pressure which is unable to resist a force greater than a pound. From these two experiments it appears that the pressure transmitted to P / is neither greater nor less than a pound, and is therefore equal to a pound. This may further be verified by loading the piston P ; so as to exert upon the liquid a pressure amounting to one pound. It will then be observed that the pistons will just balance one another. In general it will be observed, that so long as the two pistons are equally loaded, whatever be the amount of the force acting on them, they will balance each other, and neither will be displaced ; but at the moment when any force is given to one greater than that which acts upon the other, however in- considerable the excess may be, that which is urged by the greater force will descend, and will transmit a force to the other which will compel its ascent. It therefore appears that any force whatever, which acts upon a square inch of the surface of the water at P, pressing it inwards, will produce an equal force upon the square inch of surface forming the base of the piston P', tending to force it outwards. It is evident that this would be equally true if tiie surface which forms the base of the piston P f were a part of the inner surface of the vessel, and that no aperture or cylinder existed at" O'. It is also evident that the same results would be obtained, in whatever part of the vessel the aperture O might be placed ; and therefore we infer that every separate square inch of surface receives from the liquid in contact with it a pressure equal in amount to the pressure which is exerted on the water by the piston P. This important property may be further elucidated as fol- lows : We have supposed that the two apertures and the pistons which fill them were equal in magnitude. Let us now suppose that the aperture O' is ten iimes the magnitude of the aperture O (fig. 3.). It follows, from what has been already explained, that a pressure of one pound acting inwards at P will produce a pressure of one pound acting outwards on every square inch in the base of the piston P' ; and therefore the piston P' will be urged upwards by a force amounting to ten pounds. Accord- ingly, we shall find that if this piston be loaded with a weight of ten- pounds, it will resist the pressure of the liquid, and will not suffer itself to be forced upwards in the cylinder ; but, on the other hand, this weight will not enable it to force the liquid inwards, and it will merely maintain its position. If it beload- i* 6 A TREATISE ON HYDROSTATICS. CHAP. II, Fig. 3. ed with a weight greater than ten pounds, it will force the liquid inwards, and will raise the piston P ; and if it be loaded with a weight less than ten pounds, the piston P will force it upwards. It appears, therefore, that the pressure exerted on the ten square inches of surface forming the base of the piston P ; is ten pounds, and neither more nor less. In the same manner, what- ever be the proportion which the base of the greater piston P' bears to the base of the lesser piston P, in exactly the same degree will the force transmitted by the liquid from P to P' be multiplied. There are some circumstances which impair the accuracy with which the practical results of the experimental illustrations, conducted in the manner just described, represent the conclu- sions at which, by reasoning, we have arrived. That the pis- tons P, P' may move in the cylinders so as not to allow the liquid to escape between them and the inner surface of the tube, it is necessary that they should press upon that surface with a certain force ; this pressure will unavoidably be accompanied by friction ; and, before the pressure excited on one piston can produce a perceptible effect in moving the other, an excess of force must be produced sufficient to overcome the friction of both pistons. Thus, m Jig. 2., if the pistons be equally loaded, a small additional weight on either will not always cause the other to ascend ; it will only do so when its force exceeds the amount of the resistance occasioned by the friction of the pistons. This inconvenience may be removed by applying the pressure on the surface of the liquid at O and O' by some means which will not be attended with perceptible friction. Such means are easily found ; and although they may at the first view appear to confirm the theory by a more indirect process, yet, when duly considered, it will be perceived that the method is not only di- rect, but more satisfactory than the former. (4.) Let us suppose the pistons P, P' removed from the cyl- inders, and let circular plates, so formed that they shall exactly CHAP. II. EXPERIMENTAL PROOF. cover the apertures O, O, turn upon rods which extend across the holes, so that, being turned upon these rods, they will in one position completely stop the apertures, their flat faces being presented to the liquid, as in Jig. 4. ; while in another position they will leave the apertures open, having their edges turned towards the liquid, as in Jig. 5. Thus, in the position repre- sented in Jig. 4., all communication between the liquid in the vessel and the external part of the cylinder is cut off, while in the position represented in Jig. 5. there is a free communica- tion, i First, let the two valves V, V, be closed, as in Jig. 4., and let one pound of oil be poured into the cylinder C. It is evident that the valve V will now sustain a pressure of one pound ; and if that valve were removed, as the oil would not mix with the water, but rest upon it, the water would sustain the same pres- sure. Let the valve V be turned till it assumes the position represented in Jig. 5. : the weight of the oil will now press upon - the surface of the water ; and, as there will be no sensible fric- tion between the oil, and the surface of the cylinder, an undi- minished pressure of one pound will be transmitted to every square inch of the surface of the vessel, and, among others, to the surface of the valve V', which will be pressed upwards with a force of that amount. That the valve V is pressed by such a force may be made manifest as follows : Let a pound of oil be poured into the tube C' : this will press upon the valve V 7 with a force of one pound ; and if the valve V' be turned into the position represented in Jig. 5., the same pressure will act upon the surface of the water below. It will then be observed that this surface will maintain its position, neither forcing the oil up, nor being forced down by it. If less than a pound of oil had been poured into the tube C', the pressure of the water be- low Avould prevail, and its surface would rise in the tube ; and it would only be restored to its former position by pouring in so much more oil as would make the weight of the whole one pound. If still more were poured in, the pressure of the oil would prevail, and the surface of the water would sink in the A TREATISE OX HYDROSTATICS. CHAP. ii. tube. Thus it appears conclusively, that a pressure of one pound exerted at V is transmitted undiminished to V ; and in :a > C the same way is transmitted to every square inch on the surface of the vessel. (5.) By the same reasoning it may be shown, that if the cylinder C ; were greater than C,it would require a proportionally great- er weight of oil to resist the ascent of the water, and we should arrive at the same conclusions as we have obtained respecting the piston represented in Jig. 3. (o.) By this singular power of transmitting pressure, a fiuid becomes, in the strictest sense of the term, a machine, and one of unequalled simplicity and almost unlimited power: as such, it is amenable to ail the laws, and fulfils all the conditions, to which ordinary machines are subject. The surprising effects which are consequent on the property of liquids which we have just explained, exhibited under various forms, which we shall presently have occasion to notice more particularly, have ac- quired for it the name of the ." hydrostatic paradox." But, in truth, there is nothing in these effects more deserving the title of paradox than those which attend every machine. In various parts of our treatise on Mechanics, and more especially in the twelfth chapter of that volume, it has been proved that there is nothing paradoxical, or repugnant to the results of common ob- servation, in the effects produced by machinery. We shall now endeavor to show that the same principles arc applicable, and the same explanations satisfactory, when a liquid is used as a machine ; that is, as a means of transmitting fcrce from one point to another. A force of a pound acting on the piston P.fg. 6., holds in equilibrium a force of ten pounds acting on the piston P ; . In this case, however, it must not be supposed that the piston P supports the ten pounds which press down tiio piston P 7 : the bottom of the vessel sustains by its resistance nine of the ten pounds acting on the piston P ; , and the remaining pound alone is resisted by the piston P. The circumstances attending the action of these forces differ CHAP. II. A LIQUID IS A MACHINE. in nothing from those of a lever of the first kind, supporting a weight of ten pounds on the shorter arm, balanced by a weight of one pound on the longer arm. The liquid performs the office of the bar, by transmitting the effect of the lesser weight to the greater ; and the surfaces of the vessel which contains the liquid perform the office of the fulcrum, by sustaining both the power and weight.* If the piston P be used to raise the piston P', instead of merely supporting it, what has been regarded as paradoxical in the process may likewise be explained almost in the same words which have been used in explaining several machines in our treatise on Mechanics. If the piston P be made to descend one inch, a quantity of water which occupies one inch of the cylinder C will be expelled from it ; and as the vessel A B C D is filled in every part, and its sides cannot yield, the piston P' must be forced up until room be obtained for the water which has been expelled from C. But as the cylinder C' is ten times larger than the cylinder C, the height through which the piston P' must be moved to obtain this room will be ten times less than that through which the piston P was caused to descend. Thus, while one pound on the piston P was moved through one inch, a weight of ten pounds on the piston P 7 has been moved through the tenth of an inch. By repeating this process ten times, we shall move ten pounds on the piston P' through a height of one inch, by ten distinct efforts, each of which moves one pound through one inch. The force expended, and the effect produced, is therefore the same as if the weight of ten pounds, with which the piston P f was loaded, were divided into ten equal parts, and these parts severally raised by ten distinct efforts through the height of an inch. The force, therefore^ expended to produce a given effect is the same as if no ma- chine was used.f <7.) It is not the least surprising circumstance in the history * Mechanics, (311.) t U>id. (2260 10 A TREATISE ON HYDROSTATICS. CHAP. II. of physical science, that this property of liquids, though long known, and, indeed, the subject of curious observation, should have continued, until a comparatively recent period, a barren fact. The engine known by the name of the HYDROSTATIC or HYDRAULIC PRESS, and sometimes, from the name of the engi- neer who gave it its present form, and brought it into general use, BRAMAH'S PRESS, is nothing more than a simple and direct practical application of the property which we have just in- vestigated. A small cylinder, C,Jlg. 7.. is furnished with a piston or plug, A, which moves, water tight, in it ; at the bottom of this cylin- der there is a valve, B, which opens upwards and communicates with a tube below, which descends into a vessel or reservoir of \vater. In the side of the cylinder C there is a narrow tube, D, inserted in the cylinder, and communicating at E with an- other cylinder, C', of much greater dimensions. In this cylin- der there is a large piston, A', the rod of which is directed against whatever object the machine is intended to sustain or move. We shall at present suppose it applied to an ordinary press : G H I K represents a strong iron frame, and F a square plate movable in it and resting on the piston rod. As the pis- ton rod is moved up, the plate F is forced up towards the top of the press H I, so that any substance placed between the plate F and the top H I is submitted to pressure. In the tube D E there is a valve, O, which opens towards the great cylinder C' ; and in the same tube there is a stop-cock, P, by which a communication with the cistern below may bo opened and closed at pleasure. The rod of the small piston A is connected at X with a lever, L M, which plays upon a fulcrum at M. The press is worked by raisjng and depressing alternately the lever at L, and the process is effected as we shall now describe. Suppose the water, if there be any in the cylinder C', is dis- charged into the reservoir by the cock P, which is then closed ; the piston A 7 will then fall to the bottom of the cylinder. Let us also suppose that the piston A is at the bottom of the cylin- der C. If the lever L be nor/ raised, the piston A will be ele- vated, and the space below it in the cylinder, being free from air, the atmospheric pressure* will force the water in the reser- voir up through the valve B so as to lill the cylinder C : this water cannot return through the valve B, since that valve opens upwards, and the weight of the water above it only keeps it more firmly closed. Let the lever L be now depressed : the water below the piston A will be forced through the valve O, and through the tube D E, into the great cylinder C'. Let this * This effect v.-ill be explained in Pneumatics. CHAP. II. THE HYDROSTATIC PRESS. 11 process be continued until the space in the great cylinder below the piston is completely filled Avith water : when that is accom- plished, the pressure of the piston A will be transmitted to the piston A', multiplied in the proportion of the magnitude of the piston A.' to that of the piston A (3.). Thus, if the magnitude of the piston A' be a thousand times that of A, a pressure of ten pounds on the piston A will produce a pressure of ten thousand pounds on the piston A'. During the operation of the machine, at the intervals of the ascent of the piston A, it3 Fig. 7. action on piston A' is suspended ; and if the tube of communi- cation D E were open, the piston A' would press upon the valve B during every ascent of the piston A, and would resist the entrance of water into the small cylinder, and thus the operation of the machine would he obstructed : but the valve O, opening 10 A TREATISE ON HYDROSTATICS. CHAP. II. of physical science, that this property of liquids, though long known, and, indeed, the subject of curious observation, should have continued, until a comparatively recent period, a barren fact. The engine known by the name of the HYDROSTATIC or HYDRAULIC PRESS, and sometimes, from the name of the engi- neer who gave it its present form, and brought it into general use, BRAMAH'S PRESS, is nothing more than a simple and direct practical application of the property which we have just in- vestigated. A small cylinder, C,fig. 7., is furnished with a piston or plug, A, which moves, water tight, in it ; at the bottom of this cylin- der there is a valve, B, which opens upwards and communicates with a tube below, which descends into a vessel or reservoir of water. In the side of the cylinder C there is a harrow tube, D, inserted in the cylinder, and communicating at E with an- other cylinder, C ; , of much greater dimensions. In this cylin- der there is a large piston, A', the rod of which is directed against whatever object the machine is intended to sustain or move. We shall at present suppose it applied to an ordinary press : G H I K represents a strong iron frame, and F a square plate movable in it and resting on the piston rod. As the pis- ton rod is moved up, the plate F is forced up towards the top of the press H I, so that any substance placed between the plate F and the top H I is submitted to pressure. In the tube D E there is a valve, O, which opens towards the great cylinder C' ; and in the same tube there is a stop-cock, P, by which a communication with the cistern below may be opened and closed at pleasure. The rod of the small piston A is connected at X with a lever, L M, which plays upon a fulcrum at M. The press is worked by raisjng and depressing alternately the lever at L, and the process is effected as we shall now describe. Suppose the water, if there be any in the cylinder C', is dis- charged into the reservoir by the cock P, which is then closed ; the piston A' will then fall to the bottom of the cylinder. Let us also suppose that the piston A is at the bottom of the cylin- der C. If the lever L be now raised, the piston A will be ele- vated, and the space below it in the cylinder, being free from air, the atmospheric pressure* will force the water in the reser- voir up through the valve B so as to ii!l the cylinder C : this water cannot return through the valve B, since that valve opens upwards, and the weight of the water above it only keeps it more firmly closed. Let the lever L be now depressed : the water below the piston A will be forced through the 'valve O, and through the tube D E, into the great cylinder C'. Let this * This effect v.-ill be explained in Pneumatics. CHAP. II. THE HYDROSTATIC PRESS. 11 process be continued until the space in the great cylinder below the piston is completely filled with water : when that is accom- plished, the pressure of the piston A will be transmitted to the piston A', multiplied in the proportion of the magnitude of the piston A' to that of the piston A (3.). Thus, if the magnitude of the piston A' be a thousand times that of A, a pressure of ten pounds on the piston A will produce a pressure of ten thousand pounds on the piston A'. During the operation of the machine, at the intervals of the ascent of the piston A, it3 Fig. 7. action on piston A' is suspended ; and if the tube of communi- cation D E were open, the piston A' would press upon the valve B during every ascent of the piston A, and would resist the entrance of water into the small cylinder, and thus the operation of the machine would be obstructed : but the valve O, opening 14 A TREATISE ON HYDROSTATICS. CHAP. II. Fig. 7. the action of the hydrostatic press. If the funnel be removed, and six men stand on the board B C, one of them, blowing into the tube T with his mouth, may produce a sufficient pres- sure on the column of water, to raise the board and its load. (9.) If a. long narrow tube A, Jig. 8., be inserted perpendicularly into a vessel B, filled with water, the weight of a few ounces of water may be so ap- plied as to burst the vessel, whatever be its strength, provided the tube be sufficiently long and narrow. This will be easily understood upon the principles already explained. Let us suppose that the magni- tude of the bore of the tube is the hundredth part of a square inch, and that it ascends perpendicular- ly, to such a height above the vessel that it may contain an ounce of water, that part of the water in the vessel which is immediately under the mouth of the tube will receive a pressure of one ounce from the incumbent column. The magnitude of the mouth of the tube being the hundredth of a square inch, it follows, from what has been already proved, that every hundredth part of a square inch in the surface of the vessel will sustain a pressure of one ounce, and therefore every square inch will sustain a pressure of 100 ounces. A square foot contains 144 square inches, and there- fore every square foot will sustain a pressure of 14,400 ounces CHAP. II. HYDROSTATIC PARADOX. 15 or 900 pounds. Hence, if the base of the vessel measure nine square feet, and its sides thirty-six square feet, and its top nine square feet, we shall have a total surface of 54 square feet, each square foot bearing a pressure of 900 pounds, and the whole surface sustaining a pressure, tending to burst the vessel, amounting to more than twenty-one tons, and this enormous force is produced by the mechanical modification which the weight of one ounce of water undergoes. (10.) The property of liquids, which has been under consid- eration, points them out as an easy, simple, and effectual means of transmitting force to any distance, and under circumstances in which other mechanical contrivances would be totally inap- plicable. It is only necessary to carry a tube filled with a liquid from the point where the force originates, to the point to which it is to be transmitted ; and as the shape or position of the con- necting tube or pipe does not affect the property of the fluid which it contains, there is scarcely any conceivable impediment which can prevent the transmission of the force from the one point to the other. A pressure excited on the liquid at one end of the tube, will be communicated to any surface in contact with the liquid at the other end, whether the tube between the two extremities be straight, curved, or angular, or whether it pass upwards, downwards, or in an oblique or horizontal direc- tion. It may be carried through the walls of a building, through the course of a river, under, over, or around any obstruction or impediment, or, in fact, according to any course or direction whatsoever. If a tube filled with water extended from London to York, a pressure excited on the liquid at the extremity in London, would be instantaneously transmitted to the extremity at York. It has been suggested, that such means might be used for telegraphic communications, in situations where the frequency or importance would justify the expense of laying down pipes or tubes. An ingenious person in this country has tried the experiment with this view, and has laid down several miles of pipe for the purpose. Such a method of communica- tion would have the advantage of being independent of those accidental interruptions to which lights, signals, and other simi- lar contrivances are exposed. (11.) The power of liquids to transmit pressure has been pro- posed to be applied to surgical purposes by Dr. Arnott. It would indeed seem to be peculiarly applicable in cases 'where it is necessary to produce a pressure on some internal part, which cannot be approached except by a tube or channel, through which an instrument cannot be safely or conveniently inserted. Dr. Arnott considers that a liquid might be conveyed through a flexible tube, so shaped, that when filled by the liquid, the proper degree of pressure will be excited on those parts 16 A TREATISE ON HYDROSTATICS CHAP. II, which require it. An account of these instruments may be seen in Dr. Arnott's work on Physics. (12.) The animal economy presents innumerable examples of the power of fluids in transmitting pressure. The bones and harder parts of the body furnish a beautiful example of a struc- ture, in which every leading principle of mechanics, commonly so called, is illustrated. The fluids, in like manner, exhibit equally apt illustrations of the principles of hydrostatics. The heart, the fountain from which the blood is supplied to all parts of the system, is an instrument possessing great power of ex- pansion and contraction : by exciting a pressure upon the blood, it impels that fluid into the arteries, pressing forward what has already filled them through proper channels of communication into the veins. These various pipes and conduits are formed of an elastic material, capable of continuing the pressure com- menced at the heart, and thus urging forward the stream of li- quid, until its circulation is completed. As in the pipe D ,/#. 6., of the hydrostatic press, valves are provided in proper places in the various tubes through which the circulation is carried on. These valves are so contrived, that the blood is admitted to pass freely in obedience to the impulse it receives from the muscular pressure ; but when that pressure is intermitted, the fluid cannot return, and the resist- ance of the closed valve supplies the place of the moving power whose action is suspended. < The muscular power of the heart to excite a pressure on the blood is placed in a very striking point of view, by an experi- ment recorded in a work by Dr. Hales, called Statical Essays. A perpendicular tube is made to communicate with the blood of one of the arteries of an animal. The blood being 1 no longer confined, rushes into the tube, and ascends to a height above the level of the heart, which is proportionate to the pressure which it receives. This height necessarily varies in different animals ; in the larger and more powerful species, it is much greater than in the smaller ones. In the case of a horse, the column will ascend to about ten feet above the heart. The pressure to which it is subject in the veins is much less than in the arteries. Dr. Hales found that, in the human body, the pressure of the arterial blood was capable of sustaining a co- lumn eight feet in height, and amounted to four pounds on the square inch ; while the pressure of the venous blood did not exceed a quarter of a pound on the inch, and only sustained a column six inches in height. CHAP. III. PRESSURE FROM WEIGHT. 17 CHAP. III. OF THE PRESSURE PRODUCED BY THE WEIGHT OF A LIQUID. PRESSURE PROPORTIONAL TO THE DEPTH. PRESSURE ON THE HOR1 ZONTAL BOTTOM AND PERPENDICULAR SIDES OF A VESSEL. EX PERIMENTAL PROOFS OF THE PROPERTY. TOTAL PRESSURE ON THE PERPENDICULAR SIDE OF A VESSEL COMPUTED. EMBANK- MENTS, DAMS, AND FLOODGATES. METHOD OF COMPUTING THE TOTAL PRESSURE ON THE SURFACE OF A VESSEL OF ANY SHAPE. EXAMPLES. GLOBE. CUBE. VARIOUS EFFECTS PRODUCED BY THE PRESSURE OF LIQUIDS AT GREAT DEPTHS. CORK FORCED INTO A BOTTLE. WATER FORCED I'NTO THE PORES OF WOOD. LIQUIDS NOT ABSOLUTELY INCOMPRESSIBLE. EXPERIMENT TO PROVE THIS. (13.) IN the investigation contained in the last chapter, the effects of the weight of the liquid itself were left out of con- sideration, and it was merely regarded as a machine by which other forces might be transmitted and modified. In the same manner, however, and upon the same principles, as it transmits and modifies other forces, it conveys the effect of its own weight through the dimensions which it occupies in the vessel which contains it. This weight exerts a certain pressure on every part of the surface of the containing vessel with which it is in contact. The total amount of this pressure, as well as the portion of it which each part of the surface sustains, is to be inferred from a consideration of the weight of the liquid, its power of transmitting pressure, and the peculiar figure or shape of the vessel. It may, however, here be observed, generally, that the effect is totally .different from that which would be produced by a solid. (14.) There is one general principle by which the pressure of a liquid on the surface of the vessel which contains it may always be ascertained. Each part of the surface of the vessel, in contact with the liquid, sustains a pressure equal to the weight of a column of the liquid, whose height is equivalent to the depth of the part of the surface of the vessel in question below the surface of the liquid contained in the vessel. The truth of this general principle will be apparent, by considering it, first, in the more simple and obvious cases, and tracing it thence to the more complex and difficult ones. Let ABC, Jig. 9., be a long square pipe in a perpendicular position, each of whose sides is an inch broad. The base B C, therefore, is a square, each of whose sides is an inch. Suppose this base to be closed by a flat bottom, and let water be poured A TREATISE ON HYDROSTATICS. CHAP. III. Fig. 9. into the pipe until it attain an elevation B'C' one inch above the bottom of the pipe. The liquid will now }A be in contact with a square inch of surface on each of the four sides, besides the square inch of surface which forms the bottom. Let a flat plate, cut into the shape of a square inch so as to fit the tube, be now conceived to be introduced into it, and placed immediately on the surface of the water, and in con- tact with it. If any weight, as 10 pounds, be placed upon this plate, the liquid below will transmit a pres- sure of ten pounds to every square inch of the pipe with which the water is in contact, and therefore the bottom, and each of the four sides, will several- " ly sustain a pressure of ten pounds.* This is obvi- ous from what has been so fully explained in the last chapter. If the plate and the weight with which it, is supposed to be pressed be removed, and ten pounds of water be poured into the pipe, the water below the level B'C' will suffer exactly the same mechanical pressure as was before exerted by the plate loaded with the weight, and this pressure will be transmitted in the same way to the surface of the tube, by the Avater below B'C'. It thus appears that a perpendicular column of water, weighing ten pounds, standing above the level B'C', will press, not only on the bottom of the vessel, but on the sides immedi- ately below B'C', with a force amounting to ten pounds. What has been proved of the column of fluid, above the level B'C', will be equally true of any other part of the column of fluid contained in the tube. Thus the column of fluid above the level B"C", will communicate a pressure to every square inch of the surface of the vessel below that level, amounting to its own weight. To render the explanation more clear and simple, the section of the pipe has been here supposed to be square, and its magni- tude to be one inch ; but a little attention and consideration will show, that the same reasoning, with slight changes, will be applicable, whatever be the magnitude of the vessel, and whatever be the shape of its base. If any part of the column is supposed to be removed, and a flat plate fitting the vessel, and loaded with a weight equal to that of the water removed, be introduced, the force of thit weight will be transmitted by the water below, with undiminished energy, to every part of the surface of the vessel with which it is in contact. Each portion of the surface of the vessel, which is equal in magnitude to the surface of the plate, will sustain a pressure equal to the force * They will severally sustain n pressure of ten pounds in addition to the pres- sure resulting from the weight of the fluid itself. AM. ED. CHAP. III. PRESSURE PROPORTIONAL TO DEPTH. 19 with which the plate presses on the water. When the plate is removed, and replaced by an equivalent weight of water, the same effect will be continued. (15.) It therefore appears generally, that in every vessel whose sides are perpendicular, and whose bottom is horizontal, whatever be its shape in other respects, the pressure on the bottom will be equal to the whole weight of the fluid which it contains, while the pressure on each square inch of the perpen- dicular sides will be equal to the weight of a column of the liquid, whose base is a square inch, and whose height is equal to the depth of the part of the surface of the vessel in question below the upper surface of the liquid in the vessel. (16.) It appears from what has been stated, that not only the surface of the vessel which contains a liquid, but likewise every part of the liquid itself, sustains a pressure from the weight of the liquid above it, and this pressure is regulated by the same law. If any portion of the liquid be selected at any given depth below the surface, that portion is pressed equally in every possible direction by the surrounding fluid, and the amount of the pressure which it thus sustains is the weight of the column of fluid perpendicularly above it. This may be easily deduced from considering the property of liquids explained in the last chapter. It is evident that a part of the fluid, taken any where within its dimensions, sustains a downward pressure from the weight of the incumbent column ; but it transmits this pressure;, by the property just alluded to, in every direction around it; downwards, laterally, obliquely, &c. .Now it is clear that it must encounter an equal pressure in all these directions ; for if it did not, it would move away in that direction in which its force was unresisted ; but as no such motion takes place, and as the particles of the fluid remain at rest, it follows that they are maintained in these places, by forces pressing them equally Fi* 10. on ever y side an d from every possible direction, each of which is equal to the weight of the perpendicular column of fluid above the particle so pressed. (17.) This property may easily be reduced to experi- mental proof. Let A B^/Fg*. 10., be a strong metal cyl- inder, having a metal bottom at B, but open at A : in this let a spiral spring be inserted, bearing a circular plate C, which moves water-tight within the cylinder, so that a force applied to the plate C will overcome the elas- ticity of the spring, and cause the plate to move into the cylinder towards B. The farther the plate advances within the cylinder, the more powerful the elastic force of the spring will become, and the greater will be the force necessary to prevent its recoil. The amount of force necessary to press the plate to any proposed depth j| 20 A TREATISE OX HYDROSTATICS. CHAP. HI. in the cylinder, may be determined by experiment ; and it is not difficult to provide a means of registering the depth within the cylinder, to which the plate may have been forced on any oc- casion, when the presence of an observer is rendered impossi- ble. If such an instrument be plunged in a liquid to any depth, the pressure exerted by the fluid will force in the movable plate ; and, upon observing the instrument when drawn out, the amount of the pressure will be known from the space through which the plate was forced into the cyl- inder. If the instrument be successively immersed to depths of 1, 2, and 3 yards, it will be found that the pressures which have acted on the spring, are in the proportions of the numbers 1, 2, 3, and are equal to the weights of columns of the liquid whose heights are respectively equal to the depths of immersion, and whose bases are equal to the movable plate. The fact that the pressure is proportional to the depth, and equal to the weight of the incumbent column, is thus conclu- sively established. That this pressure is exerted equally in every possible direc- tion, may be shown by giving the instrument, at the same depth successively, different positions. If it be first immersed with the end A presented upwards, and the distance observed through which the plate is forced in, and then successively immersed to the same depth with the end A presented downwards, side- ways, and in any other direction, it will always be observed that the distance through which the plate is forced by the pres- sure of the liquid will be the same ; indicating thereby, that the pressures in all those directions are equal. (18.) This important law may be established experimentally by a more easy and scarcely less direct method. Let four glass tubes, T,Jig. 11., be provided, open at both ends, and let Fig. 11. one end of the first be straight ; of the second, turned upwards ; of the third, turned sideways ; and of the fourth, turned in an oblique direction. At these ends let stop-cocks be placed, which may be opened and closed at pleasure. These cocks CHAP. HI. PRESSURE PROPORTIONAL TO DEPTH. 21 being closed, let all the tubes be immersed to the same depth in a vessel of water. The water Avill then press against each of the cocks with a certain force, the amount of which it is re- quired to ascertain. We shall suppose the bores of the tubes to be equal, although that circumstance, as will hereafter ap- pear, cannot affect the result of the experiment.* Let us suppose the diameter of the bores of each of the tubes to be half an inch. The water, at the depth to which the tubes are immersed, is in this case acting against a circular surface, of the diameter of half an inch at each stop-cock. If the several stop-cocks be now opened, the pressure will cause the water to rush into the tubes, in the first upwards, in the second downwards, in the third sideways, and in the fourth obliquely. It will continue to flow into each until the weight of the column, which has risen in the tube, is sufficiently great to resist the pressure at its extremity. When that takes place, and not until then, the water will cease to flow into the tube. It will be observed, that in each tube the water will rise until it has attained the level of the water in the vessel, and it will then cease to flow It follows, therefore, that the pressure of the fluid at the ex- tremity of the tubes is equal to the weight of a column of the fluid, which extends perpendicularly from their extremities to the surface ; and since the water will always rise to the level of the fluid in the vessel, whatever direction may be given to the lower extremity by bending the tube near that point, it fol- lows, that at the same depth the pressure in every possible direction is the same. In this mode of illustration it will easily be perceived, that the column of water which is sustained in the tube performs the part of the stop-cock, with respect to the water which presses in at the orifice below, and that the weight of this column ex- actly balances this pressure. There will be no difficulty in seeing how this experiment may be generalized. The tubes may be of any magnitudes, whether equal or unequal, and still the water will rise in them to the level of the water in the vessel ; and the same will hap- pen whatever be the liquid used. The pressure exerted at any depth below the surface is always equal to the weight of a column of the liquid whose height is equal to the depth, and whose base is equal to the surface, over which the pressure is * When the boxes of the tubes are unequal, and some of them very small, ca- pillary action will sensibly affect the result, in a manner depending upon the na- ture of the fluid. The elevation or depression of the fluid in the smaller tube, depends upon the relation which subsists between the action of the tube on the fluid, and the mutual action of the particles of the fluid. By a complete analysis of all the forces concerned, it ?:i;i.y be shown in what manner their opposite effects may be produced. As:. 11^. 22 A TREATISE ON HYDROSTATICS. CHAP. III. extended. The quantity of liquid whose weight expresses this pressure, may always be determined arithmetically, by multi- plying the number of inches in depth below the surface of the liquid, by the number of square inches in the surface on which the pressure is exerted. The product of these numbers will be the number of solid inches of the liquid, whose weight is equal to the pressure. It must, however, be understood, that in this mode of calculation, the surface pressed is supposed to be horizontal, or if it be oblique, its dimensions must be very small, compared with the depth. The following experiment furnishes another illustration of the property by which the pressure of a liquid increases with the depth : Let a bladder be attached to the extremity of a glass tube, and let it be filled with mercury to a small height above the point where it is attached. Let equal small divisions be marked upon the tube, beginning from the surface of the mercury. If the bladder thus filled be immersed in a vessel of water, the pressure of the surrounding liquid will cause the mercury to ascend in the tube. Let it be immersed to such a depth that the mercury will rise through one division of the tube, and let the depth of immersion be observed ; let the tube be then immersed to twice that depth, and the mercury will be observed to rise through another division. Being immersed to three times the depth, it will rise to a third division, and so on. It therefore appears that the pressure upon the bladder increases in proportion to the depth. (19.) Concluding, then, that every part of a liquid suffers and transmits a pressure, arising from the weight of the incumbent liquid ; that this pressure is always proportional to the depth, and is equally exerted in every direction ; we may easily obtain theorems respecting the pressure sustained by the surface of vessels which contain liquids, of a much more general nature than those which have led to the preceding investigation. Whatever be the shape of the vessel which contains a liquid, each square inch of its surface suffers a pressure equal to the weight of a column of the liquid, whose base is a square inch, and whose height is the depth of that part of the surface of the vessel below the surface of the liquid. This follows immedi- ately from the principle which has just been established ; for the liquid which is in immediate contact with any part of the sur- face of the vessel, sustains a pressure in a direction perpendic- ular to that surface, to the amount just mentioned ; and it is evident that the surface must balance and resist that pressure. By the aid of the peculiar language and symbols of mathe- matical science, general rules or formularies may be given, by which the whole pressure of a liquid on the surface of a vessel of any proposed figure may be computed. Although great CHAP. III. PRESSURE PROPORTIONAL TO DEPTH. 23 practical facility, not only in calculation, but also in reasoning-, may be derived from the use of such formulae, yet they must be understood to express nothing more than what has been already explained. The method by which they express it is, however, attended with great convenience, and affords considerable ad- vantages in the application of the general principle to particular cases. (20.) An obvious consequence of the property now explained is, that the pressure produced upon the surfaces of the vessel containing a liquid, can never in any case be less than the weight of the liquid, but will not unfrequently amount to many times that weight. Since the general methods of determining the pressure on surfaces do not admit of familiar explanation, we shall endeavor to explain the principle by its application to such particular cases as can be rendered intelligible without mathematical symbols. (21.) If the surface which sustains the pressure be horizontal, every part of it, being at the same depth, will suffer the same pressure. In this case, therefore, it is evident that the total pressure which the surface sustains is the weight of all the liquid which is perpendicularly over it, or, what is the same, the weight of a column of the liquid, whose base is equal to the surface, and whose height is equal to the depth. (22.) If the surface which suffers the pressure be not hori- zontal, its several parts will be at different depths, and, there- fore, will suffer different pressures. If a point could be found whose depth is an average of all the different depths, then the total pressure would be the same as if the whole surface were uniformly subject to the pressure sustained by this- point, and the total amount of the pressure would be equal to the weight of a column of the liquid, whose base is equal to the surface pressed, and whose height is equal to the depth of that point. This will, perhaps, be more clearly comprehended by particular examples. Fig. 12. Let A B C D, Jig. 12., be a vessel with a flat square bottom and perpendicular sides ; and suppose it filled with water ; and let the side A B be supposed to be divided into ten equal parts, marked by the numbers 1, 2, 3, 4, to 10 : the pressure at the A TREATISE ON HYDROSTATICS. CHAP. Ill, Fig. 12. 8 point 1 we shall suppose to be one pound. The point 2, being- at twice that depth, will sustain a pressure of two pounds The point 3 will sustain a pressure of three pounds, and SQ on, the lowest point sustaining a pressure of ten pounds. Since, there- tore, the intensity of the pressure from A to B increases uni- formly, the point which sustains the average pressure will be found at the middle of the depth A B. This point is that which is marked 5. If we suppose the whole surface A B to sustain the same pressure as that which 'the point 5 suffers, the total pressure will be the same as at present. A very slight consid- eration of the effects will make this evident. At present the point sustains a pressure of six pounds, and the point 4 sus- tains a pressure of four pounds, making a total of ten pounds, these two points each sustained a pressure of five pounds, which is the average pressure, the total pressure would still be the same, ten pounds. In like manner, the point 7 at present sustains a pressure of seven pounds, and the point 3 a pressure of three pounds, which together make ten pounds. If each of these points sustained a pressure of five pounds, the sum would be the same. It is evident that the same reasoning will apply to all points equally distant above and below the middle point 5. The pressure on each point below it exceeds the pressure at 5 by exactly as much as the pressure on a point equally dis- tant above it falls short of the pressure at 5. Thus the excess and defect mutually compensate each other, and a general average is obtained. From what has been now stated, it appears that the total pressure on the perpendicular side of a vessel filled with a liquid, is the same as if that side were converted into a horizon- tal bottom, and half the depth of liquid rested on it. It also appears that the pressure on the perpendicular side is entirely independent of the quantity of liquid which the vessel contains. The perpendicular sides of a trough, when filled with a liquid, will sustain the same pressure whether the trough be wide or narrow. If the sides be separated by an interval of only a quarter of an inch, and the trough contains only a quart of water, the pressure on the sides win be the same as if the sides were separated many yards, and the trough contained several barrels of water. CHAP. III. PRESSURE ON VESSELS. 25 (23.) If the sides of the vessel be perpendicular, and the bot- tom be horizontal and flat, the pressure on the sides may be estimated in the same manner as above, whatever be the shape of the bottom. The point of average pressure is, in this case, always at half the entire depth below the surface of the liquid ; and the total pressure is the same as if this average pressure were uniformly diffused over the entire surface of the sides in contact with the liquid. Thus, if the vessel be cylindrical, and the circumference of its base be ten feet, the depth of the fluid in the vessel being eight feet, the total surface of the sides in contact with the fluid is eighty square feet. The medium pressure is that which is sustained by a point at the depth of four feet, and, therefore, is equal to the weight of four feet of the liquid. Of the eighty square feet, forty are subject to a less pressure than this medium, and the other forty are subject to a greater pressure : these two effects compensating each other, the total pressure is the same as if the medium pressure were diffused over the whole eighty feet. The whole lateral pressure is, therefore, the same as would be produced upon the bottom of a vessel of eighty square feet in magnitude, with per- pendicular sides, and containing the liquid to the depth of four feet. This pressure would, in fact, be the whole weight of the fluid in the vessel, the quantity of which wouid be found in solid feet by multiplying the bottom by the depth; that is, eighty by four ; that is, 320 solid feet. (24.) The rule deduced from this example, for calculating the lateral pressure, is generally applicable to all cases where the vessel containing the liquid has a flat horizontal bottom and perpendicular sides. Find the number of square feet in the sides below the surface of the liquid contained in the vessel ; multiply that by the number of feet in half the depth of the liquid : the product will express the number of solid feet of the liquid, the weight of which is equal to the lateral pressure. The number of square feet in the sides may always be found, by multiplying the number of feet in the circumference of the bottom by the number of feet in the depth of the liquid. From this rule some curious consequences follow. The pres- sure against the sides produced by the liquid may exceed in any proportion, however great, the whole weight of the fluid which causes this pressure. If the lateral surface in contact with the fluid be double the magnitude of the bottom of the vessel, then the lateral pressure will be equal to the pressure on the bottom, and, therefore, equal to the whole weight of the fluid ; for, in this case, the lateral pressure will be equal to the weight of the fluid which would fill a vessel with perpendicular sides, having a bottom of double the size, but filled only to half the depth. The quantity of liquid whose weight expresses the 3 A THBATISE ON HYDROSTATICS. CHAP III n g the saTe Vatio If th P f mcreases ' the Pressure increases Fig. 13. CHAP. III. PRESSURE ON VESSELS. 27 vessel which marks the surface of the liquid. Hence, in this case, as well as in the former, the medium pressure is that which affects the middle part of the depth marked 5. in Jig. 14. ; Fig. 14. and the whole lateral pressure will he obtained by multiplying the number of square feet on the sides of the vessel by the number of feet in half the depth of the liquid : the product will express the number of solid feet of the liquid whose weight is equal to the total pressure.* In this manner, the pressure on inclined embankments, or the sloping sides of vessels containing liquids, may be ascertained. In fig. 14. the sides of the vessel containing the liquid are represented as sloping outwards, or diverging upwards from the bottom ; and it is not difficult to conceive, that each point of the side will sustain a pressure equivalent to the weight of the column of liquid perpendicularly above it : but the same consequence would ensue if the sides inclined inwards or con- verged upwards from the bottom, as in jig. 15. In this case, also, although each point of the lateral surface have not any column of the liquid perpendicularly over it, still it is pressed by the liquid in a direction perpendicular to the side, Avith the same force as if such a column Avere perpendicularly over it. The cause of this may be conceived by the following reasoning. Let P be a particle of the liquid, at the same depth beloAv the surface as the division marked 5. on the side of the vessel ; this particle is evidently pressed downwards by the Aveight of the incumbent column P A. But, by Avlmt has been already proved, it must be pressed by the same force in every possible direc- * It is necessary that the sides t-hould bo of uniform width. For example, the above rule could not bo applied to that side of the vessel which is presented to- ward the eye in Fig. 11. AM. Eu. 00 A TREATISE ON HYDROSTATIC* CHAP m i' s may be ~- Sto each of th n 1 arm * Let water be now P 011 red tached Tt "n ^^ u ' ^Y & s pressure, the bottom is de- ^ depth of^^te^tl^^islTe 6 ^ CHAP. HI. PRESSURE ON VESSELS. There is another method of illustrating these theorems ex- perimentally, which is attended with less practical difficulty than that just mentioned. Let the movable bottom be pressed against each vessel by a string attached to it, and carried up through the vessel ; and then let the vessel be plunged in a cistern of water, as represented in Jig. 16., until it attain such a depth that the upward pressure of the water under the bottom will be sufficient to keep the bottom firmly attached to the ves- sel. Let the string be then disengaged, and let water be pour- ed into the vessel until its pressure detaches the bottom ; and let the depth of water be observed which is sufficient to effect this. Let each of the three vessels be immersed in the cistern in a similar way, and to the same depth, as represented 'mjigs. 16, 17, and 18. It will be found that the depth of water neces- Fig. 16. Fig. 17. Fig. 18. sary to be poured into the vessel in order to detach the bottom will be the same. The following experiment is a very striking illustration of the same principle : A cylindrical vessel A B, Jig. 19., has a glass tube inserted in it, water-tight, at a, and is provided with a movable bottom, which, however, fits it water-tight. This bottom is supported by a wire, which, passing up the tube, is attached to the arm of a balance, and is counterpoised by a weight in the dish sus- pended from the other arm. Suppose the vessel A B now to be filled with water to the neck, a ; and let the tube be divided into parts at 6, c, d, e, each of which shall be equal to the depth of the vessel A B. Let a sufficient weight be put into the dish to maintain the bottom of the vessel A B in its place. This weight will be found to be equal to the weight of the water 3* 30 A TREATISE ON HYDROSTATICS. CHAP. III. contained in the vessel A B. Thus it appears that this water presses down the bottom with a force equal to its weight. Let water be now poured into the tube until it rises to the level b : it will be found that exactly as much more weight in the dish D will be necessary to maintain the bottom in its place, as was required to support it when the level was at a. Thus the column a 6 produces as much pressure on the bottom as the whole of the liquid in the vessel A B. If the tube be again filled to the level c, the pressure will receive another increase, equal to the weight of the liquid contained in A B ; and a similar addition must be made to the Counterpoise, in order to main- tain the bottom of the vessel in its place. In the same manner, each addition which is made to the column in the tube equal to the depth of the vessel A B will cause a similar increase in the pressure, and will be indicated by the necessity of giving a corresponding increase to the counterpoise. In this case the box A B and the tube must be fixed in their position independently of the bottom of the vessel. The force which sustains the bottom will have a tendency to press the vessel A B upwards, amounting to the excess of the whole weight in the dish above the weight of the bottom of the vessel, together with the weight of the water in the vessel and tube. In fact, all that part of the weight in the dish which is not spent in supporting the bottom, and the water above it, is expended in producing a pressure against the top of the vessel A B, which that vessel must be so firmly fixed as to resist (28.) We have hitherto supposed the sides of the vessel to be straight and regular ; but even though they be not, the pres- sure on the bottom is determined by the same rules. In the consequences of this principle, the hydrostatic paradox reap- pears under some curious forms. CHAP. III. PRESSURE ON VESSELS. Fig. 20. Let ABC D,^o-. 20., be a square close vessel, with a small hole, O, in the top, in which a narrow tube, T O, is screwed water-tight. Let the vessel A B C D, and the tube to the level T, be filled with water. According to the principle which has been just established, the pressure on the bottom, C D, will be proportional to the depth, T M ; or, in fact, will be equal to the weight of water which would fill a vessel of the magnitude E D C F. This will be the case, however shallow the vessel, A B C D, and however narrow the tube, TO, may be ; and hence an indefinitely small quantity of water may be made to produce a pressure on the bottom of the vessel which contains it, equal to the weight of any quantity of water, however great. As the pressure depends only on the depth, and is independ- ent of the shape of the vessel, it is not necessary that the tube, T O, should be straight, but it may be bent or deflected into any irregular form whatsoever. But, whatever be its shape, the depth of the fluid is to be estimated by the perpendicular distance of the upper surface from the bottom of the vessel. (29.) In the examples already given, the sides and bottoms of the vessels considered have been flat surfaces, or have been in the perpendicular or horizontal position. The surfaces, however, of vessels or reservoirs are subject to every variety and shape ; and it is necessary in practical science to possess rules applicable generally to all surfaces which contain liquids. What has been already stated with respect to the average pressure, is the principle which, generalized, must lead to such a rule. The various parts of any surface, whatever be its form, will be subject to pressures, depending on their depths below the surface of the liquid, all points at the same depths suffering the same pressure. There is a certain pressure, or mean of all the various pressures, to which the points of the surface are subject ; and whatever this pressure be, it must be such, that, 32 A TREATISE ON HYDROSTATICS. CHAP. III. if diffused over the whole surface, the total amount of the pres- sure on that surface will not be altered. If, therefore, this me- dium pressure can be found, und the magnitude of the surface in contact with the liquid be known, the total pressure may immediately be obtained. Suppose, for example, the average pressure be 15 pounds upon every square inch, and that the magnitude of the surface in contact with the liquid be 100 square inches, then the total pressure will be 1500 pounds. The determination of the total pressure, therefore, depends on that of the average pressure. Now, as the pressure at each point is proportional to the depth of that point below the sur- face, it may be considered as represented by that depth. Thus, if a pressure of one pound be produced upon a square inch at the depth of one foot, a pressure of two pounds will be pro- duced upon a square inch at the depth of two feet, three pounds at the depth of three feet, and so on ; the number of feet in the depth always expressing the number of pounds in the pressure. Hence it is obvious that the average pressure will be produced at the average depth ; and, therefore, the question is reduced to the determination of the point whose depth below the surface is an average of the depths of all the points of the surface in contact with the liquid. By a singular though not unaccountable coincidence, the point which would be the centre of gravity of a thin sheet lying in close contact with the surface of the vessel, covered by the fluid, is placed at that depth below the surface which corresponds to the medium pressure. This arises from a property of the centre of gravity well known to geometers, and from which that point has been sometimes called the centre of mean distances. The centre of gravity of any surface is always placed at a distance from any plane surface, which is an average or mean of all the dis- tances of the various points of the proposed surface frcm the plane surface. (30.) To determine, therefore, the total pressure on any sur- face, let the position of the centre of gravity of that surface be determined by the rules established in mechanics, and let its depth below the surface of the liquid be ascertained ; then multiply the number of feet in this depth by the number of square feet in the surface of the vessel covered by the liquid : the product will express the number of solid feet of the liquid, whose weight is equal to the total pressure. Excepting the case of regular surfaces, the determination of the centre of gravity is a problem which connot be solved with- out the aid of mathematical formularies of considerable difficul- ty.* We shall, however, illustrate the theorem just explained * Cab. Cyc. Mechanic*, chap. ix. CHAP. III. PRESSURE OX VESSELS. 33 by some examples, which we can render intelligible to the general reader. Let a hollow globe be filled with a liquid through a small hole in the top. The centre of gravity of the surface of the globe is evidently at its centre : and therefore the depth of that point is half the diameter of the globe. The total pressure will, therefore, be found by multiplying the number of feet in half the diameter of the globe by the number of square feet in its surface. By the principles of geometry it is proved, that the solid contents of a globe are determined by multiplying the number of feet in half the diameter by a third part of the number of square feet in the surface. Hence it appears that the pressure on the surface of the globe is three times the weight of its contents. If a cubical vessel that is, one having a square bottom and four square side?, each equal to the bottom be filled with a fluid, the centre of gravity of each of the four perpendicular sides will be at half the entire depth of the fluid below the sur- face. Therefore the? pressure on each side will be found by multiplying the number of feet in half the depth by the number of square feet in the side. But the entire contents of the ves- sel are found by multiplying the number of feet in the entire depth by the number of square feet in any side. Hence it ap- pears that the pressure on each of the four sides is equal to half the weight of the fluid contained in the vessel. The pres- sure on alPthe four sides is, therefore, equal to twice the weight of the fluid contained in the vessel. The pressure on the bottom has already been shown to be equal to the whole weight of the fluid : and therefore it follows, that the total pressure of the fluid on the surface of the vessel, including both the sides and bottom, is equal to three times the weight of the fluid which it contains. Thus it appears, that a globe and a cube, containing equal measures of liquid, will suffer equal pressures if filled, each sustaining a pressure amounting to three times the weight of the fluid it contains. (31.) If any body be immersed in a fluid, the pressure which its surface sustains from the surrounding liquid is .to be deter- mined by the same rules, and according to the same methods, as are used for determining the pressure on the surface of the vessel which contains the liquid. Thus, if a globe be plunged in a liquid, the total pressure on its surface is found by multi- plying the number of feet in the depth of its centre, below the surface of the liquid, by the number of square feet in its exte- rior surface. (32.) The two hydrostatical theorems which we have at A TREATISE ON HYDROSTATICS. CHAP. Hf. tempted to explain in this and the preceding chapter, viz J That liquids transmit pressure equally in all directions ; Ind, 2. That the pressure produced by the weight of a liquid is pro- serve to elucidate -5r*tt If an empty bottle, or rather one containing only air be Sde ablTf i and ?i C SUnk by WGights attached t * ^ a con! water will p ? th *Y V^' ^ prGSSUre f the surrounding Jhrmmh L I' br n eak the bottle, or force the cork into it to i? Ill ^ "I ' n dra U P the b ttle, ^ n be found to i ll , the neck? ^^ ^ t0 haVG the Cork within ho 1 brnLn ^ If ^ SideS ' and be s q^e-bottomed, it will be br ^en by the pressure, the form being unfavorable to strength ; but if it be round, it will be more iFkely to resist the pressure, and to have the cork forced in. The ^hapen this case is conducive to strength, partaking of the qualities of an An experiment of the nature just described was made by Mr Campbell, author of" Travels in the South of Afrka On 1 is 3 fnt T th \ Ca / e ? f ? d H P 6 homeward, he forced a l H ,t ?| C i k f a b ttle ' so thick as to fit ^ very tightly and so that half the cork remained above the edge of the neck' of C th r e 1 W S 51 r UI l d 1 th6 C rk ' and fa8tened to ^e neck J bottle ; and the whole was covered with pitch. The bottle was connected with a weight to make it sink, and, beino- uspended by a sounding-line, was gradually let down into thf ea. When it attained the depth of about fifty fathoms, an in- crease of weight was suddenly felt. Upon drawing up the hot- e the cork was found inside, and the bottle filled with water. Another bottle was similarly corked, but a sail-needle was passed through the cork across the edge of the neck so aT resist the passage of the cork into the bottle. Thus prepared the bottle was again immersed to the depth of fifty Son" s and the same sudden increase of weight was felt. Upon draw ing up the bottle it was found fillecf with water, but the cork was not displaced. Mr. Campbell attributed this effect to the CHAP. III. COMPRESSION OP LIQUIDS. 35 which covered it not being broken, arose from the perfectly equal pressure which was excited upon it in all directions.* The equality of the pressure which a liquid exerts in all di- rections is demonstrated by the fact, that, to whatever depth a soft or brittle substance may be immersed, it will undergo no change of shape by the surrounding pressure. This is an effect which it is obvious could not be produced by any other cause than a perfect equality of pressure on every part ; for if any part were subject to a greater force than an adjacent part, that part would be pressed inwards if the body were soft, and would be broken off if it were brittle. A piece of soft wax, or a piece of glass not having any hollow part within it, being immersed to any depth in water, suffers no change. If a piece of wood which floats on water be forced down to a great depth in the sea, the pressure of the surrounding liquid will be so severe, that a quantity of water will be forced into the pores of the wood, which will be sufficient to increase its weight, so that it will be no longer capable of floating or rising to the surface/)- A diver may, with impunity, plunge to certain depths in the sea ; but there is a limit of depth beyond which he cannot con- tinue to live under the pressure to which he is subject. For the same reason, it is probable that there is a depth below which fishes cannot exist-! (33.) Liquids in general are treated in hydrostatics as incom- pressible bodies ; that is, as bodies which, being submitted to pressure, will not suffer their dimensions to be diminished ; and this is true, except in extreme cases. It was long considered that no force whatever was capable of compressing a liquid ; but experiments instituted in the year 1761 by Canton proved, Fig. 21. that under severe pressure they suffered a slight diminution of bulk : it also appeared, that upon the pressure being removed they resumed their former dimensions. It was thus established, that liquids not only were compressible in a slight degree, but also elastic.^ The pressure of liquids at great depths below the surface, furnishes an easy method of verifying by ex- periments these results. Let A B, Jig. 21. b'e a cy- lindrical vessel, having a round hole, C, in the top, * Campbell's Travels, p. 507. Brewster's Ency. xi. p. 483. f Hence the timbers of ships, which have foundered in a deep part of the ocean, never rise again to the surface, like those which are sunk near tho shore. AM. ED. J Fishes have been caught at a depth at which they must have sustained a pressure of eighty tons on each square foot of the surface of their bodies. AM. EQ. Cab. Cyc. Mechanics, p. 19. nf A TREATISE ON HYDROSTATICS. CHAP. HI. through which a piston, P M, passes water-tight. Let this vessel it' C Le? fri y m ft* WHh A T r ' the Pist n P M ^ing inserledt j f S r n 6 UP ? nthQ Plston ' with efficient friction to down f \ r m f m & b r ** own w eight; and let it be pressed down to the orifice C. Let the vessel now be plunged to SSfe% Pth ^ the S6a - Up n dra S R S wil be found hat the pressure of the surrounding water had forced the tatoed in a / reat< ;!; ^ * ^ V6SSel ; and that the water * Th] s w H KeTd r/T \ 0m P ressed into smaller dimensions. is will be indicated by the position of the rin^ which si on the piston; for that will be "found, not at thforTfi e, a b e ! fn^ T r !L n ' but f a Certain distance ab ve it. On being forced into the vessel, the piston passed through the ring which SSr^SSSi 1 " 1 S P Siti0n ^ thG 10P f the -ssel frnmedt ately surrounding the piston. Upon drawing up the vessel the removal of the pressure enabled the wat?r contained in it Lt e S e ion S di r n " nS ' and the Pist n Was forLf baTk to i s fv^th? ?n S' f S," r"? Ut f the V6SSel i1: carried the rin S "P the vessel 1 ad V H^ 06 f ? 6 ring fr m the hole C ' after ha b 2? v of w a e fp m St T?T, Veili . ent Practical P roof of the compres- 7 ate f r * Jt hkewi se establishes the elasticity of that the niton wr re f mere , ly - C mpreSsible ' without be ^ n ^ S tic, me piston when forced into the vessel would remain in it volume' ^CT MC 1,^ dcon ^ uetoretoi SiS^ Tho dP. the , force ^ich compressed it had been removed, 1 he degree of compression produced by a given force mav m^Se^t^T th t t0tal C ntents of the vessel';^ tne wate Contained m the vessel is diminished by one twenti- ' dl ensions ' Thu 20 solid inches of water f sea P en to c mmunicate with an interalvitvo c mmuncate wt an case be proportional to the depth of the cavity belo7 the top CHAP. IV. LIQUIDS MAINTAIN THEIR LEVEL. 37 (35.) In the construction of pipes for the supply of water to cities, it is necessary that those parts, which are much below the level of the reservoir from which the water is supplied, should have a greater strength than is requisite in those which are in more elevated situations. A pressure always acts upon the inner surface of the pipe, tending to hurst it, which may be estimated in the manner already explained. A pipe, the di- ameter of whose bore is 4 inches, has an internal circumfer- ence of about 1 foot, and the internal surface of 1 foot of such a pipe will be 1 square foot or 144 square inches. If such a pipe were 140 feet below the level of the reservoir, it would therefore suffer a bursting pressure, amounting to about 60 pounds on every square inch of its surface, for 28 inches is con- tained 60 times in 140 feet ; and hence a piece of the pipe 1 foot long" will sustain 144 times this pressure, that is, a bursting pressure of 8640 pounds. This pressure considerably exceeds &' oduced in most high pressure steam engines. , CHAP. IV. S MAINTAIN THEIR LEVEL. EXPERIMENTAL PROOFS. VESSEL CONNECTED WITH COMMUNICATING TUBE. SEVERAL VESSELS BETWEEN WHICH THERE IS A FREE COM- MUNICATION. HYDROSTATIC PARADOX EXPLAINED BY THIS PRINCI- PLE. SURFACE OF A LIQUID LEVEL. WHY THE QUALITY DOES NOT EXTEND TO SOLIDS. SURFACE OF THE LAND. SURFACE OF THE SEA. CURIOUS OPTICAL DECEPTION IN WAVES. SIMILAR PROPER- TY IN REVOLVING SCREW. ORNAMENTAL FOUNTAIN CLOCKS. PHENOMENA OF RIVERS, SPRINGS, WELLS, CATARACTS, EXPLAINED. CANALS, LOCKS. METHOD OF SUPPLYING WATER TO TOWNS. EXACT SENSE OF THE WORD LEVEL. COMMON SURFACE OF TWO LIQUIDS IN THE SAME VESSEL. LEVELING INSTRUMENTS. SPIRIT LEVEL. (36.) FROM the two properties of liquids established in the last two chapters, a third, and not less important one, may be de- duced. If the pressure arising from the weight of a liquid be proportional to the depth, and that pressure be transmitted equally in every possible direction, it will follow, that the sur- face of all parts of a liquid contained in the same vessel, or in two or more vessels between which there is a free communica- tion by tubes or pipes, or otherwise, must be always at the same level ; and that if any external cause accidentally disturb that level, the liquid will by its gravity return to it, the higher parts falling, and the lower parts rising, until the equality be re- stored. 4 38 A TREATISE ON HYDROSTATICS. CHAP. IV. Let A B and A' B', Jig. 22., be two perpen- dicular glass tubes, united by a third tube, B B', placed in a horizontal position. Let any liquid be poured into the tube A until the horizontal tube B B' is rilled. Let us now suppose^ that the lower end of the tube A / B' is closed by a stopcock at B'. The tube B B' being hori- zontal, the water which fills it has no ten- dency to move by its weight towards either end, and therefore ie stopcock at B' sustains no pressure from it. Let an addi- tional quantity of the liquid be now poured in at A until it fill the tube to the height C. The surface of the liquid in the hor- izontal tub e at B is now pressed by the weight of the column B U i he liquid in the horizontal tube transmits this pressure undimmished to the stopcock B', which is therefore pressed up- wards by a force equal to the weight of the column of liquid i U. 1 his pressure would evidently cause the liquid in the horizontal tube to rush into the vertical tube B' C' if the stop- cock B' were opened. Supposing it to remain closed, however let a quantity of the liquid be poured in at A! until the column J shall attain the same height as the column B C ; the stop- cock B' will then be pressed downwards by the weight of the column B' C' resting upon it, while it is at the same time press- id upwards by the weight of the column B C, transmitted to it by the liquid in the horizontal tube. It is thus pressed up- Avards and downwards by equal forces ; and therefore, if it were free to move, it would have no tendency to change its P s ^ lon : hence, if the stopcock B' be opened, and the column B U allowed to rest immediately on the surface of the liquid, it will be supported, and no motion will take place ; thus the columns B C and B' C', having equal heights, balance each other through the medium of the liquid in the horizontal tube. Fig. 23. Let us suppose the stopcock B',/g. 23., again closed, and let the column of liquid in B 7 A' be greater than the column of liquid in B A, so that C' will be higher than C. The stopcock at B' will now be pressed downwards by the weight of the column B' C', and it will be pressed up- l wards by the weight of the column B C. The downward pressure being therefore greater than the upward, if the stopcock be opened, the column B' C' will descend, and the column B C will be forced up. The level C' will therefore fall, and the level C will rise. When they attain the same height, their weights will mutually balance each other, as in Jig. 22. ; and if these were the only forces in action, all Sr^ 0n WOUld then cease * ? ut in the descent of the column U & the whole mass of liquid in the tubes has acquired a cer CHAP. IV. LIQUIDS MAINTAIN THEIR LEVEL. 39 tain velocity, which, by reason of its inertia,* it has a disposi- tion to retain. The level C will therefore continue to rise, and the level C f to fall, after they have attained the same height; but when the column B C becomes higher than B' C' its down- ward pressure exceeds the upward pressure transmitted to it from B' C', and this excess resists the tendency to continue its motion upwards, and finally destroys it. The level C will then begin to descend, and the level C' to rise, and this will continue until the level C' has attained the height which it had at the commencement of the process ; it will then fall, and the oscil- lation will continue. We have here, however, set aside the"consideration of the effects of the friction between the liquid and the tubes which contain it. This, by continually resisting the motion of the li- quid, will cause it to rise to a less height in the tubes, at each oscillation, than it did at the preceding one, and at length will reduce it to a state of rest. In this state the surfaces C C' will be at equal heights above the horizontal tube B B'. (37.) We have hitherto supposed the tubes A B and A' B' to be perpendicular, but the same consequences will ensue if they have any oblique position, as in Jig. 24. As before, let a stop- cock be placed at B' and closed ; let the horizontal tube B B' be filled with liquid, and let a column be also poured into the oblique tube A B, the surface of which is at C. According to what has been proved in the last chapter, the column B C presses on the liquid in the horizontal tube with a force propor- tioned to the perpendicular height of the surface C above B. In fact, it presses with a force equal to the weight of a column whose height is B D, the line drawn from B perpendicular to the horizontal line from C. This pressure, therefore, is trans- mitted by the liquid in the horizontal tube to the stopcock B r , which is pressed in the direction of the tube B' A' with that force. If a quantity of liquid be now poured in at A', until the height of the surface C' above B' be equal to the height of the surface C above B, the downward pressure on B' will be equal to the upward pressure transmitted from the column B C ; for this downward pressure is equal to the weight of a column whoss height is B' D', which is equal to B D, Cab. Cyc. Mechanics, p. 21. et scq. 40 A TREATISE OX HYDROSTATICS. CHAP. IV. By reasoning precisely similar to that which has been used with respect to the perpendicular tubes, it may be proved, that if the stopcock B' be opened, the liquid will remain at rest ; and also that if the surface C' be not at the same level with the surface C, an oscillation will take place, which being continued for a certain time, the surfaces will at length settle at the same height above the horizontal tube. (38.) We have hitherto supposed that the tubes containing the liquid, whose weight produces the pressure, are equal in bore. The same consequences may, however, be deduced, if they be unequal, or if, instead of being tubes, they be vessels of any form whatever. Let A B, Jig. 25., be an oblique tube Fig. 25. communicating with a reservoir A' B', a stopcock being placed at B'. Let the tube and reservoir be now filled to the same height, C C', the stopcock at B' being closed. The same hori- zontal line, C C', will mark the level of the liquid in the tube, and the liquid in the reservoir. The liquid B C, in the tube B A, will press on the liquid in the horizontal tube, with a force equal to the weight of a column of the liquid whose height is B D, and whose base is equal to the section of the tube at B. This force will be transmitted by the liquid in the horizontal channel B B', so that each square inch of the surface of the stopcock B' will be pressed by a forco equal to the weight of a column whose base is a square inch, and whose fieight is equal to B D. The liquid in the vessel A' B' presses on each square inch of the other side of the stopcock, with a force which is equal to the weight of a column whose base is a square inch, and whose height is B' D'. If, therefore, as we have already supposed, B 1 ' D' be equal to B D, the stopcock will be pressed equally on both sides ; and if it be opened, no motion will take place in the liquid. But if, on the other hand, B' D' be not equal to B D, the higher surface will subside, and the lower one rise, and the oscillating motion already described will en- sue, and will continue until, at length, the surfaces C and C' settle at the same level. An apparatus, to illustrate experimentally the property by which liquids maintain the same level in communicating vessels, CHAP. IV. LIQUIDS MAINTAIN THEIR LEVEL. 4J is represented in Jig. 26. A, B, C, D, E, are glass vessels, of various shapes, communicating by short tubular shanks with a horizontal tube, which passes beneath them, and which in the figure is concealed by the stand which supports the vessels. In the shank of each is placed a stopcock, K, which when closed insulates the vessels, and when opened leaves a free communi- cation between them by means of the tube. Let all the stop- cocks be now closed, and let water be poured into the several vessels, so as to stand at different heights : if the several stop- cocks be opened, so that the vessels shall have a free commu- nication with each other, the higher surfaces will fall, and the lower ones rise, until they attain the same level, and then all motion will cease. If the stopcocks be again closed, and water poured into the vessels, so as to give the liquids different levels, the experiment may be repeated by opening the stopcocks. It will always be found, that, when the stopcocks are opene'd, the liquid will settle itself to the same level in all the vessels. A teapot, kettle, or any other vessel containing a liquid, and having a spout, must be so constructed that the lip of the spout shall be on a level with the top of the vessel, or at least on a level with the highest point to which the vessel is to be filled ; otherwise, upon filling the vessel above the level of the end of the spout, the liquid in the vessel, having a tendency to rise above the level of the end of the spout, will issue from it. If the vessel be inclined with the spout downwards, it takes a po- sition in which the level of the water in the vessel is above that of the lip of the spout, and accordingly the liquid flows out. (39.) Various examples of that class of effects which have been called the Hydrostatic Paradox, and which have been al- ready noticed, may be shown to be equivalent to this property by which fluids maintain their level. We shall confine our- selves here to one example. Let ABC D, ./!. 27., be a large vessel, with perpendicular sides, and communicating by B E with a perpendicular tube, E F, If water be poured into A B C D until it rises to the level K L, it will stand at the same level, H, in the tube E F. Now, snppos? all the water in the vessel A B C D above tha A TREATISE ON HYDROSTATICS. CHAP. IV. level IVI N to be removed, and its place supplied by a piston, M N, which moves water-tight in the vessel ; and let this piston be loaded with weights, so that the weight of itself and its load shall be equal to the weight of the water which has been re- moved : the piston will then press on the water below it with the same force as the water removed previously pressed upon it ; and as the water removed was sustained by it, the piston with its load will also be sustained. Thus it appears, that this piston is supported by the pressure of tile column of water in E F. It will easily be perceived thut this is identical with the hydrostatic bellows explained in (8.). If the column of water in the tube above the level O be re- moved, and its place supplied by a piston of equal weight, this piston, O, will support the groat piston M N. This effect is equivalent to the principle of the hydrostatic press explained in (7.). (40.) After what has been already proved, it is nearly self- evident that every part of the surface of a fluid confined in a vessel must, if at rest, bo at the same level. If this were not the case, it would evidently be possible that the surfaces of the same fluid, in communicating vessels, might have different levels ; for if we suppose two different parts of the surface of a liquid in a vessel to have different heights, as represented in the vessel ABC T>,Jig. 28., let us divide the vessel into two Fig. 28. by a solid partition, E P, leaving, however, between the two parts, .a communication, O, at the bottom ; and let this partition CHAP. IV. MOUNTAINS AND VALLEYS. 43 so divide the liquid, that the higher part of the surface, H, shall occupy one division, and the lower part, L, the other. We should thus have a liquid in communicating vessels standing at different levels ; a result which would be inconsistent with what was formerly proved. Therefore it follows, that all parts of the surface of a liquid contained in any vessel must stand at the same level when at rest. Indeed, this theorem is nothing more than a manifestation of the tendency of the component parts of every body to fall into the lowest position which the nature of their mutual connection, and the circumstances in which they are placed, admit. Moun- tains do not sink and press up the adjacent valleys, because the strong cohesive principle which binds together the constituent particles of their masses, and those of the earth beneath them, is opposed to the force of their gravity, and is much more pow- erful : but if this cohesion were dissolved, these great eleva- tions would sink from their lofty eminences, and the interven- ing valleys would in their turn rise an interchange of form taking place ; and this undulation would continue until the whole mass would attain a state of rest, when no inequality of height would remain. All the inequalities, therefore, observa- ble on the surface of land, are owing to the predominance of the cohesive over the gravitative principle ; the former depriv- ing the earth of the power of transmitting, equally and in every direction, the pressure produced by the latter. On the other hand, if the sea, when in a state of agitation, were suddenly congealed, the cohesive principle taking a strong effect, the mass of water would lose the power of transmitting pressure, and those inequalities which, in the liquid form, were fluctuating, would become fixed ; every wave would be a hill, and the intermediate space a valley. There is a curious optical deception attending the alternate elevation and depression of the surface of a liquid, which it may be useful here to notice. The waves thus produced appear to have a progressive motion, which is commonly attributed to the liquid itself. When we perceive the waves of the sea appar- ently advancing in a certain direction, we are irresistibly im- pressed with a notion that the sea itself is advancing in that direction. We consider that the same wave, as it advances, is ccmposed-of the same water, and that the whole surface of the liquid is in a state of progressive motion. A slight reflection, however, on the consequences of such a supposition, will soon convince us that it is unfounded. The ship which floats upon the waves is not carried forward with them ; they pass beneath her, now lifting her on their summits, and now letting her sink into the abyss between. Observe a sea fowl floating on the water, and the same effect will be seen. If, however, the wa- 41 A TIU VTIM ON n\ DROS1 il H ( HAl*. IV. tor itself partook of the motion which wo ascribe to its wave*, tho ship and tho foul would each bo carried for\\ aid, and would I motion in common with tho liquid. Once on tho summit of a wave, thoro thoy would continually vomain, and their mo- tion \\ould ho as smooth as if thoy \\orepropelloduponthecalm snrt'aoo of a lako. Or if once in tho vailoy between two ^ likewise thoy would continually remain, the ono wa\o continually preceding thom and the othor follo^ In liko inannor, if \\ o observe tho waves continually npproai'h- injr tho sluuv, wo must bo oonvnu'od that this apparont motion is iu>t ono in which tho water has any share ; for uoro it so, tho waters of the son \\onlu soon bo lumped upon tho shores, and would inundate the adjacent country : but so far from the wa- ters partaking of tho apparent motion of the waves in approach- ing the shore, this motion of tho uavos ccntinues, oven when .ire retiring. If wo observe a tlat strand when tho tide is ebb;- -.11 still find tho waves moving 1 towards tho shore. Th;>t the apparent motion of the \\aves is, therefore, an illu- vvo can no louder doubt ; but we are naturally curious to kuo\\ what is tho causo of this illusion. Thnt a proj:'.. . t.ikos place in .>Mj7/ii.'?ir. wo have proof, from tho ovi- fience of sijfht That no pro^rossi\o motion takes place in tho luniid, wo have also proof, both from the end;- t, and from othor still more unquestionable testimev,\ . To \\hat then iloOvS Uu> motion bolonjr ? \Vo answer, tv> the/o;v;j of the \\ , \ D, and tut to tho liquid \\hich composes it K. K.' ru Let tho ummlatinjT line in fs;. Q$>. bo supposed to rep- tho surface of the sea, nnd lot'A 1U' bo tho crests of thn cessive wnvos, and a b c tho intermediate valleys' lot LM Wpresont the bottom of the SCau At \. fthc water i* represented by tho lino A K and tho tleptli hero is represented by m' K . The summit of \. \ tor tlu:n t w'. Tho pressure of the oohunn A K bring ^ratcr than Una (HAP. IV. WAVi;s. 45 of;;/.' K', tho point, A has a tendency to full, niul the point m 7 to rise by reason ol' this excess oi' pressure. Therefore in' will rise to ti.e. point A', while A sinks to tic- level in. Tims the points A iuid in' have intercham'vd levels; the point m' I>MII- now raised U> IA great :i hei'Mit :ihove the Imttom L INI as the point A h:il before the change, Mini the point A having fallen to the bright whirl: m' hid. In like manner it will he round th;:l, lor every point in the first posilion of the wave, there is another point in the second position with whirh it, intercliam-r.; ulevations. If theae circmiraances he elosely considered, it will nol he di'.licnlt to perceive that, in the interval which we h:ue supposed. Hie v.irioe.s points on the surface of the w;i(er, such : : in', winch were helore on the sloping sides of the waves, have i;o\v hecoine their summits, A' !>' ( ', A c. Not that the points A IJC, \T. have advanced to A' 15' < '', S. c., hut that they ha\e 1'allrn iVoin t.heir former elevations, while the latter have risen. It appears, therefore, that the undulations of the sur- face are produced by its ditlerent points ascending and descend- ing r 1 !.. T.:.it,:dy in a ' perpcndicnlar direction, witliout any kind of progressive, motion. To make this still umro clear, lot us aupi)ose that perpendicu- lar lines he drawn from every part of the surface AaB&Cc, &C.totfce coire.spondinn- points in the surface A' a' B' V C' c', v.id let the interval between the periods at which the sur- f the liijuid assumes these two forms be conceived to bij one se. -OIK! ; in that time the several points of the first surface, A\ !iic!i are marked by the letters /J,'fall in the direction of the l lines perpendicularly downwards to the points mark'-d //, ;n: .! tin- jittini : marked the rollers, the cloth being kept sta- iionarv, the progressive motion of waves will be produced, the cloth will appear to advance.* if -i ropOtlyini itraigUl >>n -.-, floor, have mio of its emln olovatod, and then Mi.i.ii-niv iic;i', Jar Illusion \\iii be |M...in,-,.,i, t'ty of water, which, independently of level norT+lt rec l ul8lte J raise the surface of the water to'that of the higher scendin" lt? quantity required to pass, in the case of ascending and de- lock thf bSftom n of r wr T ' ?" mm ***?' When a descending boat'enters a tn ' ,'. n o e par o the lower level, behind it, a por- tion of water equal to the immersed part of the boat; and the gates bein- closed elnnd it, a quantity of water is required to pass into the lock from the upper level C PaC ' l i i r , Part , f the Iock > situated ^tween the upper and lower levels, diminished by the bulk of the immersed part of the boat and this last being the quantity forced out by the boat on entering, it is evident/that with on entering, it is evidentthat with s of as- d the eaviy aen e oat, an the more exact its adaptation to the lock, fftina ti i 6 ( : x p f ondltu 1 re - Thc foregoing considerations would be useful for regu! ting the heights, and consequently the number of locks, the forms of their hot- m^i a ni en i Y1 d l1 ^ rclatlV , t0nna S e ' " Ascending and descending, large and small, and loaded and empty boats. This i, not the place for more minute dH CHAP. IV. SUPPLY OF WATER FOR TOWNS. 51 It is therefore often better, where it can be accomplished, to carry the canal through a circuitous course, than to take a shorter route with a greater number of locks. Owing to the small quantity of friction which exists between the particles of a liquid and a solid, the slightest inclination in the channel is sufficient to cause the water to flow. In a straight and smooth channel a descent of one foot in about four miles will cause the stream to flow at the rate of three miles an hour. The average slope of the principal rivers of the world is, however, greater than this. (43.) It is necessary at all times to know the level of the water in the boiler of a steam engine ; but that being a close vessel formed of metal, it is impossible by any external indica- tion to perceive the water within. A glass tube, A B, Jig. 32., Fig. 32. -' "**! C" .' is inserted in the side of the boiler ; one end, A, passes into the boiler near the top, and the other end, B, near the bottom. The water in this tube must always stand at the same level with the water of the boiler ; arid the tube being of glass, this level may always be observed. The indication of the tube would not in this case be correct, if the upper end A were not inserted in the boiler, but left open to the atmosphere. The surface of the water in the boiler is subject to the pressure of the steam, which is there confined ; and in order that the sur- face of the water in the tube should have the same level, it must be subject to the same pressure. This will necessarily be the case, if the top of the tube communicate with the steam by being inserted in the boiler at A. (44.) The method of supplying water for towns depends on the property of maintaining its level ; a reservoir is selected in some situation more elevated than those places to which the water is to be supplied. This reservoir is fed either from nat- ural sources or by mechanical power. Pipes are conducted from it, usually under ground, through all parts of the town ; and from the main pipes smaller ones ramify, and pass into each house. These pipes may be carried in any direction which may be desirable, and alternately up and down the steep- 53 A TREATISE ON HYDROSTATICS. CHAP. IV. est hills, and to the tops of the highest houses, providing that the level of the water in the reservoir be above the highest points to which the pipes are carried. By such means a constant and abundant supply of water for domestic purposes may be introduced into the upper apart- ments, and when used may be carried off by waste pipes Ignorance of this principle, by which liquids return to' their level, is shown m the construction of aqueducts by the ancient' for supplying water to towns. If it were requisite to conduct water across a valley, a bridge was constructed on arches, sup- porting a canal through which the water was carried. A pipe conducted under ground across the valley would have served tne same end, with far less expense ; for the water would rise other m P1PG n thC ne Slde aS it: had descended on the (45.) Taken in a loose popular sense, the term "level" is easily comprehended ; it is necessary here, however, to explain its import more exactly. The figure of the earth is that of a globe, or nearly so ; there are inequalities on its surface, but they are so insignificant, that, when compared with its own magnitude, the most enormous mountains resemble impercepti- le particles of dust, resting on those globes which are used to represent the earth, and on which its natural and Apolitical di- visions are depicted. These inequalities, small as thev are cease to exist on the surface of the waters when thev are not agitated by wind. They present, in that case, a surface uniformly curved, and which, if continued in every direction without mterruption would assume that figure which is ascribed > the earth. If a line be drawn from the centre of the earth to any part of this surface, that line will represent the direction in which the attraction of gravity acts. It will be the direction Fig. 33. in which a plumb-line will hang when at rest and /;;- -V % X << he surface of the earth, such as it has been' just "~ descnbed > wil1 be every where perpendicular to ; lines thus drawn.* Below and above the actual ! surface of the earth, other concentrical surfaces may be conceived, as represented mfig. 33. by the dotted circles. Each of these surfaces will enjoy to the surface, unless the earth were a perfect globe, or sphere ' "" C P fetaf '! - t h T S ' " n0t Ciefl y ow * ^its moiains, thef feet [of which might be here neglected, but to its oblateness, or its being flattened at the poles, and protuberant at the equator. Many instances occur il the text cle , ntlfic Precision would require the use of vertical has beefl employed ' to avoid the a-*-* CHAP. IV. SURFACE OF SEA CURBED. 53 the same properties as have been already ascribed to the sur- face of the earth. Each of them will be every where perpen- dicular to straight lines diverging from the centre, and will ba every where equally distant from that point. Every part of each of these concentrical surfaces is said to form the " same level ;" and one level is said to be " above" or " below" another level, according as it is more or less distant from the centre.* When a liquid mass placed upon the earth is quiescent, eve- ry part of its surface settles itself in the same level, and all parts which are disposed in any other level under its surface are subject to tiie same pressure ; that pressure being great in proportion to the depth of the level in question below the surface. (46.) Notwithstanding the globular form of the earth, a sheet of water on a calm day appears to exhibit a plane surface, no curvature whatever being perceivable. The cause of this is easily discovered in the small proportion which such a surface bears to the whole earth. Let us suppose a circular lake of four miles in diameter, and conceive a straight line to be drawn, or a cord stretched across it, between two opposite points. By reason of the curvature of the surface, this cord would be under the water towards the middle, if it only touched the water at the extremities ; and its depth would be greatest at the centre of the lake. Nevertheless, in the case we have supposed, its depth at that point would only be 15| inches ; the curvature, therefore, in a circuit of two miles round a given point, will not raise that point 16 inches above the plane surface, passing through the extreme points of the circuit. It is not wonderful, then, if fluid surfaces of small extent appear to be, and practically speaking really are, plane, the de- gree of curvature being insignificant. Any plane surface of a small extent is, then, said to be level, when it is parallel to the surface of a liquid which is quiescent ; and all particles of a liquid which are disposed in the same plane, parallel to its sur- face, are said to be in the same level. Although, as we have just stated, the curvature of the surface of a liquid be very small, yet, if that surface have sufficient ex- tent, the curvature may be ascertained by observation. When a distant vessel first comes within sight at sea, the point of the mast only is perceived ; as it approaches the mast gradually rises ; and last of all appears the hulk, which, from its magni- tude, would be the first seen, if the swelling curve of the sur- face of the sea had not obstructed the view of it. (47.) The law, by which all parts of the surface of the same * The concentrical surfaces are expressed in French authors by the term " couches do nivean." 54 A TREATISE ON HYDROSTATICS. CHAP. IV. liquid rest in the same level, will not be violated if one liquid be placed upon another, or even if a series of liquids were placed one above another. If a glass vessel, /g-. 34., be partly Fig. 34. filled with water, W, and on the water, oil, O, be poured, the surface of the water will continue to be level, bearing the oil upon it. Again, if another liquid, as ether, E, be poured upon the oil, the surface of the oil on which the ether rests will con- tinue to be level ; and so on. In these cases, however, the pressure of the liquids on any stratum is not proportional to the depth of the stratum. The pressure at any level is equal to the weight of the incumbent column of liquid. But that column is not, as in the cases formerly considered, composed of the same liquid, and, therefore, it is not true that any part of the column has a proportional weight. The various appearances produced in ornamental water- works are the effects of pressure transmitted through pipes from a head of water, considerably raised above the orifices from which the water is required to be projected. The form and direction of these orifices determine the figure which the jet or fountain will assume ; and the height of the water trans- mitting the pressure will determine the altitude to which the water of the fountain will be projected. (48.) Instruments for leveling or determining the direction or position of horizontal lines, or the relation between the lev- els in which different objects are placed, are constructed by means of the property by which liquids maintain their level. Let A, Jig. 35., be a straight glass tube, having two ether glass tubes, B and C, united with it at right angles. Let the tube A, and a part of each leg B and C, be filled with a liquid, the legs B and C being presented upwards. On the surfaces a b of the liquid in the legs, let floats be placed, carrying upright wires, to the ends of which are attached sights, S T, consisting of two fine threads or hairs stretched at right angles across a square : CHAP. IT. LEVELING. these sights are placed at right angles to the length of the in- strument, and a front view of them is represented at S' T ; ; and they should be so adjusted that the points where the hairs in- tersect shall he at equal heights above the floats. This ad- justment may be made in the following manner : Let the eye be placed behind one of the sights, looking through it at the other, so as to make the points where the hairs intersect cover each other, and let some distant object covered by this point be observed. Let the instrument be now revers- ed, and let the points of intersection of the hairs be viewed in the same way, so as to cover each other. If they s,re observed to cover the same distant point as before, they will be equal heights above the surfaces of the liquid. But if the same dis- tant point be not observed in the direction of these points, then one or the other of the sights must bo raised or lowered, by an adjustment provided for that purpose, until the points of inter- section be brought into that direction. These points will then be properly adjusted, and the line passing through them will be truly horizontal. All points seen in the direction of the sights will then be in the level of the instrument. The principles on which this adjustment depends are easily explained : if the intersection of the hairs be at the same dis- tance from the floats, the line joining those intersections will evidently be parallel to the lines joining the surfaces a b of the liquid, and will, therefore, be level. But if one of these points 56 A TREATISE ON HYDROSTATICS. CHAP. IV. be more distant from the floats than the ether, the line joining the intersections will point upwards if viewed from the lower sight, and downwards if viewed from the higher one. On re- versing the instrument this line must take a different direction, and therefore will not be presented to the same object. The accuracy of the results given by this instrument may be increased to any extent, by lengthening the tube A. (49.) Another instrument for leveling is known by the name of the spirit level: it consists of a cylindrical glass tube filled with spirits of wine, except a small space which is occupied by air ; the ends are hermetically sealed, to prevent the escape of the fluid. In whatever position the tube be placed, the liquid will always tend to the lowest part of it ; if either end be raised above the other, at that extremity will the bubble of air be found, the liquid having retired to the other. If the extremities be at the same level, the bubble of air will settle at the highest inter- mediate point. The tube is not strictly straight, but is slightly curved, the convexity being presented upwards. Whatever be the position of the tube, the air bubble will rest at the highest x )oint of the curve ; and if the extremities be at the same height, this will be the middle point. The tube in a horizontal position, with the air bubble resting in the centre, is represented in fig. 36. Fig. 36. The method of mounting the level for the pui pose of fixing a plane in a horizontal position, is commonly to fix the tube in a block of wood, or in a case of brass, A B,J%. 37. The block is fixed in such a position, that when the lowest surface, D E, is horizontal, the bubble will stand in the centre between two lines, a and &, cut upon the tube. The instrument may be ad- justed by the following method : Let a plane surface be con- structed as nearly horizontal as possible, and let the surface D E be placed upon it. Let the tube be fixed into the block in CHAP. IV. SPIRIT LEVEL. 57 such a manner that the bubble will stand between the wires a and b ; this being accomplished, let the instrument be now re- versed, the extremities D and E exchanging places. If the bubble stand still in the middle, it proves the instrument to be correct ; if not, the end towards which it retires is the higher extremity. The bubble must then be brought back to the cen- tre, partly by lowering the extremity of the tube toward which it moves, and partly by adjusting the plane surface on which the instrument is placed. The instrument must now be once more reversed, and the same process repeated, until the change of position of the instrument no longer deranges the position of the bubble. The principle on which this adjustment depends, is that the bubble will fix itself at the highest point of the tube, and that a horizontal line is at right angles to a vertical one. When by adjusting the tube the bubble is fixed in the centre of the wires a and 6, let us suppose a vertical line, c ulk of water. Whether a vessel, however, wffl sink by being water-lodged, will depend as much upon the nature of the cargo a* the vessel itself, A vessel laden with iron, or with any other heavv substance, will, in such a case, sink ; while one laden with cork, timber, or any other light substance, will (60.) An iron boat will float with perfect security ; and, if H be formed with double plates of metal, including between them a sufficient hollow space, and so united as to exclude the water, no circumstance can sink it; for, whatever be' its position, it "iD displace more water than is equal to Hs own weight A contrivance to prevent ships foundering at sea, founded on fc tahbWJtom Hf fr:-.:^s :: rorrr ttmrttwi ^ Hrt "":;./;:, - T fettea^fcW^*tomrthft*Md (fflJ ft* f IWM! At **er aitagctiker *- <*tfce*n<*krfessfe,*l& to tenets Vc JwM estn^edl Vr tihr 4n& of i^Mnaoa* - " v - ~ / t m fflMHMM 3C5BW * EBN * * nMBBr^R VV vBV^ in as mvcki fivc^ to ncsi 4ww as B MMRT MM! to 00 wog^ f tfc> w^erwtoA It fciplirBi. JfWfcATll W _ *.* - ^ >fc.- : " - -- ^ <8f codc t? avyji IS Nv ^Hfr L^ -^M^^^ ^^ MR MK : mmv w ant mga* wrss V^IHP wvv c ' ~ > - - ^ - ^> - . - ~ -'-- - - > ^ - "_>--- . .- T --> * t m - - *. j * ^^ , ltm *\ m __ J ^"t^fc - % - - - - - - !-.-.-;-.>-- ' - >.: - - : 7 Triiah^ M< ttC t^Tfritiitt UBfa^i "& tiii%oyg *&mh^tke. :,.. _ i:. "">:..:: -. : .'.:? -"> ?: "." > --; f ~ HA ribMT aatone o4 fcr avpphiHr ter ftr < Afc***M*i< sa t2 esffa ^adi a? W - 78 A TREATISE ON HYDROSTATICS. ( CHAP. V. the extremity of this pipe in the cistern, is placed a stop cock, which is worked by a lever, at the extremity of which there is a large hollow metal ball, which is raised by its buoyancy with the surface of the liquid, and falls by its weight when the sur- face descends. The cock is thus closed when the surface rises to a certain height, and stops the supply of water ; but when the surface falls the cock is again opened, and water is ad- mitted. Many contrivances, upon this principle, have been suggested for raising sunken vessels. Hollow boxes made water-tight, and including only air, may be carried to the bottom by heavy weights attached to them. The boxes being secured to the vessels to be raised, the weights which sunk them may then be detached. If such a number of these boxes be attached to the vessel as will displace more water than is equal in weight to the vessel to be raised, and the boxes themselves, the whole will float to the surface. A machine upon the same principle, called the camel, for lift- ing vessels over shoals, is the invention of a burgomaster of Amsterdam named Bakker. In the Zuyder Zee, opposite the mouth of the river Y, there are two sand banks, between which there is a shallow passage, impassable to vessels of large size. It was the practice for such vessels to take in their cargo after they had passed beyond this strait ; but the accumulation of sand became at last so considerable, that some means were necessary to transport the vessels themselves over this obstacle. In 1672, large chests, filled with water, were fastened to the bottom of the vessel ; the water was subsequently pumped out of these, so that they acquired a buoyancy or upward force equal to the weight of the water discharged : the ships were thus raised and enabled to pass the shalloAv. A similar contri- vance had been previously used at Rome by a Dutch engineer named Meyer, but not so complete or effectual a one as that of Bakker.* The camel, of which we have just explained the original idea, consists of two large hollow chests, so constructed as to extend along the sides of a vessel, and shaped on one side so as to lie close to her sides, being square upon the outside. Being filled with water, they sink, and are, without difficulty, brought close to the sides of the vessel, to which they are at- tached by ropes which pass round each of them and under the keel ; the water is then pumped out, and the buoyancy of the chests raises the ship in the water so as to enable it to float over a shoal. An East Indiaman that drew fifteen feet of watei; was so much elevated by means of this machine, that it only * Prewster'3 Encyclopedia, v. 296. CHAP. V. * LIFE-PRESERVERS. 79 drew eleven feet ; and the largest ships of war in the Dutch service, of from 90 to 100 guns, were always enabled to sur- mount the different sand-banks of the Zuyder Zee. Such ma- chines are likewise used in Venice and in Russia. Life-preservers, provided in case of accident at sea, are con- structed upon the same principle. A hose, or flexible tube, is composed of a cloth prepared by a solution of caoutchouc or India rubber, by which it becomes impervious to air or water, and which is also insoluble in water. It is made of such a length, that it may surround the waist and be secured by a buckle in front : a mouthpiece and valve are provided at one extremity of the tube, through which it may be inflated. When thus filled with air, it becomes light when compared with its own bulk of water ; and, when surrounding the waist, it gives the body such buoyancy that the upper part of the person will continually be kept above the water. The benefit of this contrivance in case of accidents at sea, and more especially when, as usually happens, they occur near the shore, might be rendered much more extensive. A long hose of water-proof cloth might be constructed, of such a mag- nitude as, when inflated, it would have sufficient buoyancy to sustain a considerable number of persons ; straps might be attached to it at proper intervals, to be secured round the waists of those whom it was necessary to support. Such an apparatus, when not inflated, might be folded in a very small bulk ; and a sufficient number of them to save the crew or passengers of any vessel would neither be expensive to construct nor inconvenient to carry;. With such aid it would be possible for the ordinary boats, with which vessels are always provided, to tow the crew and passengers to shore. It would be advisable to divide a large hose for such a pur- pose, into a number of separate air cells, to provide against the accidental rupture of any part of it. Such an accident would thus be productive of no injury, as it would allow the air only to escape from one cell. (63.) The weight of the human body is very nearly equal to that of its own bulk of water ; its magnitude, however, is sub- ject to a small variation, caused by the action of breathing : when the lungs are inflated, the volume of the body is greater than after they collapse. It is true that in this case the weight of th body as well as its magnitude, strictly speaking, under- goes an increase ; but the change of weight is comparatively small, being that of a few grains of air, which are alternately inspired and breathed out. The change of volume produces, however, a sensible effect when the body is immersed in tho liquid. When the chest is inflated with air by drawing in the breath, 80 A TREATISE ON HYDROSTATICS. CHAP. V. the body is somewhat lighter than its own bulk of water and t it be immersed in that liquid, it will displace its own weight re total immersion takes place. If the head be presented upwards and inclined backwards, so as to keep the mouth an* nose in the highest possible position relatively to the remainde, of the body, a person may float with about half the head above water when the chest is filled with air ; but when he breathes out, his lungs collapse, and the bulk of his chest is diminished his weight, however, remaining the same, he must sink deeper in order to displace his own weight of water. A living body floating on water is, therefore, in a state of continual oscillation alternately rising and sinking : this effect is increased by the' inertia of the body ; for when it descends it will not cease to sink exactly at that depth at which it displaces its own weight of water, but it will continue to move with the velocity it has acquired,* until the increasing weight of the water displaced forces it to return upwards : its alternate ascent is similarly in- creased. This effect may be observed by pressing a piece of cork m water to a greater depth than that at which it naturally floats ; an oscillation will ensue which will continue for some time. Hence arises one of the difficulties which are found in float- ing on water ; for, in the alternate sinking of the body the mouth and nostrils may be so choked as to intercept the breath- ing : a slight action of the hands or feet is therefore necessary to resist the tendency to sink after each expiration from the chest. The lighter the body is in relation to its magnitude, the more easily will it float, and a greater portion of the head will remain above the surface. As the weights of all human bodies do noi 3ear the same proportion to their bulk, the skill of the swimmer is not always to be estimated by his success : some of the con- stituent parts of the human body are heavier, while others are lighter, bulk for bulk, than water. Those persons in whom the quantity of the latter bears a greater proportion to the former will swim with a proportionate facility. Sea water has a greater buoyancy than fresh water, beino- latively heavier ; and hence it is commonly said to be much easier to swim in the sea than in a river : this effect, however appears to be greatly exaggerated. A cubic foot of fresh water weighs about 1000 ounces ; and the same bulk of sea water weighs 1028 ounces : the weight, therefore, of the latter ex- ceeds the former by only 28 parts in 10CO. The force exerted by sea water to support the body exceeds that exerted by fresh nt which it dis- * The velocity is variable; after the body arrives at the clrnth at a n'n-f 8 W " * We - ght of water > its velocity is continually diminished, though not a uniform rate, in conscrjusnce of the increase of the upward pressure. AM ED CHAP. V. FLOATING. 81 water by about one thirty-sixth part of the whole force of the latter.* It has been proved that in whatever position a body floats on a liquid, the same bulk must be immersed ; it follows, therefore, that if a person floating raise his hand above the surta.ee of the water, an equal portion of his head must sink. Hence the dan- ger arising to persons drowning is increased by the involuntary effort by which they stretch out their arms. (64.) The bodies of some animals are much lighter than their own bulk of water. Many species of birds, such as ducks, geese, swans, and water fowl generally, present examples of this. The feathers with which they are covered contribute much to their buoyancy ; and, in many instances, a very small portion of their body will displace a quantity of water equal to their weight. Fishes have a power of changing their bulk by the distension of an air vessel with which they are provided ; they can thus at will displace a greater or lesser quantity of water. When they enlarge their bulk, so as to displace more water than their oAvn weight, they rise to the surface ; and when, on the other hand, they contract their dimensions, so as to displace less water than their own weight, they sink to the bottom. When a human body is first drowned, the air being ex- pelled from the lungs, it is heavier, bulk for bulk, than water ; and, therefore, remains at the bottom. The process of decom- position subsequently produces gases, by which the body is swelled and increased in bulk so much, that it displaces more water than is equal to its own weight, and therefore rises to the surface. When the vessels, containing the gases thus * We are not, however, to infer, that it requires only one thirty-sixth part lesa force to sustain the body in sea water than in fresh water. For this force is, in either case, equal to the difference between the weight of the body and that of an equal bulk of the fluid, and this difference being small, the proportion or (more properly) ratio, in which it is diminished, when the body is transferred from fresh to salt water, is much greater than that in which the weight of a given bulk of the fluid is increased. If we suppose the weight of the body to be 190 Ibs., and that of its own bulk of fresh water 180 Ibs., the weight of the same bulk of sea water, being one thirty-sixth part greater, would be 185, and it would require a force of 10 Ibs. to sustain the body in fresh water, and only 5 Ibs. in sea water. If the body is still heavier compared with its bulk of water, the force required to sustain it in sea water, compared with that in fresh water, will be still less. We have as yet supposed the human body to be heavier than either fluid. If it be lighter than either salt or fresh water, as Dr. Franklin and others have ascertained it to be in many cases, even after an ordinary expiration of the air ; then it will require no force to sustain it, but only the presence of mind necessary to direct the face upwards, and to avoid struggling, (allowing the lower parts of the body to sink gradually till it comes into a vertical position ;) and to avoid, both in breath- ing and speaking, those violent and long-continued expirations, which occasion a greater exhaustion of the chest than occurs in an easy and natural respiration ; and lastly, incase of an accidental immersion of the face, to refrain from any at- tempt at breathing until the mouth or nose shall have risen again above the sur- face. An observance of these rules might save many lives. AM. ED. 82 A TREATISE ON HYDROSTATICS. CHAP. V. generated, burst, the body will again contract its dimensions and sink. (65.) Philosophical toys are constructed on this principle. A small glass vessel is constructed in the form of a balloon, which is hollow, and the lower part of which is open ; it is immersed in water with its mouth downwards, so that the air included within prevents the water entering beyond a certain point. This balloon is placed floating on the surface of water contain- ed in a deep glass jar filled nearly to the top ; a bladder is tied on the top, so as to confine a small quantity of air between it and the surface of the water in the jar. A pressure being ex- cited by the hand on the bladder, is transmitted by the air under the bladder to the water, and the water again transmits it to the air included in the balloon ; this air being elastic, yields to the pressure and contracts its dimensions, allowing a greater quantity of water to enter the balloon : the balloon thus displaces a less quantity of water, while its own weight, including the air in it, remains unaltered. At length the water it displaces is less than its own weight, and it sinks slowly to the bottom of the jar. When the bladder is relieved from the pressure, the air in the balloon again expands, the water displaced by it increases, and it slowly ascends to the surface. A solid having air enclosed, which is exposed to the pressure of the liquid in which it is immersed, may arise to the surface if it be immersed only to a certain depth ; but if it be immersed to such a depth that the hydrostatic pressure of the^ surrounding liquid so condenses the- air within that the solid displaces a less quantity of liquid than its own weight, it can no longer rise. A diver who plunges in the sea is lighter when he enters than his own bulk of water ; but if he proceed to a certain depth, his dimensions will be so contracted by the pressure of the sea, that he will displace a less quantity of water than his own weight, and, therefore, cannot rise by mere buoyancy, but must ascend by the exertion of his limbs, swimming/as it were, upwards. It is known that in the process of congelation, water under- goes a considerable increase of bulk ; thus a quantity of water, which at the temperature of 40 measures a cubic inch, will have a greater magnitude when it assumes the form of ice at the temperature of 32. Consequently ice is, bulk for bulk, lighter than water. Hence it is that ice is always observed to collect and float at the surface. A remarkable effect produced by the buoyancy of ice in water is observable in some of the great rivers in America. Ice col- lects round stones at the bottom of the river, and it is sometimes formed in such a quantity that the upward pressure by its buoyancy exceeds the weight of the stone round which it is CHAP. VI. LIGHTER LIQUIDS FLOAT ON HEAVIER. 83 collected ; consequently it raises the stone to the surface. Large masses of stone and ice are thus observed floating dow> the river to considerable distances from the places of then formation. CHAP. VI. OF DIFFERENT LIQUIDS IN COMMUNICATING VESSELS. LIGHTER LIQUIDS FLOAT TO THE TOP. OIL, WATER, AND MERCU- RY. CREAM OF MILK. INGREDIENTS OF THE BLOOD. OIL AND SPIRITS. PROOF SPIRITS. WATER AND WINE. WATER IN THE DEPTHS OF A FROZEN SEA LESS COLD THAN AT THE SURFACE. A LIQUID MAY BOIL AT THE SURFACE, WHILE THE LOWER PARTS ARE COLD. METHOD OF APPLYING HEAT TO BOIL A LIQUID. METHOD OF APPLYING ICE TO COOL WINE. DIFFERENT LIQUIDS IN A BENT TUBE. METHOD OF RAISING WATER BY IMPREGNATING IT WITH AIR. (66.) ALL that has been proved in the previous chapter re- specting the ascent and descent of solids in liquids is equally applicable to two or more liquids in the same vessel. In this case, providing that no chemical combination takes place be- tween the liquids, the lighter will always ascend and remain above the heavier. And if more than two liquids be contained in the same vessel, they will severally arrange themselves in the order of their weights, the lighter being above the heavier. If oil and water be mixed by shaking them in the same bot- tle, they will speedily separate when the bottle is placed at rest on the table. The particles of the oil will rise, and those of the water fall, until they are totally disengaged from one an- other ; the water occupying the lower part of the vessel and the oil the higher. If mercury, which is heavier than water, be added to the mixture, it will take the lowest place, leaving the water immediately above, and the oil at the top. These effects are only manifestations of the principle which has been already so fully explained in its application to solids immersed in liquids. A particle of a lighter liquid immersed in a heavier displaces a portion of that heavier equal to its own bulk, and it is urged upwards by a force equal to the difference between its weight and the weight of the heavier liquid which it displaces. What is true of one particle is equally true of any number ; and when two liquids of different weights are mixed together, we may consider the particles of the lighter to be urged upwards, by the predominating effort of the heavier to sink to the bottom. A TREATISE ON HYDROSTATICS. CHAP. VI. There are numerous familiar effects which are manifestations of the principle now explained. When a vessel of milk is all lowed to remain a certain time at rest, it is observed that a stratum of fluid will collect at the surface, differing in many qualities from that upon which it rests. This is called -ream- and the property by which it ascends to the surface is its rela- ive levity: it is composed of the lightest particles of the milk, which are in the first instance mixed generally in the fluid ; but wnich, when the liquid is allowed to rest, gradually rise through it,^and settle at the surface. When blood taken from an inflamed patient is suffered to remain a sufficient time in a vessel at rest, it resolves itself into three parts, which arrange themselves in the order of their weights one above another. The heaviest element, called sc- rum, settles at the bottom; above that a lighter substance called coagulum, arranges itself; and at the top the lightest component part, called buff, is collected. If oil, which rises to the surface of water, be mixed with al- cohol or some other spirits, it will settle at the bottom A weaker spirit is heavier, bulk for bulk, than a strong one, and s strength may be so far reduced that it will no longer float on the surface of oil, but will sink below it; this is the test which fixes the strength of proof-spirit. All spirit which floats upon oil is said to be above proof. As all spirits are lighter than water, they will float upon its surface if they be not mixed through it. But if these liquids e mixed, chemical effects will ensue, which will resist that separation which mechanical causes would produce. If a ves- sel be half filled with water, and a piece of paper be laid upon its surface, and wine be poured over the paper, on carefully removing the paper so as to produce the least possible agitation in the liquids, the wine will continue to occupy the upper part of the vessel, and the water the lower. But if, on the other hand, the vessel be first filled with wine, and the water be similarly poured over it, it will immediately sink through the wine, and the liquids will be mixed, their chemical affinity re- sisting the tendency of the wine to rise to the top. By the following contrivance, however, the wine and water may be made to change places without intermixture. Fig 48 Let A and B > /# 48 -> be two vessels connected _Jl-_. by a narrow neck C. Let E be a tube from the JS lower vessel B to the upper vessel A, and let D -A-^ j|lp be a tube from the upper "vessel A to the lower vessel B, and let all communication betAveen the ffj BL vessels except by these tubes be stopped. Let B be filled with water to the neck C, and let A be filled with wine to a level above the mouth of CHAP. VI. HEATED LIQUIDS. 85 the tube E. The water in the lower vessel, and the wine in the upper vessel, will thus be in contact in the neck C, but they will continue separate, the wine will not descend into the wa- ter. The vessels being now emptied, let the lower vessel be filled with wine and the upper one with water. The water which fills the upper vessel, pressing on the wine in the tube D, will force it down, and compel it to ascend in E. The wine in the lower vessel will thus be gradually discharged in the upper, while the water in the upper will be deposited in the lower. If the lower part of the vessel be concealed or formed of any substance not transparent, such a vessel is used as a toy, by which water is apparently converted into wine. The fact that water at temperatures between the freezing point and 40 is lighter, bulk for bulk, than at higher tempera- tures, has been already noticed.* It follows, therefore, that water at this temperature will float upon the surface of water at higher temperatures. Hence it follows that the water im- mediately beneath a sheet of ice floats above the less cold water which is at greater depths ; and this liquid being a bad conductor of heat, the lower region of a frozen sea may be at a very mod- erate temperature, while the most intense cold prevails above. Animal life may be thus preserved in the lower parts of the deep, which would be destroyed if the heat, thus confined there, were permitted to escape. The lighter stratum of fluid under the congealed surface forms a barrier, in a great degree, imper- vious to the heat, and thus preserves the marine animals which are in the lower parts of the sea. If heat be applied at or near the surface of water contained if. a vessel, the higher strata of the liquid may be made to boil, while the lower parts retain their original temperature. For, like all other substances, water expands when heated, and therefore becomes lighter ; consequently, the hot water at the surface will not descend into the lower part of the vessel, and the imperfect manner in which the liquid conducts heat prevents the lower strata from receiving any effect from the increased temperature of the surface.f On the other hand, if the water in the bottom of a vessel be heated, it will be rendered lighter by expansion than the cold ^ * It is lighter than at some higher temperatures near 40, though not lighter than at all higher temperatures. The expansion of water whilst in the fluid state, has been found to be very nearly the same for any number of degrees below, as for the same number above, 40. Hence, at no temperature below 40, until the water is congealed, will it be as light, bulk for bulk, as water at high temperatures. AM. ED. t If, however, the water be below 40, and the heat be applied very gradually, so as to elevate the temperature of the surface but a few degrees, it is evident, from the principles just stated, that the water at the surface will be rendered heavier, and that an intermixture will take place throughout the whole mass until its torn pcrature has risen to 40. AM. ED. 8 A TREATISE ON HYDROSTATICS. CHAP. VI. water which is above it ; and, conformably to the principles al- ready explained, it will ascend through the cold water above it m the same manner as the particles of oil would ascend from the bottom of a vessel of water and float at the top. The lower and higher strata thus interchange places, and the latter in its turn becoming heated more than the former again interchanges places with it. Thus so long as the lower strata continue to receive increased temperature, a constant interchange of posi- tion will be produced between the higher and lower strata of the liquid : ascending and descending currents will be constantly maintained until the liquid boil. This effect may be exhibited in such a manner as to be easily observed. Let a tall glass jar be filled with cold water, and let a small quantity of amber reduced to powder be thrown into it Amber being very nearly equal in weight, bulk for bulk, to water, the difference of weight produces so slight a tendency in it to sink, that this tendency is overcome by the molecular attraction of the water for its particles ; it, therefore, remains suspended in the liquid, being mixed through every part of it, and is distinctly visible to the eye. Let the jar be now im- mersed to a small depth in a vessel of hot water, so that the lowest strata of water in the jar may be gradually heated. The water at the bottom of the jar will be observed continually to ascend, carrying up the particles of amber with it, while the upper strata descend. This will be rendered visible by the ascent and descent of the particles of amber. In like manner if the jar be totally submerged in another glass jar of boiling water, the portion of water near the surface of the submerged jar will first become heated, and will there- fore be lighter than the water near its centre. In this case we shall observe a current of amber particles continually ascending near the surface of the submerged jar, while a contrary current is constantly maintained near its centre. The heated water near the surface thus continually interchanges places with the colder water in the centre. When a liquid has attained a certain temperature, which is always the same* in the same liquid, but which differs in dif- ferent liquids, it will be incapable of any further increase. If the vessel which contains it be exposed to fire, or any other source of increased heat, the effect produced upon the liquid will not be to make it hotter, but to convert it into vapor or steam. If the lowest stratum, as is usually the case, be that k The temperature at which this takes place varies according to some circum- stances, the most important of which is the degree of pressure on the fluid. It will be obvious from this, when the subject of atmospheric pressure shall have 'een considered, that boiling water cannot always be equally hot. Its tempera- ture is found by experiment to vary at the same place, and to be much lower on the tops of high mountains than at the level of the ocean. AM. ED. CHAP. VI. HEATED LIQUIDS. 87 which is exposed to the fire, the water in it will be first con- verted into steam, which will be produced in bubbles at the bottom of the vessel. These, being many hundred times lighter than the liquid, will rise with great rapidity to the surface, where they will escape into the air, producing that agitated appear- ance on the surface of the liquid which is called boiling or ebullition.* From the above reasoning it will be evident, that, if fire be applied for a sufficient length of time to the lowest part of a vessel containing a liquid, the whole of the liquid in the vessel, however remote it may be from the fire, will ultimately become heated ; for the water occupying the lowest strata will continu- ally ascend by its increased levity, until the whole mass of liquid receives the highest temperature of which it is capable. An apparatus for the warming of houses is constructed on this principle. A small metal boiler, made water tight, is placed upon a fire in the lowest part of the building. A tube proceeds from this vessel, and is carried' through all the apartments which are required to be heated, passing along the walls in any convenient direction. The tubes and boiler are completely filled with water. A fire is kept lighted under the boiler so as to heat the water which it contains. As this becomes lighter by increased temperature, it ascends through the tubes, and is replaced by the colder water descending ; and this continues until the water in all the tubes is raised to the boiling point : the metal of the tubes becomes ultimately heated to the tem- perature of boiling water, and imparts an increased tempera- ture to the air which surrounds them. The same tubes being furnished in proper places with cocks will supply hot water for baths and other domestic purposes in every part of the building. The same reasoning which proves that to heat a liquid the source of heat should be applied to the lowest strata, necessa- rily leads to the conclusion, that to cool a liquid the source of cold should be applied to the highest strata. If the lowest part of a vessel containing a liquid be plunged in melting ice, the liquid near the bottom, imparting its heat to the ice, will be cooled, and being rendered heavier than the liquid above, it will remain at the bottom. In this case the only part of the vessel which will be cooled will be the lower strata ; the upper parts will maintain their former temperature. But if the highest stratum of the liquid in the vessel be surrounded by melting ice, it will be first cooled, and being rendered thereby heavier * These bubbles, whilst they remain at the bottom, impede the entrance of the heat into the water. Is not a deficiency of upward pressure, in consequence of their contact with the bottom of the vessel, one of the causes which protract meir etay at the bottom ? AM. Ho. I 88 A TREATISE ON HYDROSTATICS. CHAP. VI. \ will sink to the bottom, displacing the warmer liquid below. This process will be continued so long as the highest stratum has a temperature above that of the cooling application.* Hence it appears, that when ice is used to cool wine, it will be ineffectual if it be applied, as is frequently the case, only to the bottom of the bottle ; in that case the only part of the wine which will be cooled is that part nearest the bottom. As the application of ice to the top of the bottle establishes two cur- rents, upwards and downwards, the liquid will undergo an effect in some degree similar to that which would be produced by shaking the bottle. If there be any deposit in the bottom whose weight, bulk for bulk, nearly equals that of the wine, such de- posit will be mixed through the liquid as effectually as if it had been shaken; in such cases, therefore, the wine should be transferred into a clean bottle before it is cooled. (67.) We have shown that the same liquid, in communicating vessels, will always stand at the same level ; this property de- pends on the circumstance of columns of equal heights having equal weights : consequently it follows, that if communicating vessels contain different liquids, of which equal columns have different weights, they will not stand to the same level. The vessel which contains the lighter liquid will have its surface at a greater height, because a column of equivalent weight to the heavier will necessarily be higher ; and not only so, but higher exactly in that proportion in which the liquid is lighter. This will be more clearly understood by the following illustration : Let B B', Jig. 49., be a horizontal tube con- nected with two upright tubes, A B and A' B', and let a stopcock be placed at B'. Let the horizontal tube B B' be rilled with quicksilver, and let two liquids lighter than quicksilver, and which, bulk for bulk, have different weights, be poured into the tubes A B and A' B' to any heights as C and C'. It is evident that the stopcock B' is pressed downwards by the weight of the column C' B' : also it appears that the mercury at B is pressed downwards by the weight of the column C B ; and this pressure is transmitted by the mercury to the stopcock B'. The stopcock is, therefore, under the effects of two opposite pres- sures, viz. the weight of the column C' B' downwards, and the weight of the column C B upwards. If either of these pres- sures be greater than the other, a corresponding motion would take place on opening the stopcock ; thus, if the weight of the column C f B' were greater than that of the column C B, the _ * It will be continued until the whole mass of the liquid is cooled to 40 ; at this time the currents cease. Hence, ice floating or resting on deep tranquil water does not reduce the whole mass to its own temperature. AM. ED. CHAP. VI. PRESSURE OF DIFFERENT LIQUIDS. mercury would be pressed towards B, and the liquid in C' B would enter the horizontal tube. If, on the contrary, the weight of the column C B were greater than that of C' B', the upward pressure at B' would be greater than the downward ; and, on opening the stopcock B', the mercury would be pressed up the tube B' A'. In order, therefore, that the liquids in the two tubes should be in equilibrium, on opening the stopcock it is necessary that the weights of the columns in the upright tubes should be equal ; in which case, whether the stopcock is open or closed, equilibrium will be preserved. From this conclusion it is apparent, that the surfaces C and C' will not stand at the same level unless the liquids in the upright tubes have, bulk for bulk, the same weight ; for if one be lighter than the other, bulk for bulk, it will, in the same proportion as it is lighter, require a greater height of column to give the same weight as the heavier liquid. Thus, if a pint of the lighter liquid weigh forty ounces, and a pint of the heavier weigh fifty ounces, it is evident that a column of the latter, for- ty inches in height, will exert the same pressure as a column of the former fifty inches in height ; or in general it may be stated, that the two columns will exert equal pressures, provid- ing that the height of the column of heavier liquid shall bear, to the height of the column of lighter liquid, the proportion of forty to fifty, or of four to five. The communicating vessels in this case are represented as tubes of equal magnitudes ; but, by comparing the conclusions at which we have just arrived with the reasoning used in (38.), it will be apparent that these inferences may be generalized ; and that liquids, contained in any communicating vessels of whatever shape or position, will, when in equilibrium, have their surfaces at heights determined on the principles just laid down. The surfaces of the lighter liquids will be more elevated than those of the heavier in proportion as their weights, bulk for bulk, are less. Let A B Cjjlg. 50., be a bent tube, open at the ends A and Fig. 50. C, and let oil and water be poured into it ; let S be the surface of the water on which the oil rests, and draw the horizontal 8* 90 A TREATISE ON HYDROSTATICS. CHAP. VI. line S M. If the oil were removed from the leg A B, and the water above M also removed from the leg C B, the water be- low S M in the curved tube would remain in equilibrium, since the surfaces S M are at the same level. That this equilibrium may be continued when the oil is introduced into the leg A B, and the additional water into the leg C B, the pressures which these liquids excite at S and M must be equal ; but the pres- sure at S is equal to the weight of a column of oil, whose height is S N, and the pressure at M is equal to the weight of a col- umn of water, whose height is M P, as has been proved in (37.) (38.), &c. Hence the height S N must be greater than the height M P, in the same proportion as water is heavier than oil ; and a similar conclusion may be obtained with respect to any other liquids. The property by which a short column of a heavier fluid will support a long column of a lighter one, has been used by M. Dectot in machines invented by him, called hydreoles, for the purpose of forcing water above its original level. In these ma- chines water is, by an ingenious contrivance, mixed with air ; the mixture is of course lighter, bulk for bulk, than pure water, and a short column of the latter will support a long one of the former. There are different methods of impregnating the liquid with air ; one in particular is by forcing the air into the water by a bellows, through a plate pierced with a number of very small holes, like the cover of a sand bottle, or the rim of a gas burner ; the air thus enters the water in extremely minute glob- ules, so that their buoyancy is insufficient to overcome the molecular force which attaches them to the particles of the water. An upright tube containing the water thus impregnated with air, communicates with a reservoir containing pure water ; and the liquid hi this upright tube will stand as much higher than the water in the reservoir as pure water is heavier than the water surcharged with air. The reservoir answers the double purpose of supplying the water and pressing it up in the tube ; for, as it passes from the reservoir to the tube, it encoun- ters the jets of air which charge it. CHAP, VII. FLOATING BODIES. 91 CHAP. VII. EQUILIBRIUM OF FLOATING BODIES. CONDITIONS OF EQUILIBRIUM. CASES OF STABLE, INSTABLE, AND NEUTRAL EQUILIBRIUM. EXPERIMENTAL PROOF. FEAT OF WALK- ING ON THE WATER. LIFE PRESERVERS. STABILITY OF SHIPS.* POSITION OF CARGO. BALLAST. DANGER OF STANDING UP IN A BOAT. INCLINATION OF A SAILING VESSEL. HOW AVOIDED IN STEAM VESSELS. (68.) THE circumstances under which a solid will sink, rise, or "be suspended in a liquid, have been fully explained in chap. iv. But these circumstances are insufficient to determine the exact state of the body with respect to motion or rest. A body may be in equilibrium with reference to any perpendicular motion towards or from the surface of the liquid ; that is, it may nei- ther rise nor sink, but yet it may not be in a state of absolute rest. Again, to say that a solid rises or sinks in a liquid with a certain force, does not describe its state with exactness ; wh*ile it rises or while it sinks, it may also have motions of another kind ; such as motions in an oblique direction, or rotatory mo- tions. To explain fully, therefore, all the conditions which affect the state of a solid immersed, all the particulars here alluded to must be investigated. The motions of which a solid body is susceptible may in gen- eral be reduced to two, viz. progressive motion, and rotatory motion. In progressive motion, all the particles of the solid are carried forward in parallel lines with the same speed : in rotatory motion, the body remains in the same place, but turns round some point within it as a' centre. Let ABC T),Jig. 51., be a solid body, and let E F and E' F' be the directions of two forces acting on it in parallel and contrary directions ; if these two forces be equal, it is evident that they cannot give the body any motion in the direction E F or in the direction E 7 F' ; for, since the forces are equal, there is no reason why the body should move in the one direction rather than the other. Such a supposition would necessarily involve some distinction between the two forces, whereas no such distinction exists. A force of a pound weight drawing a body towards the north, and another force of the same weight drawing the same body to- wards the south, evidently cannot produce motion in either of these directions. The effect of two such forces as are supposed to act in Jig 92 A TREATISE ON HYDROSTATICS. CHAP. VII. 51. will be to give the body a motion of rotation in the direction ABCD. But if the equal forces, instead of acting in parallel lines, acted in the same right line, and in contrary directions, then they would be mutually neutralized, and the body would be kept at rest. Fig. 51. If the forces represented in Jig. 51. were unequal, then the body would receive a progressive motion in the direction of the greater force ; but as a consequence of the forces not being in the same straight line, the body would also receive a motion of rotation in the direction ABCD. It would be carried along in the direction of the prevailing force, and during its progress it would spin or revolve. If, however, the unequal and contrary forces act not in parallel lines, but in the same line, then no rotation will ensue, but the body will advance with a progressive motion only according to the direction of the prevailing force. These general mechanical principles being clearly understood, all the effects produced by the immersion of a solid in a liquid may be rendered easily intelligible. Let us suppose a solid body of any proposed figure immersed, whether totally or partially, in a liquid. A downward force equal to the weight of the solid is opposed, as has been shown in chap, v., by an upward force equal to the weight of the liquid which the solid displaces. If either of these forces be greater than the other, the body will have a tendency to rise or sink proportional to their difference ; and if they be equal, the body will be in equilibrium as to its ascent and descent in a perpendicular direction ; but it still remains to be decided, whether the solid may not move in the liquid with- out either rising or sinking. To determine tlys it will be necessary to ascertain the exact CHAP. VII. FLOATING BODIES. 93 directions of the two forces downwards and upwards which act upon the body. The downward force being the weight of the solid, acts in a direction pointing perpendicularly downwards from its centre of gravity.* The direction of the upward force is not, however, so obvious. It is to be considered that the liquid presses upon the solid exactly in the same manner as it would press upon the liquid whose place the solid occupies. Now it is certain, that if the space in the liquid, occupied by the solid, were occupied by the liquid which the solid has displaced, that liquid would remain at rest. Consequently, the downward pressure of that liquid would be neutralized by the upward pressure of the sur- rounding liquid. Therefore, whatever that upward pressure be, it must be equal to the downward pressure of the liquid dis- placed by the solid, and it must act upward in the same line as the latter acts downward. But it is easy to perceive that the downward force of the liquid displaced by the solid is equal to the weight of such liquid, and acts perpendicularly downwards from the centre of gravity of such liquid. Hence, it is evident that the upward pressure which acts upon an immersed solid is equal to the weight of the liquid displaced, and that it acts di- rectly upwards in a line from the centre of gravity of the liquid so displaced. This may be also explained as follows : Suppose the place ' which the solid occupies in the liquid to be filled by another solid of uniform density, and whose weight is equal, bulk for bulk, to that of the liquid. Such a solid, as far as relates to any effects of weight or pressure, is equivalent to the liquid whose place it occupies ; and as that liquid would in its situa- tion remain at rest, it will also remain at rest. Hence, it ap- pears that the upward pressure upon it must be directed in the same line as that in which its weight is directed downwards ; but this direction is that of the perpendicular line passing through its centre of gravity. It is evident that the upward pressure against such a solid must be the same as against any other solid, the immersed part of which occupies exactly the same place ; and therefore it may be inferred generally, that the upward pressure is in the direction of a line drawn directly upwards from the centre of gravity of that part of the solid which is immersed, the density of that part being, like the liquid, supposed to be uniform. Let A B C D be a solid immersed in a liquid, either partially, as in Jig. 52., or totally, as in Jig. 53. Let E be the centre of gravity of the solid, and let E' be the centre of gravity of the liquid which the solid displaces. The weight of the solid acts * Ca 1 !. Cyc. Mechanics, chap. ix. 94 A TREATISE ON HYDROSTATICS. CHAP. VII. downwards in the direction E F, and the pressure of the sur- rounding liquid acts upwards in the direction E' F'. These two lines are both perpendicular to the surface of the liquid ; Fig. 52. they are in the vertical direction, and are parallel to each other. It is evident from the position of these lines, that whether the downward and upward forces be equal or unequal, they have a Fig. 53. tendency to make the solid revolve or roll in the direction A D C B. If the downward and upward forces be unequal, this rolling motion will be accompanied by an ascent or descent of the solid in the liquid, according as the upward or downward force predominates ; and if they be equal, no vertical motion will accompany the revolving one. Let us now suppose the position of the solid immersed to be such, that the points E and E 7 shall be in a straight line perpen- dicular to the surface of the fluid. In this case the point E may either be above E', as in Jig. 54. and jig. 55., or below it. In either case the contrary forces upward and downward are di- rectly opposed to each other, and have no tendency to produce rotation. The solid will in this case sink or rise according aa the upward or downward force predominates. CHAP. VII. STABILITY OF FLOATING BODIES. 95 If the immersion be such in these cases that the liquid dis- placed is equal in weight to the solid, no motion whatever will take place, and the solid will be in absolute equilibrium, neither rising, sinking, nor rolling. Fig. 54. (69.) A solid immersed in a liquid may have several distinct positions of equilibrium, possessing all the various characters of stability, instability, and indifference, explained in MECHAN- Fig. 55. ics.* It has been just shown that whatever species of equilib- rium the body may be in, it is an indispensable condition, that the line drawn from its centre of gravity to the centre of gravity of the liquid which it displaces, should be perpendicular to the surface of the liquid, or in other words, that it should be in the direction of a plumb line. If this be the case, the solid will be in equilibrium ; but to distinguish the peculiar kind of equi- librium in which it will be placed, it is necessary to attend to other circumstances. . If the figure and position of the solid be such, that upon a slight change of position, by which it still displaces its own * Cab. Cyc. Mechanics, (159.) et seq. 90 A TREATISE *ON HYDROSTATICS. CHAP. VII. weight of fluid, its centre of gravity takes a higher position than it had when in equilibrium, then the equilibrium will be stable ; because the centre of gravity having always a tendency to descend will return to its former position, and will oscillate from side to side of that position, until the solid, by its friction with the fluid, at length attain a state of rest. Such is the character of stable equilibrium. If the position of the solid in equilibrium is such that a slight disturbance, which still causes it to displace its own weight of liquid, will make the centre of gravity take a lower position, the body will not return to its former position of equilibrium, nor will it oscillate from side to side of that position as in the former case ; for to do so it would be necessary that the centre of gravity should ascend, an effect which is contrary to its char- acteristic property. The centre of gravity will therefore continue to descend until it gets into another position, such that the line joining it with the centre of gravity of the fluid which it displaces shall be perpendicular to the surface of the fluid. Any disturbance from this position must necessarily cause the centre of gravity to ascend, and therefore this is a position of stable equilibrium. The shape and position of the body may be such, that, what- ever be the position in which it displaces its own- weight of the liquid, the elevation of its centre of gravity will be the same : in other words, any motion which it may receive, allowing it still to displace its own weight of liquid, will cause its centre of gravity to move in a horizontal plane, and, as in this case the centre of gravity neither ascends nor descends, it will rest in equilibrium in all positions. Such is the state of indifferent or neutral equilibrium. (70.) If the solid be totally immersed, the liquid which it dis- places will be equal, both in shape and bulk, to the solid, and the centre of gravity of this liquid will therefore be the same as the centre of gravity of the solid, if the latter have, like the former, a uniform density ; but if the solid be heavier in one part than in another, which would be the case if different parts were composed of different materials, then the centre of gravity of the solid will not be in general in the same place in which it would be if the solid were of uniform texture, and therefore will not coincide with the centre of gravity of the liquid dis- placed. If the centre of gravity of the solid have that situation which it would have if the texture^of the solid were uniform, then upon total immersion the points marked E and E', injig. 53., will be one and the same, and the lines E F and E' F' can never be parallel to each other whatever be the position of the body in the liquid, but will always be directly and immediately op- CHAP. VII. STABILITY OP FLOAT&G BODIES. 97 posed. Hence the downward and upward forces, the directions of which are expressed by those lines, can never act in such a manner as to cause the body to revolve, but can merely give it a tendency to ascend or descend in the liquid without any other change of position. If in this case the weight of the solid be equal to that of its own bulk of the liquid, it will be suspended in equilibrium in any position whatever when it is totally sub- merged. In this case the solid, when totally submerged, is always in a state of neutral equilibrium. If the centre of gravity of the solid be not in that situation which it would have if the solid were of uniform texture, then its- position will not coincide with that of the liquid whose place it occupies when totally submerged. If the weight of the solid be equal to that of its own bulk of the liquid, there are in this case only two positions in which, when submerged, it will be in equilibrium. These are the positions in which the centre of gravity of the solid is immediately above and immediately below the centre of gravity of the liquid whose place it occu- pies. If the centre of gravity of the solid be immediately above that of the liquid displaced, it is in the highest position which the circumstances of the case admit it to have, and there- fore, the least disturbance must cause it to descend, which it will continue to do, until it takes the other extreme position in which it is immediately below the centre of gravity of the liquid displaced. The former, therefore, is the position of instable equilibrium, and the latter, of stable equilibrium. (71.) These various effects of total submersion may be easily verified experimentally. Let a hollow brass ball be provided with a small weight within it, movable by a screw, in such a manner, that the centre of gravity of the ball may be made at pleasure, either to coincide with its centre, or to take other positions at any distance from its centre ; and let the weight of the ball be so adjusted that it shall be equal to the weight of the liquid which it displaces. First, let the centre of gravity of the ball be so adjusted as to coincide with its centre. It is evident that it will thus have the same position, as the centre of gravity of the liquid which it will displace. If the ball be now totally submerged in the liquid, it will be found that it will rest in any position whatever, in which it is placed ; whatever point of the ball be presented downwards will remain so. Let the screw be now so adjusted that the centre of gravity of the ball shall be at some distance from its centre, and let the ball be totally submerged. It will be found, if such a position be given to the ball, that its centre of gravity shall be immedi- ately below its centre, the ball will remain steady in its posi- tion ; but if it be placed with its centre, of gravity presented in 9 A TREATISE ON HYDROSTATICS. CHAP. VII any direction sideways, the ball will turn on its centre, and the centre of gravity will fall towards that position in which it is mmediately under its centre, and the body will vibrate until s friction of the fluid reduces it to a state of rest. If the ball be submerged in such a position, that its centre of gravity shall e immediately above its centre, then the ball will remain in equilibrium for an instant, while it sustains no disturbance it its balance will be tottering and instable, and will almost immediately be lost, and the ball will reverse its position, throw- ing its centre of gravity into the situation immediately opposite to that in which it was placed. (72.) But the conditions of stability are of much greater in- terest and practical importance in their application to solids which are lighter, bulk for bulk, than liquids. In this case the degree of immersion which produces equilibrium, is always partial, and the centre of gravity of the liquid displaced does not, as in the former case, coincide with the situation which the centre of gravity would have if the texture of the solid were uniform. Therefore a solid of uniform texture, or having its mtre of gravity in the same situation as one of uniform tex- ire, will not float in equilibrium in every position. It will only be in equilibrium when the centre of gravity of the liquid displaced, shall be either immediately above or immediately below the centre of gravity of the solid. In this case, the situa- tion of the centre of gravity of the liquid displaced, will depend on the shape of the body, and the part of it which is immersed. >t all the various positions which can be given to a solid lighter than the liquid, in which it will displace its own bulk of the liquid, if there be one in which the centre of gravity will be lower than in any of the others, that one will be a state of stable equilibrium, and it will be one which the body will al- ways endeavor to attain whatever other position mav be given to it. The shape of a body may be such, that in whatever position it floats its centre of gravity will be at the same depth : such a ody is always in a state of neutral equilibrium ; the least dis- turbing force will cause it to change its position, and it will re- mam in any new position which may be given to it. Let the hollow brass ball already described, have its weight so adjusted, that it shall be lighter, bulk for bulk, than water; and let the screw be moved until its centre of gravity coincides with the centre of the ball. From the round form of the ball it is evident that, in whatever position it is immersed, it will be at the same depth when it has displaced its own weight of water. Therefore its centre of gravity will in this case be at the same height or depth in every possible position in which it can float. It will be found, therefore, that it will float on the CHAP. VII. WALKING ON WATER. 99 water steadily in any position in which it is placed ; it will be in a state of neutral equilibrium. Let the screw be now so adjusted as to remove the centre of gravity from the centre of the ball, it will be found that it will only float steadily when the centre of gravity is immedi- ately below the centre of the ball ; it will turn from any other position, and settle itself into this. If it be placed so that the centre of gravity is directly over the centre of the ball, the equilibrium will be momentary, and upon the slightest change of position the ball will be overturned, and the centre of gravity will settle its elf Immediately below the centre of the ball. (73.) From these observations, it will be apparent that any body, the parts of which have different weights, will only float steadily when the heavier parts are immersed ; for the centre of gravity is always situated among these or near them, and therefore, when it has the lowest position, these must also be placed in the lower parts of the body. A feat of dexterity has been exhibited by a person walking on the surface of water, having inflated bladders, or some other bodies which are lighter, bulk for bulk, than water, attached to the feet. The body of the exhibiter is, in this case, in a state of instable equilibrium. His centre of gravity is directly over that of the water which he displaces, and his skill consists in keeping his centre of gravity balanced in that position. This feat may be facilitated by carrying a staff with an inflated blad- der tied at the end of it, by which three points of support may be occasionally commanded. For the same reason that buoyant bodies are in this case at- tached to the feet, they are attached to the waist in the case of life-preservers. Their position and magnitude should always be regulated, so that the centre of gravity of the body* shall be in the lowest position when the person is upright. The weight of the several component parts of a ship and its cargo should always be so regulated that the centre of gravity of the whole should be at the lowest possible point, when the ship is in the upright position. Hence arises the necessity of stowing the heaviest part of the cargo in the lowest possible position, and so that its centre of gravity shall be immediately over the keel ; in that case, any inclination of the vessel on either side would cause the centre of gravity to rise, to accomplish which would require the ex- ertion of a force proportionate to the weight of the vessel, and the height through which the centre of gravity would be so elevated. When a vessel is without a cargo, and empty, the weight of the masts and rigging might raise the centre of * That is, the common centre of gravity of the human body, and the buoyant substance . AM. ED. 100 A TREATISE ON HYDROSTATICS. CHAP. VII. gravity of the whole to such a height, as to render the equilib- rium instable : hence, in such cases, it becomes necessary to introduce heavy bodies into the lower part of the vessel, to bring down the centre of gravity, and. to give stability to the ship. Hence bodies used for this purpose are called ballast. The equilibrium of a boat may be rendered instable by the passengers standing up in it ; for, in this case, the weight of their bodies may place the whole in the same predicament as persons having bladders tied to their feet. The slightest dis- turbance, under such circumstances, would overturn the boat. If the position of the centre of gravity of a vessel and her freight be not directly over the keel, the vessel will incline to that side at which the centre of gravity is placed : and if this derangement be considerable, danger may ensue. The rolling of a vessel in a storm, may so derange the position of a loose cargo, that the centre of gravity may be brought into such a situation, that the vessel may be thrown on her beam ends and irretrievably lost. When the centre of gravity is immediately over the keel, a side wind acting on the sails will incline the vessel the oppo- site way ; this inclination would be much more considerable, were it not that the weight of the vessel, acting at the centre of gravity, counteracts it, and has a tendency to restore the vessel to the upright position. The several forces which main- tain the vessel in the inclined position produced by a side wind, may be illustrated as follows : Let A B,/g-. 56., represent the Fig. 56. position of the vessel ; let S represent the point at which the wind acts upon the sail, and let S W represent the direction of the wind : let E be the centre of gravity of the vessel and her cargo, and let E F be the direction in which her weight acts. Let C be the centre of gravity of the water which the vessel displaces, and E' F' the direction of the upward pressure. If the effect of the upward and downward forces at E and E 7 , be CHAP. VII. POSITION OF A SHIP. 101 considered for a moment, it will be perceived that they have a tendency to incline the vessel to the side opposite to that to- wards which it is inclined by the wind. By the principles of the resolution of force established in MECHANICS,* the force S W may be replaced by three others, two of which being equal, and directly opposed to the downward and upward forces at E and E', neutralize them ; and the third, acting parallel to S W, merely carries the vessel sideways perpendicular to its keel, producing what is called lee-way. In sailing vessels, this sideward inclination is a matter of comparatively slight importance, inasmuch as it does not dimin- ish the impelling power of the wind : but in steam vessels, in which sails are occasionally used, it is attended with considera- ble loss of the impelling power, one of the paddle wheels being lifted out of the water, and the other being almost, if not en- tirely, submerged. The upright position may, however, be generally maintained by the due management of movable weights placed on the deck of the vessel. In steam vessels, small carriages heavily laden with iron, and furnished with wheels, are usually placed on the deck, and may be rolled from side to side, or placed in the middle, so as to regulate the po- sition of the centre of gravity according to the way in which the vessel is affected by the wind. By moving these carriages to the side of the vessel against which the wind is directed, the centre of gravity is moved from over the keel towards that side. Let E, J?g, 57., represent the place of the centre of grav- Fig. 57. JB K ity when over the keel, and let G represent the point to which the centre of gravity is transferred by moving the carriages to the side of the vessel ; let S be the point where the wind acts upon the sail S W ; the weight of the vessel acting at G, has a tendency to make it incline towards M ; and the force of the * Cab. Cyc. Mechanics, chap. v. 9* 102 A TREATISE ON HYDROSTATICS. CHAP. VIII. wind, acting at S in the direction S W, has a tendency to make it incline towards L. These two forces counteract each other, and the vessel maintains its upright position. CHAP. VIII. SPECIFIC GRAVITIES, DIFFERENT SENSES OF THE TERMS HEAVY AND LIGHT. "WEIGHT AB SOLUTE AND RELATIVE.' SPECIFIC GRAVITY. STANDARD OF COM PARISON FOR SOLIDS AND LIQUIDS. FOR GASES. DENSITY. THE IMMERSION OF SOLIDS IN LIQUIDS GIVES THEIR SPECIFIC GRAVITIES. METHODS OF ASCERTAINING SPECIFIC GRAVITIES. HYDROSTATIC BALANCE.- SIKES ; S HYDROMETER. NICHQLSON ; S HYDROMETER. DE PARCIEUX'S HYDROMETER. METHOD OF DETERMINING THE CONSTITUENT PARTS OF COMPOUND BODIES. ALLOYS OF METALS. SPIRITS. ADULTERATION OF MILK AND OTHER DOMESTIC LIQUIDS. HIERO'S CROWN. PENETRATION OF DIMENSIONS. (74.) IN the preceding chapters, we have had frequent occasion to compare the weights of different bodies, bulk for bulk ; and not only in science, commerce, and the arts, but even in ordi- nary colloquial intercourse, bodies are denominated heavier or lighter, according as the weights of the same bulk are greater or less. We say familiarly that lead is heavier than copper, and that copper is heavier than cork ; yet it is certain that quantities of lead, copper, and cork may be taken which have equal weights. Thus, let us suppose a pound of lead, a pour of copper, and a pound of cork, to be ascertained and set apa. it is clear that these have equal weights, and that any two c them, placed in the dishes of a balance, would maintain equilib- rium. Yet still we do not cease to declare that cork is lighter than copper, and copper lighter than lead. To perceive with precision what is meant in this case, let us suppose parcels of any three distinct substances placed before us, such as quick- silver, water, and alcohol, and let it be proposed to ascertain which of these liquids is the heaviest : we shall take any meas- ure of the quicksilver, and, having weighed it, afterwards weigh the same measure of the water and of the alcohol successively. Having found that the measure of quicksilver is heavier than that of water, and water than that of alcohol, we shall immedi- ately conclude that quicksilver is a heavier liquid than water, and that water is a heavier liquid than alcohol. We shall form this conclusion, even though the whole quantity of alcohol un- der examination shall weigh more than the quantities of the water or quicksilver. It appears, therefore, that when the weights of substances CHAP. VIII. SPECIFIC GRAVITY. 103 are spoken of relatively to one another, without any reference to particular quantities or masses of them, the weights meant to be compared are those of equal bulks. A substance is sometimes said to be heavy or light, apparent- ly without reference to any other substance. Thus air is said to be a very light substance, and gold a very heavy one ; but, in such cases, a comparison is tacitly instituted between the weights, bulk for bulk, of these substances and those of the bodies which most commonly fall under our observation. When we say that air is light, we mean that a certain bulk of air is much lighter than the same bulk of most of the substances which we commonly meet with ; and when we say that gold is heavy, we mean that any portion of that metal is heavier than a portion of the same dimensions of the most ordinary substances that we meet with. This familiar use of a positive epithet to express a comparison between any quality as it exists in an individual instance and a similar quality as it exists in the average of ordinary examples, is very frequent, and not confin- ed to the case just alluded to. We speak of a very tall man and a very high mountain, meaning that the man or mountain in question have much greater height than men or mountains commonly have. A man of twenty yeais of age is said to be a very young man, while a horse of twenty years of age is de- clared to be a very old horse, because the average age of man is much above twenty, and the average age of horses below it, From what has been now explained, it appears that the term weight is applied in two distinct, and sometimes opposite senses. A mass of cork may have any assignable weight, as 100 tons. This weight is truly said to be considerable, and the mass is correctly said to be heavy ; but yet the cork which composes the mass is said, with equal truth and propriety, to be a light substance. (75.) These two ways of considering the weight of a body may be denominated absolute and relative. The absolute weight of a body is that of its whole mass, without any reference to its bulk ; the relative weight is the weight of a given magnitude of the substance compared with the weight of the same magni- tude of other substances. The term weight, however, is com- monly used to express absolute weight, while the relative weight of a body is called its specific gravity. The origin of this term is obvious. Bodies which differ in other qualities are found also to differ in the weights of equal volumes. Thus a cubic inch of atmospheric air has a weight different from a cubic inch of oxygen, hydrogen, or any of the other gases. The number of grains in a cubic inch of gold is different from the number of grains in the cubic inch of platinum, silver, or any of the other metals. A cubic inch of 104 A TREATISE ON HYDROSTATICS. CHAP. VIII. water contains a number of grains different from a cubic inch of sulphuric acid, alcohol, or other liquids. Hence, it appears that the weight of a given bulk of any substance, being differ- ent from the weight of the same bulk of other substances, may be regarded as an index or test of its species, and by the weights of equal bulks bodies may be separated and arranged in species. Hence the term specific weight, or specific gravity. (76.) When bodies are to be compared, in respect of any common quality, a standard of comparison becomes necessary, in order to prevent an express reference to two bodies in every particular case. Thus, if we would express the height of any body without some standard measure, we could only do so by declaring it to be so many times as high, or bearing such a proportion to the height of some other body. But a foot, or a yard, being known lengths, it is only necessary to state that the height of the body is so many feet, or so many yards. In like manner, if we would express the specific gravity of lead, we should state that it had such a proportion to the weight of some other body, the weight of a certain bulk of which is known. But if one substance be selected, to which, as to a standard, all others shall be referred, then the specific gravity of any sub- stance may be expressed simply by a number which has the same proportion to one or the unit as the weight of any bulk of the substance in question has to the weight of an equal bulk of the standard substance. The body selected as the standard or unit of specific gravity should be one easily obtained, and subject as little as possible to variation by change of circumstances or situation. For this purpose water possesses many advantages ; but, in deciding the state in which it is to be considered as the standard, several circumstances must be attended to. First, The water must be pure, because the admixture of other substances will affect the weight of a given volume of it ; and since at different times, and in different places, water may have different substances mixed with it, the standard would vary, and therefore the specific gravities of substances ascer- tained with reference to it at different times and places would not admit of comparison. Thus, if the proportion of the weight, bulk for bulk, of gold to the weight of the water of the Seine were ascertained at Paris, and the weight of another specimen of that metal relatively to the water of the Thames were ascer- tained at London, the specific gravities of the two portions of metal could not be inferred unless it were previously known that the water of the Thames and the water of the Seine were composed of the same ingredients, or if not, unless their rela- tive weights, bulk for bulk, were previously determined. That the standard therefore may be invariable, it is necessary that CHAP. VIII. STANDARD OF SPECIFIC GRAVITY. 105 all substances which may be combined with the water shall be extricated. Such heterogeneous matter as may be suspended in the liquid in a solid state may be disengaged from it by filtration ; that is, by passing the liquid through a solid substance whose pores are smaller than the solid impurities to be extricated. If any sub- stances be held in solution by the water, or be chemically com- bined -with it, they may be disengaged by distillation ; that is, by raising the temperature of the liquid to a point at which the water will pass off in vapor, leaving the other substances be- hind ; or, if those other substances vaporize at a lower heat, they Avill pass off, leaving the water behind : in either case the water will be separated from the other bodies with which it is combined. It is evident that this latter process of distillation also serves the purposes of the former one of filtration. Secondly, The water being thus obtained in its pure state, and free from admixture with any other substance, it is to be considered whether there be any other cause which can make the same bulk of the liquid weigh differently at different times and places. We have already more than once alluded to the way by which bodies are affected in changes of temperature. Every increase of temperature, in general, produces an increase of bulk, and therefore causes a given volume, as a cubic inch, to weigh less. Hence, in comparing the weights, bulk for bulk, of any substances, at different times or places, with the weight of pure water, the results of the investigation would not admit of comparison unless the different states of the water with re- spect to temperature were distinctly known. In addition, there- fore, to the purity of the water taken as a standard, it is expe- dient that some fixed temperature be adopted. It has been al- eady explained that water, as it decreases in temperature, also ;ontracts its dimensions until it attains the temperature of about 40 ; it then again begins to expand : at this temperature of 40 it is therefore in its least dimensions, and it is known that when the water is pure, its state at this temperature is independent of time, place, or other circumstances ; it is the same at all parts of the earth, and under whatever circumstances it may be submitted to experiment. The temperature at which pure water has its dimensions most contracted is called the state of greatest condensation, because then the mass of the liquid is reduced to the smallest possible dimensions, and its particles have the greatest possible proximity. The weight of a given bulk of distilled water in the state of greatest condensation is, therefore, the standard of specific gravity.* * This is the best standard, though water at the temperature of 60 has been mor generally adopted by English philosophers. AM. ED. 106 A TREATISE ON HYDROSTATICS. CHAP. VIII. As it may not be always convenient to obtain water at this temperature, when experiments on specific gravity are to be made, numerical tables have been constructed expressing the change of weight which a given bulk of water sustains with every change of temperature ; so that when the specific gravi- ty of any substance has been found with reference to water c.t any proposed temperature, it may be reduced by a simple pro- cess of arithmetic to that which would have resulted, had it been compared, in the first instance, with water at the temper- ature corresponding to the state of greatest condensation. (77.) If the bulk of 1000 grains of pure water,* at the tem- perature of 40 of Fahrenheit's thermometer, be ascertained, the number of grains in the same bulk of any other body will express its specific gravity, that of water being 1000 ; or if the specific gravity of water be expressed by 1, the specific gravity of other substances will be expressed by a thousandth part of the former numbers. This only requires that three decimal places should be taken. Thus it is found that a volume of gold, equal in bulk to 1000 grains of water, weighs 19,250 grains. Therefore, if 1000 be the specific gravity of water, 19,250 will be that of gold ; or if 1 be the specific gravity of water, the thousandth part of 19,250, which is 19|, will be the specific gravity of gold ; which, expressed by the decimal notation, is 19-250. A vessel which would be filled by a thousand grains of water would contain 19,250 grains of gold. Bodies which exist in the gaseous or aeriform state are so much lighter than water, that it is generally found expedient to refer them to another standard, which has a known relation to water : their specific gravities in relation to water would be expressed by numbers inconveniently small. The standard usually selected for bodies of this form is atmospheric air ; and to it the specific gravities of all bodies in the gaseous, aeriform, or vaporous state are referred, in the same manner as bodies in the solid or liquid are referred to water. Observations respecting this standard of gaseous specific gravity may be made similar to those already given respecting the liquid standard ; but, in the determination of the specific gravities of gases, there are many circumstances to be attended to of too delicate and complicated a nature to admit of being explained, with any degree of detail, in a treatise designed for popular use. We shall, however, notice some of them slightly as we proceed with the subject. Atmospheric air is still more susceptible of changes in its volume, arising from change of temperature, than any bodies in the liquid or solid form. It is, therefore, the more necessary, in * It may be convenient to remember that a cubic foot of pure water at the tern perature of 60 weighs, with greet precision, 1000 ouncea avoirdupois. CHAP. VIII. SPECIFIC GRAVITY OF GASES. 107 fixing the standard, that the temperature should be settled. The temperature which has been selected for this purpose is that of melting ice, which corresponds to 32, or the freezing point, of Fahrenheit's thermometer ; this being a point which is independent of the arbitrary divisions of thermometers in differ- ent countries. The only cause which can affect the dimensions of a given weight of pure water is the temperature to which it is exposed. Although it is not absolutely incompressible, nor inelastic, yet it will undergo no sensible change of dimensions by any change of pressure to which, under ordinary circumstances, it is liable. Therefore, in fixing the state in which it is to be regarded as a standard of specific gravity, all variation of external pressure is disregarded. The case is, however, altogether different with atmospheric air, which is sensibly affected in its dimensions even by the slightest change in external pressure. While the temperature of this fluid remains the same, the dimensions which a given weight of it occupies may be subject to changes, almost without any assignable limit, and independently of any change of temperature. To fix the state of atmospheric air, in which it shall be considered as a standard of specific gravity, it is necessary to declare the amount of the pressure to which it is subject. The pressure selected by Biot, who has investigat- ed the specific gravities of gases with great success, is one which is equal to the pressure of the atmosphere when the ba- rometer stands at six hundredths of an inch below 30 inches.* The weight of atmospheric air and other gases is also affect- ed by the quantity of moisture which they hold suspended. An instrument, called a hygrometer, has been contrived for the purpose of showing the relative state of gases with respect to this moisture. A due attention to the indications of this instru- ment is therefore also necessary to settle the state in which atmospheric air is to be regarded as the standard. The state of the standard being then settled, the dimensions of 1000 grains of atmospheric air are determined. The num- ber of grains, and fractions of a grain, of any other gases filling the same dimensions, will express their specific gravities, that of the standard being 1000. In order to ascertain the specific gravity of any gas with reference to water, it is only neces- sary to consider the specific gravity of the standard, atmospheric air, in reference to water. A portion of the former, equal in bulk to 1000 grains of the latter, will weigh one grain and 22 hundredth parts of a grain. (78.) From all that has been explained, there are several in- ferences which may be made respecting the relation between * This will be more easily comprehended afteF our treatise on Pneumatics has been studied. 108 A TREATISE ON HYDROSTATICS. CHAP. VIII. the weights and bulks of bodies, which will be found useful in all investigations which relate to specific gravity. If two bodies have equal magnitudes, their absolute weights will be in the same proportion as their specific gravities. Thus, suppose a certain bulk of copper weighs 7600 ounces, and the same bulk of brass weighs 7824 ounces, then the specific grav- ities of the two metals will be in the proportion of these two numbers, because both are related to the same standard, viz. water; and, in fact, the magnitude of 1000 grains of water is equal to that of 7600 grains of copper, and to 7824 of brass. If two bodies have equal absolute weights, then their specific gravities will be in what is called the inverse proportion of their magnitudes ; that is, the body which has the greater magnitude will have a specific gravity as much less than the other as its magnitude is greater. Suppose A and B are two bodies of equal weight, the dimensions of A being twice those of B. If A be divided into two equal parts, each will have a bulk equal to that of B, and therefore the specific gravities of the two bodies will be in the same proportion as the weight of half of A is to the weight of B. But the weight of B is equal to the weight of A, and therefore the specific gravity of A is in the same proportion to that of B as the weight of half A is to its whole weight. Hence, the specific gravity of A is half the specific gravity of B, while the dimensions of B are half the di- mensions of A. Thus the dimensions and the specific gravities of bodies are oppositely related when their absolute weights are the same. From the two properties just explained, it appears that the specific gravity of bodies may be ascertained either by deter- mining the exact dimensions of quantities which have equal weights, or the exact weights of quantities which have equal dimensions. (79.) It has been seen that the specific gravity of every body changes with its temperature, because the change of tempera- ture necessarily infers a change of dimensions. But an inquiry naturally presents itself: Does not the increase of dimension, produced by imparting heat to a body, arise from the body re- ceiving an additional quantity of matter insinuated through and among its particles, so that in its altered state it ought to be viewed not as the original mass with increased dimensions, but as a compound of the original body, and a new portion of mat- ter added thereto ? This inquiry is tantamount to the question, whether the principle of heat be material. Nothing has been supposed in this case to be imparted to the body except heat ; and the heat so imparted has at least exhibited one essential quality of matter, viz. the occupation of space, since it has forced asunder the constituent particles of the original body, which CHAP. VIII. IS HEAT MATERIAL! it has penetrated, and compelled them to stand at a greater dis- tance to make way for its admission. It is true that this effect may be imagined to be produced in other ways beside supposing the particles of heat to be material ; but, however it be produced, the fact is certain, that when heat penetrates the dimensions of a body, or, if we may be allowed the phrase, when it is mixed with a body, the dimensions of the compound suffer an increase in the same manner as the dimensions of any two fluids, as wa- ter and alcohol when mixed together are greater in bulk than the water was existing separately. The question, whether the increase of magnitude, caused by raisino- the temperature of a body arises from its having receiv- ed any addition of a material substance to its mass, can only be decided by previously fixing some one quality which will be regarded as inseparable from matter, and therefore the pres- ence or the absence of which being ascertained will decide the presence or the absence of the additional portion of matter un- der inquiry. The quality which seems best adapted for such a test is weight ; and the question, whether the increased dimensions of a heated body proceeds from its having received any increase of ponder- able matter, becomes one which is to be decided by direct ex- periment. Experiments to ascertain this fact have been insti- tuted, attended by every circumstance which could contribute to ensure accurate results. The same body, at different tem- peratures, and therefore under different dimensions, has been accurately weighed, but no change of weight has been observ- ed. We are, therefore, entitled to conclude that, whatever be the nature of the principle which gives increased dimensions to a body whose temperature is raised, whatever it be which fills the increased interstitial spaces from which its constituent particles are expelled, it is not a ponderous substance, it is not one on which the earth exerts any attraction, it is not one which if unsupported would fall, or if supported would produce any pressure on that which sustains it. It follows, then, that the change produced in the specinc gravity of a body, by any change in its temperature, depends solely upon the change produced in its dimensions, and not upon any change which takes place in its weight. We are, therefore, entitled to conclude, that the specific gravity of any body at different temperatures is inversely as its magnitude ; that is, in the same proportion as the dimensions of the body are increased by heat, in that proportion exactly is its specinc gravity diminished. . . (80.) Density is the term used to denote the proximity or closeness of the constituent particles of any body to each other, and the density of a body is said to be uniform when its con- 10 110 A TREATISE ON HYDROSTATICS. CHAP. VIII. stituent particles are uniformly and evenly distributed through its dimensions, so that the same number of particles occupy the same space in every part of its magnitude. This is the ordi- nary notion of density ; but it is one which, strictly speaking, is unphilosophical, because it is founded upon the supposed ex- istence of ultimate constituent particles, or molecules of bodies, the aggregate of which form their mass. However probable the existence of such molecules may be, they are not within the sphere of sensible observation, nor can their number or magni- tude under any circumstances be ascertained. In a strictly scientific sense, the term density can be regarded as scarcely different from specific gravity. A body is more or less dense when a given volume of it contains more or less ponderous mat- ter, and it is uniformly dense when equal magnitudes of it, how- ever small, in every part of its dimensions have equal weights. When any body suffers a change of dimensions, either by ex- ternal pressure, or by the effects of heat, since it still contains the same quantity of ponderable matter, its density must be in- creased in the same proportion as its bulk is diminished, or vice versa. In whatever sense the term density be used, this is ob- vious ; for if it be supposed to refer to constituent particles, or atoms, it is evident that the same particles exist in the different states with a greater or lesser quantity of space between them. If the term density be applied to bodies of different kinds, such as silver and gold, it can only be used with strict propriety synonymously with specific gravity. If it have any reference to the proximity of constituent particles, and in that sense the density of gold be declared to have the same proportion to that of silver as the weights of equal magnitudes of these metals, it will be evidently implied, that the ultimate constituent particles of the gold are equal in magnitude to those of the silver, but that nineteen particles of the former are included within a space equal to that which contains only ten particles of the latter ; these numbers being taken to represent the specific gravities of those metals. The hypothesis on which such conclusions as this are founded is not necessary in physical investigation ; and, indeed, the term density is rarely used, except when it is applied to the same body when subject to a variation in its di- mensicns. (81.) In the effects produced by the immersion of solids in liquids, we find many relations developed between the weights and bulks of the solids and of the liquids in- which they are im- mersed. Such effects, therefore, have a necessary connection with the specific gravities of these classes of bodies ; and when properly examined, it will be found that they will lead directly to practical L.ethods of ascertaining the specific gravities of bodies, both in the solid and liquid state. CHAP. VIII. SPECIFIC GRAVITY. Ill It has been shown that a solid, heavier, buiK for bulk, than a liquid, will sink in the liquid, and that its apparent weight when immersed Avill be less than its true weight, by the weight of the liquid which it displaces. As the weight of the solid, and the weight which it loses by immersion, are the weights of equal magnitudes of the solid and liquid, they will be propor- tional to their specific gravities. Hence we infer, 1 . That a solid will sink in any liquid which is specifically lighter than it. 2. That the specific gravity of the solid bears to that of the liquid the same proportion as the weight of the solid bears to the weight which it loses by immersion. (82.) If a solid be lighter, bulk for bulk, than a liquid, it will float on the surface, displacing as much liquid as is equal to its own weight. It has been proved that when bodies have equal weights, their specific gravities are in the inverse proportion of their dimensions. (78.) Hence we infer, 1. That a solid will float on the surface of any liquid which is specifically lighter than it. 2. That the specific gravity of the solid bears to that of the liquid the same proportion as the part of the solid immersed boars to its whole dimensions. (83.) It has been proved that if the weight of a solid be equal, bulk for bulk, to that of a liquid, it will remain suspended when totally immersed, neither rising nor sinking. Hence it appears that this phenomenon is an indication that the specific gravities of the solid and liquid are equal. (84.) If the same solid be successively immersed in different liquids which are specifically lighter than it, the weights which it will lose by immersion in each of them will be the weights of portions of the several liquids, equal in bulk to the solid, and therefore equal in bulk to each other. Thus if a solid, measur- ing a cubic inch, be successively immersed in water, sulphuric acid, and alcohol, and the weights which it loses in each be ob- served, we shall obtain the weights of a cubic inch of each of these liquids. These weights will therefore be in the propor- tion of the liquids severally. Hence we infer, " That a solid, successively immersed in several liquids which are specifically lighter than it, will lose weights which are pro- portional to the specific gravities of the several liquids." (85.) If a solid which is lighter, bulk for bulk, than several liquids, be made to float successively on their surfaces, it will displace portions of them which in each case are equal to its own weight, and therefore equal in weight to each other. But it has been shown, that the specific gravities of bodies having the same weight are in the inverse proportion of their rnagni-r tudes. Hence we infer, 1 12 A TREATISE ON HYDROSTATICS. CHAP. VIII. " That if the same body float successively on the surfaces of different liquids, the parts of it which are immersed in any two of them will be in the inverse proportion of the specific gravities of these liquids." Thus, if the liquids be sulphuric acid and ether, the specific gravity of the sulphuric acid will have the same proportion to the specific gravity of the ether as the portion of the solid which sinks in the ether has to the portion of it which sinks in the sulphuric acid. (86.) If several solids, heavier, bulk for bulk, than a liquid, be successively immersed in it, they will sustain losses of weight equal to the weight of the liquid which they severally displace ; consequently these losses will be proportional to the magnitudes of the bodies. If the solids be previously so ad- justed as to be equal in weight, the specific gravities of any two of them will be in the inverse proportion of their magni- tudes. (78.) Hence we infer, " That solids of equaj. weight immersed in the same liquid, which is specifically lighter than them, lose weights which are in the inverse proportion of the specific gravities." Thus, if an ounce of silver and an ounce of gold be immersed in water, the weight lost by the gold will bear the same pro- portion to the weight lost by the silver, as the specific gravity of the silver bears to the specific gravity of the gold. (87.) If several solids which are lighter, bulk for bulk, than a liquid, float upon it, they will displace portions of the liquid equal to their own weight ; therefore the parts of them which will be immersed will be proportional to their weights. In this case, therefore, if the solids have equal magnitudes, the parts immersed will be in the same proportion as their specific grav- ities. (88.) It has been proved, that when different liquids have been placed in communicating vessels without mixing with each other, their surfaces will rest at different levels, and that the heights of these levels respectively above the surface at which they meet are greater in proportion as the liquids, bulk for bulk, are lighter. Let A B C,Jig. 58., be a tube, as describ- CHAP. Till. SPECIFIC GRAVITY. 113 ed in ((37.), containing two liquids of different weights, bulk for bulk, or of different specific gravities. It has been already proved, that when they are at rest, the height S N will have the same proportion to 'the height PM as the weight of a given bulk of the heavier liquid to a weight of the same bulk of the lighter ; hence it appears that the heights of the surfaces O and W, of the two liquids above the level of the surface S at which they meet, are inversely as the specific gravities of the liquids. Thus, if S O be oil, and S B W be water, then the specific gravity of water will bear the same proportion to the specific gravity of oil, as the height S N bears to the height P M. (89.) The methods of practically determining the specific gravities of bodies depend upon the properties which have been just explained. The details must, however, be different for different bodies, and must be suitable to their peculiar forms and properties. The specific gravity of a solid which is not soluble in water, and which is specifically heavier than that liquid, may be de- termined by observing the weight which it loses by immersion. The proportion which this weight bears to the actual weight of the solid, will determine the specific gravity. Example. A piece of pure gold, cast and not hammered, weighing 77 grains, is immersed in water, and is observed to weigh only 73 grains ; it therefore follows, that it displaces 4 grains of water. The proportion, therefore, of the weights of equal magnitudes of the metal and the water is 77 to 4, or 19| to 1. Hence 19,-j; is the specific gravity of gold, 1 expressing the specific gravity of the standard liquid. Example. A piece of flint glass, weighing 3 ounces, is im- mersed in pure water, and observed to weigh only 2 ounces. Hence the weight of the water which is displaced is 1 ounce. The specific gravity of the glass is therefore 3. (90.) If the solid" be soluble in water, this method cannot be practised. In this case the solid may be defended from the water by a varnish, or a thin coating of wax, or some other sub- stance not affected by the water. The specific gravity of salts and like substances may be thus found. As, however, the coat- ing used in this case produces an increase of bulk, the solid, when immersed, will displace more than its own bulk of water. The weight of the solid, if ascertained without the coating, will bear a less proportion to the loss of weight than it doss to its own bulk of water ; and therefore, the specific gravity ob- tained from such an experiment, would ia this case be too small.* But if the weight of the solid be ascertained after tl\3 * This will depend wholly upon the speciric gravity of the coating. If the same as that of water, it will not affect the water weight of the body ; coating will havo the name effect as the water displaced by it ; and as sue! If this ha for th such coat- 10 114 A TREATISE ON HYDROSTATICS. CHAP. VIII. coating is put on, then the specific gravity which is obtained is not the specific gravity of the solid, but of the solid and coating together. Where great accuracy is not required, the effect produced by the coating may be neglected ; but if the result is to be obtained with a high degree of accuracy, the following method is preferable : Find the proportion of the specific grav- ity of the solid to that of some liquid in which it is not soluble, and which is specifically lighter than it. This may be done by observing the weight of the solid and the weight which it loses by immersion. Then find the specific gravity of that liquid with respect to water by the method Avhich shall be hereafter explained. If the solid consist of many minute pieces, or be in the form of powder, a cup to receive it ought to be previously suspended in the water, and accurately counterpoised. (91.) To determine the specific gravity of a solid lighter than water, let the part immersed when it floats on water be observ- ed, the proportion which this bears to its whole magnitude, will be that of its specific gravity to the specific gravity of water. (82.) When the solid floats, the proportion of the part immersed to the whole bulk, may be ascertained in the following manner : Let the vessel which contains the water have perpendicular sides, and be as narrow as the magnitude of the solid will ad- mit. Let the point on the vessel which marks the surface be- fore immersion be observed. Let the point to which the surface rises, when the solid floats, be next observed ; and, finally, let the solid be totally submerged, and the point to which the surface then rises observed. The elevations of the surface produced by the partial and total submersion, indicate the portions of the solid in each case immersed, and are therefore in the ratio of the specific gravity of the solid to that of the liquid. There is another method of ascertaining the specific gravity of a solid lighter than water, which ought to be noticed here. Let the solid whose specific gravity is to be ascertained, be at- tached to another which is heavier than water, and of such a magnitude that the united weights of the two will be greater than the weight of water which they displace ; they will there- fore sink when immersed. The weight of the whole being observed, let the weight which they lose by immersion be noted ; this will be the weight of as much water as is equal in magnitude to the united bulks of the solids. Let the lighter solid be then detached, and let the weight which the heavier ing can be easily prepared, the specific gravity may be accurately determined by this method. But without this precaution, the specific gravity obtained by this method may be either greater or less than the true specific gravity, according as the coating is specifically heavier or lighter than water. AM. ED. CHAP. VIII. SPECIFIC GRAVITY. 115 loses by immersion be ascertained ; this will be the weight of as much water as is equal in bulk to the heavier solid. If this loss of weight be subtracted from the loss sustained by the combined masses, the remainder will be the weight of as much water as is equal in bulk to the lighter solid : the proportion of the weight of the lighter solid to this will determine its specific gravity. (92.) There are several methods by which the specific gravi- ties of liquids may be found. If a solid specifically heavier than water, and also specifically heavier than the liquid whose specific gravity is to be determin- ed, be successively immersed in water and in that liquid, the losses of weight will be proportional to the specific gravities of water and the liquid. If the number expressing the loss of weight in the liquid be divided by the number expressing the loss of weight in the water, the quotient will express the spe- cific gravity of the liquid. Example. A piece of glass, immersed in sulphuric acid, is observed to lose 3700 grains of its weight. The same solid, immersed in water, loses 2000 grains ; hence the proportion of the specific gravity of the sulphuric acid to the specific gravity of the water is that of 37 to 20, or of 1850 to 1000 : therefore if 1000 express the specific gravity of water, 1850 will express that of sulphuric acid. The specific gravity of a liquid may also be found by means of a solid which is specifically lighter than it, the same solid being also specifically lighter than water. Let the solid float successively on the two liquids, and observe the magnitudes of the parts immersed, which may be done by observing the change of level, if the vessels containing the liquids have equal bottoms, and perpendicular sides : the parts immersed will be inversely as the specific gravities. (85.)* Example. The same solid floats successively on water and muriatic acid, and the proportion of the parts immersed is ob- served to be that of 10 to 12. Hence the specific gravity of muriatic acid is 12, that of water being 10. (93.) The specific gravities of liquids may be ascertained by observing the weights of two different solids floating on their surfaces with equal parts immersed. In this case the specific gravities will be proportional to the weights of the solids. But perhaps the most direct method of determining the specific gravities of bodies, as well in the liquid as in the gaseous state, is by actually weighing them in a flask or bottle of known mag- nitude. Let such a one be provided with a stopper which * Hence a ship will draw more water, i. e. sink farther, on entering a fresh water river, than when at sea. AM. ED. 116 A TREATISE ON HYDROSTATICS. CHAP. VIII. nicely fits it, and let it be filled with pure water and weighed, and subsequently filled with any other fluid and again weighed ; if the weight of the flask be exactly known, the weight of its contents may in each case be found. In this manner the weight of air may be determined by weighing the flask first filled with air in the ordinary state, and, subsequently, after the air has been abstracted from it, by the air-pump, an instrument which will be explained in a subsequent part of this volume. It is thus ascertained that a cubic foot of common atmospheric air weighs about 527 grains. This weight, however, fluctuates from causes already alluded to, and which will hereafter be fully explained. The empty flask may in like manner be filled with any other species of gas, and its weight relatively to that of air may be at once determined. Instruments for the practiced measurement of specific gravities. (94.) The form and construction of instruments for determin- ing specific gravities, vary according to the degree of accuracy J-.J required in the results, and according to the nature of the bodies to which they are intended to be applied. In scientific CHAP. VIII. HYDROSTATIC BALANCE. 117 investigations, where the most extreme accuracy is sought, the measurement of specific gravities is effected by a very sensible balance furnished with certain additions, and mounted in a manner from which it has received the name of the hydrostatic balance. A front view of the hydrostatic balance is represented in Jig. 59., and a side view in^g-. 60. The corresponding parts being marked by the same letters. A pillar, A B, fixed in a stand, C D, supports the instrument. On the stand, placed in a horizontal position, is a screw S, which, turns in a fixed nut at T. This screw is terminated by a hook, which holds the loop of a silken string, the two parts of which, passing in the grooves of wheels or rollers at P, are carried from thence to the top of the pillar and there pass over the grooves of rollers at R, and their ex- tremities finally support a horizontal arm at E. To the centre of this arm e, a very nice balance is suspended : beneath the beam of this balance are placed rests, at m, so that when the beam is not in use, by turning the screw S, it will be allowed to descend upon the rests ; and the knife edges, on the accu- racy of which the sensibility of the instrument depends, will be relieved from pressure. The board G H, attached to the pillar immediately below the dishes, is movable on the pillar, and may be fixed in any position by means of an adjusting screw ; also the nut in which the screw S turns is capable of being moved towards or from the pillar, so as to raise or lower the balance, in a greater degree than would be allowed by the play of the screw S. Thus the balance and all its accompaniments may be raised or lowered at pleasure. To the centre of the bottom of the dishes hooks c d are attached, from which brass wires are suspended, which pass freely through holes in the board G H. At the lower extremities of these wires are hooks h and g. To the hook g-, a graduated rod g k is suspended, which ^Iso terminates in a hook at k. The rod g k bears a scale of equal divisions ; an index N O turns on a rod M N with a horizontal motion, and may be applied to the scale g k or may be removed at pleasure ; this index may be also moved upwards and downwards by means of a screw M, which playa in a nut in the board G H. A brass ball of about | of an inch diameter, is suspended from k, by a brass wire k Z, of such a thickness that one inch of it will displace half a grain of water. From the hook h t a glass bubble i is suspended by a horse-hair. The brass ball and the glass bubble are so adjusted that they will hang about the middle of the glass vessels X Y, in the ordinary position of the balance. If the dish c preponderate, the wire k I will become more immersed ; and for every inch it sinks, the weight which draws down the dish c will be diminish- ed to the amount of half a grain, that being the weight which 118 A TREATISE ON HYDROSTATICS. CHAP. VIIL an inch of the wire loses by immersion. In like manner if a preponderate, the wire k I will be drawn up ; and for every inch which is raised above the surface of the water, an additional weight of half a grain will act upon the dish c. Now suppose the balance so adjusted that its tongue points directly upwards at e, and that the beam a 6 is therefore horizontal ; let the index N O be fixed at the middle point of the scale g k by means of the screw M. Suppose the scale g k so divided, that its middle point will be marked zero, or ; and let each half of it, being two inches long, be divided into a hundred equal parts, being numbered upwards and downwards from the middle point. "Let the substance to be weighed be placed in the dish c, and let grain weights be placed in the dish 3 value of any article formed of such a material can be s determined, it is necessary to find the exact proportion of alloy : which itt contains. i Theso considerations suggest a class of problems respecting the specific gravities of compound bodies and their constituent elements, the solution of which is of great practical importance. This solution, however, does not entirely depend on mechani- cal principles, as we shall presently explain ; and even so far as it doe B depend on such principles, many previous conditions are necessary to render such problems determinate. If two bodies, whose specific gravities are known, be mixed in a givon proportion, and in their union no other effect be pro- duced t) lan the transfusion of the particles of each through and among those of the other, the specific gravity of the compound is a matter of easy computation. The general principle for the solution of such a problem will be collected without difficulty from an example. Example. Let gold and copper be united, in the proportion of 20 measures of gold to 3 of copper. The specific gravity oi the goltd is 1925, and that of the copper 890, the specific gravity of water being 100. Hence the calculation may be made as follow.')! ; the denomination of weight used being immaterial, providing it be tho same throughout the whole investigation: 124 A TREATISE ON HYDROSTATICS. CHAP. VIII. Weight of a cubic inch of water ....... 100 Weight of a cubic inch of gold 1,925 Weight of a cubic inch of copper , 890 Weight of 20 cubic inches of gold 38,500 Weight of? cubic inches of copper (5,230 Weight of 27 cubic inches of the compound . . 41,730 Weight of one cubic inch of the compound . . l.,656f Hence the specific gravity of the compound is J,656f, that of water being 100. If the proportion of the ingredients be given in weight;, as so many grains of gold mixed with so many grains of copper, the magnitudes or measures of these weights may be computed from knowing their specific gravities, which is in fact the weight of a given magnitude. The preceding method of calculation may then be applied. If more than two bodies be united, the principle on whi-sh the computation is conducted will be the same. In the example just given, the specific gravity of th.e com- pound was the object of inquiry, the specific gravities of the components being supposed to be given. The same method of calculation would, however, discover any of the other quan- tities which enter the investigation with a sufficient nvjnber of data. Thus, suppose it were required to determine one of the ingredients of a compound substance, the nature and quantity of the other ingredient being known. Let the specifi c gravity of the compound be determined by the usual means, and let the quantity of the given ingredient be subtracted from the whole quantity of the compound, and the remainder will be the quan- tity of the required ingredient. But it is necessary to < letermine its specific gravity. Example. Let the compound body under investigation be supposed to be composed of two substances, of whiciS gold is one ; and let the total quantity of the compound be 27 cubic inches, the quantity of the gold being 20 cubic inche s. Sup- pose that we ascertain the following results by experii nent : Weight of 27 cubic inches of the compound . . 44,730 Weight of one cubic inch of gold 1,925 Weight of 20 cubic inches of gold 58,500 Weight of 7 cubic inches of the alloy .... -6,230 Weight of one cubic inch of the alloy .... 890 Hence the specific gravity of the alloy will be 890 ; a nd that CHAP. VIII. INGREDIENTS OF COMPOUNDS. 125 being 'Known to be the specific gravity of copper, the quality of the alloy is determined. When tne quality of the alloy is known, it may be required to determine the proportion in which it is mixed with the pre- cious metal. In this case the specific gravities of the constitu- ent parts are supposed to be given. Example. Let the compound be one of gold and copper as before, the specific gravities of which are 1925 and 890. Weight of a cubic inch of gold ....... 1,925 Weight of a cubic inch of copper ...... 890 Difference .............. 1,035 ____ ____ Weight of a cubic inch of the compound by experi- ment ........... .... l,656f Wieight of a cubic inch of copper ...... 890 Difference ........ ...... 76Gf As the former difference 1035 is to the latter 7(>6f , so is 1 to tlio number which expresses the proportion in which the metals are mixed. Thus, by the Rule of Three : 1035 : 766$ : : 1 : 766| divided by 1035, or which is the same, -. Hence the proportion of gold contained in a cubic inch of the com- pound is 20 parts in 27, and there are, therefore, 7 parts of al- loy. The demonstration of the proportion used in this solution .scarcely admits of a sufficiently elementary explanation to be introduced with propriety in the text.* If the object be to detect the* exact quantity and quality of the impure or heterogeneous matter contained in any compound, it will not be sufficient that the specific gravity of the compound and that of the principal ingredient be v previously known. . Thus, in manufactured gold, it is not enough to know the specific gravity of pure gold, and that of the alloyed specimen under investigation, in order to determine the quantity and quality of * Let ^represent the proportion of gold, and i/ that of copper, contained in ona cubic inch of the mixture. Let g be the rpocirtc gravity of the gold, c that of the copper, and m that of the mixture. The weight of gold contained in a cubic inch of the mature is xg, and tho weight of coppor ?/c, and the weight of a cubic inch of the mixture is ?:i. Hence we have x:r~\-ycm -M-2,-1 '*= - gc or, g c : m c ! ; 1 : x. That i^ the difference between the npeciric gravities of tho gold and copper is to the differe the prrtion of gold which e^tj in a i ubic inch. 126 A TREATISE ON HYDROSTATICS. CH. IP. VIII. the alloy. It is indispensably necessary, either that the ; specific gravity of the foreign matter intermixed with the pi incipal ingredient be given, or that some data may be furnisl aed by which it may be computed. Although in the cases of alloyed metals, or adulterated 1 .iquids, it is rarely possible to detect the exact quantity and qur Jity of foreign matter which may be intermixed, yet we may ge nerally pronounce with certainty on the presence of some adult, eration or alloy. The specific gravity of the pure substance; being known, if that of the specimen under inquiry differ fron i it, the intermixture of foreign matter is no longer doubtful'.. But what that heterogeneous matter is, and in what quantit/ it is present, is a problem which requires the aid of other princi pies. It has been already stated that spirits of every kind usod in commerce, are mixtures of pure alcohol and water in different proportions, and their strength depends on the quantity of alco- hol which is mixed with a given quantity of water. The indi- cations of the hydrometer immediately betray this. The adulteration of milk by water may always be deti ttted by the hydrometer, and in this respect it may be a usefu I ap- pendage to household utensils. Pure milk has a greater sp( jcific gravity than water, being 103, that of water being ICO. A very small proportion of water mixed with milk will produce a ^quid specifically lighter than water. Although the hydrometer is seldom applied to domestic uses, yet it might be used for many ordinary purposes which oould scarcely be attained by any other means. The slightest adul- teration of spirits, or any other liquid of known quality, msy be istantly detected by it. And it is recommended by 'its cheap- ness, the great facility of its manipulation, and the simplicity of its results. (97.) The first notion of using the buoyancy of solids in a liquid, as means of determining the nature of their con iponent parts, is attributed to Archimedes, the celebrated mathen latician and natural philosopher. It is said that Hiero, king of S} -racuse, haying engaged an artist to make him a crown of gold, wished to know whether the article furnished to him was cor. aposed, according to the contract, of the pure and unalloyed met al, and yet to accomplish this without defacing or injuring the crown, tie referred the question to Archimedes. The philc sopher while meditating on the solution of this problem happei ling to bathe, his attention was directed to the buoyancy of his 1 >ody in the water, and thence to the general effect produced upc >n the apparent weights of solids by their immersion in liquids. The whole train of reasoning which has been followed in thi J pre- ceding chapters instantly flashed across his mind. He pe rceiv- ed at once that the degree of buoyancy or the weightiest - vould CHAP. VIII. TO DETECT ADULTERATION. 127 betray the weight of the metal composing the crown, compared, bulk for bulk, with pure gold. He rushed from the chamber in a transport of joy, ' exclaiming aloud, "Eureka! Eureka!" (/ have found it ! I have found it .') If the tale be true, the joy of Archimedes was produced not by the solution of the particular question respecting the crown, but by perceiving the important consequences to which the ex- tension of the principle on which he had fallen must lead. (98.) The calculations which have been just explained, for ascertaining the specific gravities of compound bodies when those of their component parts are known, proceed upon the supposition that the bulk or magnitudes of the bodies united are not altered by their combination. Thus, if ten cubic inches of gold be alloyed with seven cubic inches of copper, it is assum- ed that the mass of compound metal thus obtained will measure 17 cubic inches. In like manner, if a pint of water be mixed with a pint of spirits, the computed specific gravity of the mix- ture proceeds upon the assumption that it will measure a quart. Experience proves this supposition to be, in most cases, un- founded. When the constituent atoms of two bodies are trans- fused through one another by intimate mixture, it is found that certain properties are manifested which exhibit a reciprocal relation between them, in virtue of which they are either drawn together into closer contact and compelled to occupy a less space, or are mutually repelled and made to occupy a greater space by attractive or repellent forces, which are called into operation by the contiguity of the molecules of the different bodies. In fact, it is found that equal measures of two different Bodies, being combined by mixture, will produce a compound, the measure of which will be either less or Fig. 64. greater than tvtfice the measure of either of the bodies so combined. Thus, a cubic inch of gold mixed with a cubic inch of copper will produce a mass of metal measuring less than two cubic inches. It follows, therefore, that the component particles of these bodies have been forced into a less space than that which they occupied separately ; and there- fore, that corresponding affinities or attractive energies have been awakened by their com- bination. In like manner, if a pint of pure water and a pint of sulphuric acid be mixed together, the compound will measure less than a quart. This experiment may be very easily exhibited in the following manner : Let A, Jig. 64., be a hollow glass ball, having a neck at the top B, furnished with a ground glass stopper made ex- 128 A TREATISE OX HYDROSTATICS. CHAP. VIII. actly to fit it, and water tight, and with a long narrow tube C D proceeding from the bottom and closed at the lower end D ; let this vessel be filled through the neck B with sulphuric acid as far as the top of the tube C ; then let water be carefully poured in till the ball is completely filled to the neck ; this liquid, being lighter than sulphuric acid, will remain in the ball resting on the surface of the sulphuric acid in the tube below. Let the stopper be inserted in the neck, so that the vessel being closed will be completely filled with the two liquids : holding the stop- per firmly in its place, let the vessel be now inverted, the tube being turned upwards and the stopper downwards. The sul- phuric acid will, by its superior weight, fall into the ball, and the water will rise into the tube, a partial mixture taking place by reason of the affinity of the liquids : this inversion being several times repeated, the liquids will at length be perfectly mixed. If the instrument then be held steadily with the tube upwards, it will be four/d that the liquids no longer fill it, but that several inches at the top of the lube will be empty. Thus the dimensions of the liquids will be considerably contracted by intermixture ; and of course the density or specific gravity will be much greater than if the liquids were mechanically united without any diminution of their volume. The effect here described will be found to be attended with another very remarkable one. The liquids at the commencement of the process being at the ordinary temperature of the atmos- phere, it will be found that after they are mixed they will acquire so great a degree of heat, that the vessel which con- tains them cannot be held in the hand without pain. This ef- fect bears a close relation to the expansion of bodies by heat. If the communication of heat to a body causes its dimensions to increase, it might noturaliy be expected that any cause which would produce a diminution of dimension would compel the body to part with heat. Thus the condensation produced by the admixture of the two liquids is accompanied by the evo- lution of heat. It is sufficient barely to notice this effect here, as it will be more fully explained in another part of the Cyclo- paedia. Although the method of completing the specific gravity of a mixture, "upon the supposition that its constituent elements suffer no change of dimension, is inapplicable for the actual de- termination of the specific gravities of compounded bodies, yet such computation is not useless.* The only exact method of *Let c and c 1 be the specific gravities of the component parts, and m the specific gravity of the mixture ; 'let a and a' be the magnitudes of the component parts, and a-f-a' will be the magnitude of tho mixture. The weights of the components will be a c and a' c', and the weight of the rr-ixturc will bo a c+a 1 c', which is the sum of the weights of the components : but tlie weight of the mixture will r.leC be ex- pressed by (rt-f-rr) r,i ,- hence CHAP. VIII. PENETRATION OF DIMENSIONS. 129 ascertaining the degree in which suhstances contract or ex- pand their dimensions by mixture is by computing the specific gravity which the mixture would have were such change of dimension not to happen, and comparing such computed spe- cific gravity with the actual specific gravity of the compound body observed by experiment. The process of measurement is not susceptible of the same accuracy, nor, indeed, of any degree of accuracy sufficient for scientific purposes : were it so, however, it would scarcely be so simple as the comparison of the computed and observed specific gravities. The quanti- ties of the two substances mixed should be accurately measur- ed before mixture, and the measure of the compound should be afterwards accurately ascertained. The difference between the sum of the measures of the constituent parts and the measure of the whole would give the contraction or expansion produced by their combination. ffl C-fffl' C' m =-THT [ In fact, this result is nothing more than an expression denoting that the specific gravity of the compound is equal to its weight, divided by its magnitude, the mag- nitude being supposed to be equal to the sum of the magnitudes of the components In some cases, the weights and specific gravities of the components are given, b not their magnitudes. Let w and to' be the weights ; then w=a c, and w'=a' c'. Therefore a = and o' = - . Hence c c' tc_j_w' tr-f-w' _ (+') e c' - " I 130 A TREATISE ON HYDROSTATICS. CHAP. IX CHAP. IX. HYDRAULICS TELOCITY OF EFFLUX FROM AN APERTURE IN A VESSEL, PROPOR- TIONAL TO THE DEPTH OF THE APERTURE, EQUAL TO THE VE- LOCITY ACQUIRED IN FALLING THROUGH THAT DEPTH. EFFECT OF ATMOSPHERIC RESISTANCE. VENA CONTRACTA. RATE AT WHICH THE LEVEL OF THE WATER IN THE VESSEL FALLS. LATERAL COMMUNICATION OF MOTION BY A LIQUID. RIVER FLOW- ING THROUGH A LAKE. CURRENTS AND EDDIES. EFFECTS OF THE SHAPE OF THE BED AND BANKS OF A RIVER. FOBCE OF A LIQUID STRIKING A SOLID, OR VICE VERSA. EFFECT OF AN OAR. WINGS OF A BIRD. DIRECTION OF THE RESISTING SURFACE. EFFECT OF THE VELOCITY OF THE STRIKING BODY. SOLID OF LEAST RESISTANCE. SHAPE OF FISHES AND BIRDS. SPEED OF BOATS AND SHIPS LIMITED. COMPARATIVE ADVANTAGES OF RAIL- ROADS AND CANALS. (99.) WE have hitherto confined our attention chiefly to those effects which are produced by the pressure transmitted by liquids, either arising from their own weight or from other forces applied to them, when confined within certain limits. When any of the limits or boundaries which confine a liquid are removed, the force which before was expended in exciting pressure on such boundary or limit, will now put the liquid in motion, and cause it to escape through the space from which the opposing limit has been removed. The phenomena exhib- ited under such circumstances, form the subject of a branch of the mechanical theory of liquids usually called hydraulics. It embraces, therefore, the effects attending liquids issuing from orifices made in the reservoirs which contain them ; water forced by pressure in any direction through tubes or apertures, so as to form ornamental jets ; the motion of liquids through pipes and in channels ; the motion of rivers and canals ; and the re- sistance produced by the mutual impact of liquids and solids in motion. It is the peculiarity of this branch of hydrostatics, that, from various causes, the phenomena actually exhibited in nature or in the processes of art deviate so considerably from the results of theory, that the latter are of comparatively little use to the practical engineer. They also lose a great part of their charm for the general reader, from the impossibility of producing from the familiar objects, whether of nature or art, examples appo- sitely and' strikingly illustrative of the general truths derived from scientific reasoning. It must not, however, be supposed that the results of such investigations are false, or that the sci- CHAP. IX. HYDRAULICS. 131 ence itself, or the instruments by which it proceeds, are defec- tive. The difficulty here lies rather in the peculiar nature of the phenomena, and the number of disturbing causes which render them incapable of that accurate classification and gener- alization which is so successfully applied in almost every other department of physical science. The only really useful method of treating a branch of knowl- edge so circumstanced, is to accompany a very concise account of such general principles as are least inapplicable to practice, by proportionately copious details of the most accurate experi- ments which have been instituted, with a view to ascertain the actual circumstances of the various phenomena. Such details, however, would be wholly misplaced in the present treatise ; we shall, therefore, confine ourselves to a few observations on some of the most important and striking phenomena of hydraul- ics ; tracing their connection, where it is possible, with the various analogous effects in the other parts of the mechanics of solids and fluids. (100.) If a small hole be made in the side of a vessel which is filled with a liquid, the liquid will issue from it with a certain velocity. The force which thus puts the liquid in motion is that which, before the orifice was made, exerted a pressure on the surface of the matter which stopped the orifice. It is obvi- ous, that the moving force of the water which thus issues from the orifice must be adequate and proportional to the power which produces it. But this power, being the same which pro- duced the pressure upon the surface of the vessel, will be proportional to the depth of the orifice below the level of the liquid in the vessel (14.). Hence we may at once infer, that water will issue with more violence from an orifice at a greater depth below the surface, than from one at a less depth ; but it still remains to be determined what the exact proportion is be- tween the rapidity of efflux and the depth of the orifice. Let A B C D, Jig. 65., be a vessel with perpendicular sides, having a very small orifice O near the bottom. Let it be filled with water to a certain height, E F, above O. The pressure corresponding to the depth O E, will cause the water to flow from O with a certain velocity. Suppose this velocity to be 10 feet in a second ; and suppose that by this means a gallon of water is discharged from O in one minute, water being in the mean while supplied to the vessel in such a quantity as to maintain the level of the water in the vessel at E F. The pres- sure at O being therefore always the same, the velocity of efflux will be uniform. It is clear, that if water be now poured into the vessel, so as to fill it to a level higher than E F, the pres- sure at O being increased, the velocity of efflux at O will be also increased. Let it be required to determine how much 132 A TREATISE ON HYDROSTATICS. CHAP. IX, Fig. 65. A E higher than E F it will be necessary to fill the vessel, in order that the velocity with which the water is discharged at O shall be double the former velocity. The momentum or moving force communicated to the water discharged from the orifice in one minute would in this case be four times that which was com- municated to it in the former case ; for, since the rapidity with which the water is discharged, is double its former velocity, double the quantity of water will be put in motion in one minute ; out this double quantity is also moved with a double speed ; hence the entire moving force produced in a minute will be four times the moving force produced in the former case in the same time. If the same quantity of water only had been put in mo- tion with a double velocity, the moving force would be doubled ; but the quantity of water moved being doubled as well as its speed, the moving force is quadrupled. Hence it follows, that the power which produces this effect must have four times the energy of that which produced the effect in the first case ; but this power is the pressure produced at the orifice O, which is proportional to the depth of O below the surface. Hence it follows that to give a double velocity of discharge a fourfold depth is necessary. If the vessel A B C D be filled to the level E' F', so that E' O shall be four times E O, then the veloci- ty of discharge at O will be double the velocity when the level was at E F. By similar reasoning it may be concluded that, to obtain a threefold velocity, a ninefold depth is necessary; for a fourfold velocity, sixteen times the depth will be required, and so on : in fact, in whatever proportion the velocity of efHux is increas- ed, the quantity of liquid discharged in a given time must be also increased ; and, therefore, the pressure or the depth must not only be increased in proportion to the velocity, but also as many times more in proportion to the quantity discharged. Thus the depth of the orifice, below the surface, will always be CHAP. IX. TELOCITY OF EFFLUX. 133 in proportion to what, in mathematics, is called the square of the velocity of discharge. If in a vessel A B C D, Jig. 66., filled with a liquid, a small Fig. 66. to - ///' O hole, O, be made at one inch below the surface E F ; and an- other, O 7 , at 4 inches below it ; a third, O", at 9 inches ; a fourth, O"', at sixteen inches ; and a fifth, O"", at 25 inches ; the velocities of discharge at these several holes will be in the proportion of 1, 2, 3, 4, and 5. If the upper line in the follow- ing table express the several velocities of discharge, the lower one will express the corresponding depths of the orifices : Velocity. 1 1 2 4 3 9 4 le" 5 25~ 6 36 7 49 8 9 81 10 100 Depth. 64 It is impossible to contemplate the relation exhibited in this table without being struck by the remarkable coincidence which it exhibits with the relation between the height from which a body falls and the velocity acquired at the end of the fall.* To produce a two fold velocity, a four fold height is neces- sary. To produce a threefold velocity, a ninefold height is re- quired. For a fourfold velocity, a sixteenfold height is required ; and 30 on. Thus it appears, that if a body were allowed to fall from the surface F of the water in the vessel downwards to- wards C, and unobstructed by the fluid, it would, on arriving at 12 * Cab. Cyc. Mechanics, p. 66. 134 A TREATISE OX HYDROSTATICS. CHAP. IX. each of the orifices above described, have velocities proportional to those of the water discharged at the orifices respectively. Thus, whatever velocity it would have acquired on arriving at O, the first orifice, it would have double that velocity on arriv- ing at O, the second orifice, three times that velocity on arriving at the third, O", and so on. Now, it is evident that if the velo- city of efflux at any one of the orifices be equal to the velocity acquired by the body in falling from the surface F to that orifice, then the velocities acquired at each of the orifices will be equal to the velocities of discharge respectively. Thus, if the velocity acquired in falling from F to O be equal to the ve- locity of discharge at O, then the velocity acquired in falling from F to O' being double the former, will be equal to the velocity of discharge at O' ; and in like manner the velocity ac- quired at O" being three times the velocity at O, will be equal to the velocity of discharge at O". In order, therefore, to es- tablish the remarkable fact that the velocity with which a liquid spouts from an orifice in a vessel, is equal to the velocity which a body would acquire in falling unobstructed from the surface of the liquid to the depth of the orifice, it is only necessary to prove the truth of this principle in any one particular case. Now it is manifestly true, if the orifice be presented down- wards, and the column of fluid over it be of very small height ; for then this indefinitely small cdlumn will drop out of the ori- fice by the mere effect of its own weight, and therefore with the same velocity as any other falling body ; but as fluids trans- mit pressure equally in all directions, the same effect will be produced whatever be the direction of the orifice. Hence it is plain that the principle just expressed is true when the depth of the orifice below the surface is indefinitely small ; and since it is true in this case, it must, according to what has been al- ready explained, be also true in every other. (101.) From this theorem it follows, as a necessary conse- quence, that if the orifices from which the liquid is discharged be presented upwards, the jets of liquid which would escape from them would rise to a height equal to the level of the liquid in the vessel. Thus, in Jig. 67., if E F be the surface of the liquid, and O, O', O". O'", be four orifices at different depths, all opening directly upwards, the liquid will spout from each of them with the velocity which a body would acquire in falling from the level of the surface E F G to the orifices respectively, and consequently the liquid must rise to the same height before it loses the velocity with which it was discharged. Hence the jets severally issuing from the orifices will rise to the height F G. (102.) These important theorems must, however, be submit- ted to considerable modifications before they can be considered CHAP. IX. CONTRACTED VEIN. 135 Fi S . 67. D as applicable in practice. In the preceding investigation, we have considered the orifice to be indefinitely small, so that every point of it may be regarded as at the same depth below the surface ; we have also considered that the fluid in escaping from the orifice is subject to no resistance from friction or other causes ; and also that in its ascent in jets it is free from atmos- pheric resistance. In practice, however, all these causes pro- duce very sensible effects ; and the consequence is, that the actual phenomena vary very considerably from the results of theory. The velocity of efflux is, from the moment the orifice is opened, diminished by the friction of the liquid against the sides of the pipe or opening through which it passes. After it escapes, the resistance of the air produces a sensible effect upon the movement of the fluid particles. This resistance in- creases even more rapidly than the velocity, so that the jets which escape from the lower orifices are still more resisted in proportion than those from the higher, and consequently they do not rise even near the level of the fluid in the vessel. As the liquid is gradually discharged from the orifice, the mtents of the vessel descend, the various particles falling in ..nes nearly perpendicular; but when they approach near the orifice from which they are to escape, they begin to change their direction, and to tend toward the orifice, so that their mo- tion is in lines, converging towards the opening, and meeting at a point outside it. These effects will be produced whether the opening be in the bottom or in the side of the vessel. They 136 A TREATISE ON HYDROSTATICS. CHAP. IX. Fig. 68. may be rendered visible by using a glass vessel filled with water, in which filings or small fragments of solid substances are suspended, and which are carried along by the motion of the currents. If a vessel be allowed to empty itself by an orifice in the bottom, the surface of the liquid will gradually descend, main- taining its horizontal position; but, when it comes within a small distance, about half an inch, of the bottom, a slight de- pression or hollow will be observed in that part of the surface which is immediately over the orifice. This will increase until it assume the shape" of a cone or funnel, the centre or lowest point of which will be in the orifice, and the liquid will be ob- served flowing in lines directed to this centre. This effect will be better understood by referring to jig. 68., where the direction of the currents and the contracted vein are exhibited. As the particles of liquid in approaching the orifice move in directions converging to a point outside it, it is plain that the column of fluid which escapes from the vessel will be narrower or more contracted at the point towards which the motion of the liquid con- verges than it is either before it arrives at that point or after it has passed it. This contraction of the jet produced by the pe- culiar directions which the motions of the fluid particles take, was first noticed by New- ton, who gave it the name of the vena con- tracta or the contracted vein of fluid. The distance from the orifice at which the great- est contraction of the jet takes place depends, with certain limitations, on the magnitude of the orifice. If the orifice be circular and small, its distance is equal to half the diame- ter of the orifice, and the magnitude of the jet at its most contracted point bears to the magnitude of the orifice, according to New- ton, the proportion of 1000 to 1414, and ac- cording to, Bossut, the proportion of 1000 to 1600. It will be evident, upon very slight consideration, that if the liquid be suffered to escape by a cylindrical tube, the contrac- tion of the vein will be greatly diminished. In this case the proportion of the magnitude of the most contracted part to that of the bore of the tube is 1000 to 1200. As the same quantity of fluid which passes in any given time through the orifice must pass in the same time through the CHAP. IX. RATE OF EFFLUX. 137 narrower space of the contracted vein, it follows that it must pass through this place with a proportionally greater velocity. Its velocity, therefore, at the point called the contracted vein, is greater than at the orifice in the proportion 1414 to 1000, according to Newton's calculation. In applying the theorem which has been established respect- ing the equality of the velocity of the efflux to that of a body which has fallen from the surface to the orifice, it is the veloci- ty of the contracted vein which should be regarded, that being the point at which the pressure produces its greatest effects. (103.) In the preceding investigation we have supposed liquid to be supplied to the vessel as fast as it is discharged, so that the surface is maintained at the same height above the orifice. The pressure is therefore constant, and the velocity of efflux uniform. But if a vessel discharge its contents by an orifice in the lower part, then the surface will continually de- scend. The pressure at the orifice will be continually dimin- ished, and the square of the velocity of discharge, which is proportional to this pressure, will suifer a corresponding dimi- nution. Hence it appears that the velocity of discharge is continually less until the surface falls to the level of the orifice. It is not difficult to perceive, that an invariable proportion must subsist between the velocity of discharge and the velocity with which the surface of the liquid in the vessel falls. Sup- pose that the magnitude of the orifice is the hundredth part of the magnitude of the surface of the liquid, and that the rate of discharge at any moment is such that a cubic inch of the liquid would be discharged in one second : in that time a column of the liquid will pass through the orifice, whose base is equal to the orifice, and whose height is such that its entire magnitude will be a cubic inch. In the same time the level of the liquid in the vessel will fall through a space which would require a cubic inch of the liquid to fill. This space will be just as much less than the height of the former column, as the magnitude of the orifice is less than the magnitude of the surface of the liquid ; that is, in the instance assumed, the space through which the surface will descend in one second will be the hun- dredth part of the space through which the liquid projected from the orifice would move in a second, if its velocity were contin- ued uniform. By the same reasoning, it may be inferred generally, that the velocity with which the surface descends bears to the velocity of discharge the same ratio as the magnitude of the orifice bears to the magnitude of the surface. Since it has been already proved that the square of the velo- city of discharge is proportional to the depth of the orifice, it follows, from what has been just stated, that the square of the 138 A TREATISE ON HYDROSTATICS. CHAP. IX. velocity with which the surface descends is also proportional to the depth of the orifice. It is proved in mechanics, that when a body is projected upwards, commencing with a certain velocity, the square of its velocity diminishes in proportion t its distance from its point of greatest elevation. It therefor>. follows, that such a body is retarded as it approaches its great- est height, according to the same law as the velocity of the surface of a liquid in descending is retarded as it approaches the orifice at which it is discharged. Thus all the properties established in mechanics respecting bodies projected upwards and retarded by the force of gravity, may be applied to the descent of the surface of a vessel which is emptied by an aperture in any part below that surface. The initial velocity of the surface is easily found. The velocity of efflux at the orifice is that which would be acquired by a body falling from the surface to the orifice, and may be determined by the ordinary principles of mechanics.* This velocity, being diminished in the proportion of the magnitude of the surface of the liquid to the magnitude of the orifice, will give the initial velocity of the surface in its descent. The velocity at any other elevation may be calculated upon the principle that the squares of the velocities at any two elevations above the ori- fice are proportional to these elevations. It is proved in mechanics, that if a body be projected up- wards with a certain velocity, the height to which it will rise will be equal to half the space through which it would move in the same time with the velocity of projection continued uni- form. Hence, by analogy, we infer, that the time which the surface of a liquid takes to fall from any given elevation to the orifice, is equal to the time it would take to move through twice that elevation with the initial velocity continued uniform. NOAV as this initial velocity is known, the time which the surface would take to move through twice the elevation with it may bo computed ; and, therefore, the time which the surface takes to move from any given elevation to the orifice will be obtained. Hence it is "easy to infer, that the time in which a vessel will empty itself through a hole in the bottom is equal to the time it would take to discharge twice the quantity of fluid contained in the vessel, if the initial velocity were continued uniform. (104.) If a stream of liquid be impelled through a reservoir, in which the liquid is at rest, it is evident that it will drive be- fore it those parts of the liquid which impede its course ; but, independently of this, it will produce other motions in those parts of the liquid in the reservoir neer which it passes. Let us suppose a river to enter an extended lake at one extremity, * Cab. Cyc. Mechanics, chnp. vii. CHAP. IX. LATERAL MOTION. and to issue from it at the other ; the bed of the river being more shallow and contracted than the lake. If a hollow chan- nel or aqueduct were formed across the lake, equal in magni- tude and shape with the bed of the river, the water of the river would flow across the lake without producing any effect upon the waters of the lake, being separated from them by the chan- nel or aqueduct which we have supposed. If the surface of the river, flowing in the channel, coincide with the level of the sur- face of the lake, the channel or aqueduct will sustain no pres- sure or strain, or, more properly, the pressures which it will suffer on all sides will be equal ; the waters of the lake press- ing it upwards and inwards, with forces exactly equal to those by which the waters of the river press it downwards and out- wards. It is clear, therefore, that the channel has no effect in sustaining or neutralizing any hydrostatical pressure, and that its removal will not call into action any force of this kind. Suppose it then removed, and the waters of the lake themselves to form the channel through which the waters of the river flow. Shall we conclude, that in this case the waters of the river will continue to flow through those of the lake, the latter remaining quiescent, and the two masses of liquid being unmingled ? It has been found by experiment that such will not be the effect. The current of the fiver flowing in contact with the waters of the lake will impart to them a share of its own motion ; and these again will communicate the motion to those beyond them, until at length the waters of the lake, to a great extent, on each side of the course of the river, are put in motion. The following experiment was instituted by Venturi to illus- trate the principle of the lateral propagation of motion by a liquid. A horizontal pipe A B, jig. 69., was introduced into a Fig. 69. vessel C D E F, which was previously filled with water to the level G H. Opposite to the mouth of A B, and at a short dis- tance from it, was placed a small rectangular canal K L M N of A TREATISE ON HYDROSTATICS. CHAP. thin metal, with a curved bottom, perpendicular sides, and open at the top. This canal was so placed as to be capable of con- ducting a stream, flowing in at N K, over the edge of the vessel F and discharging it at M L. The pipe A B communicates with a reservoir R, kept constantly filled to the^ame height, so that the water issues from B continually, with the same rapidity Ihe current flowing from B passes through the water in the reservoir C D E F in the space between B and K, and enters the curved canal K L : it is forced up this by the velocity with which it issues from B, and flows out at L. By this arranffe- |nt a current, equal in magnitude to the pipe A B, is contin- ually flowing through the water in the reservoir C D E F in the space between B and N K. n ,i r been found b y ex P e rmient to be, that the who e of the liquid m the vessel C D E F, which is above the level B K is carried with the liquid which passes from the tube A B up the canal K L, and discharged at L. The surface G H gradually falls, and is soon reduced to the level B K, where it remains. The lateral communication of motion by fluids, here describ- ed is not confined to the case where the fluid to which the toon is imparted is of the same kind as that from which the motion ls received. A current of water passing through the 21*5 g V t0 he ^mediately contiguous to it a motion in Same / I ; rect ; on - jf a feather, or any other light body, be ovefthe'sn f 7 f nr fine , si]ken thread > and ^Id immediately e aapid i i a / api sream ' ut not in c ntac t *ith it, be found to be driven along in the direction of the stream bksnf Same n Th ner i S U W Uld happen Were * expose d to a blast of air. this effect, as might naturally be expected, is greatly increased when the velocity of the stream is very con! mderable. A cascade, which falls from a great elevation, pro- duces a current of air, the force of which can scarcely be whh- tood Venturi, who investigated and explained this phenome- non, observed a remarkable example of it, in a waterfall, which R Che Mel0 *> n ^ *i ^ La ' 1' re PJ? se J t the surfac e of- a river, N R and O S K S pe /i 3 b ^ lks ; SUppose the current to run in ^e of theb IT ' ? - 1Ct 5 A be an dbstade P r J ectin g ^om one the banks and impeding its course : the water will thus be e e theD e omtr e ^ g Gr ab V f B A ' and t0 discha ^e itself round the point A with increased velocity. The liquid i n the space CHAP. IX. EDDIES OF RIVERS. 141 B D C A being protected from the force of the descending stream by the obstacle B A, will at first be quiescent ; but the rapid flow of the water from the point A will communicate mo- tion to the lateral particles in the space C, and will convey them forward. The particles at E will then become slightly depress- ed, and the remoter particles towards D will have a tendency to fill the depression ; the current from A to C will, however, continue to carry them off, and a hollow will continue in the centre of the space A C D. The water between A and C is thus acted upon by two forces ; viz. the force communicated to it laterally, and tending to carry it down the stream in the direction A C, and the tendency which it has by its gravity to fill toAvards the centre of the cavity E. These two forces are precisely analogous to those by which a body is caused to move in a circular orbit, viz. a projectile force at right angles to the radius of the circle, and an attractive force continually solicit- ing the body to the centre. The water by this means is whirled round in an eddy, which is continually maintained by the acr tion of the stream in rushing from the point A. A sudden contraction of the bed of the river, followed imme- diately by a widening of the banks, as at N O P Q, will produce 'he same effect as two obstacles, such as B A, placed on oppo- site sides of the river ; consequently, under such circumstances, eddies will be observed on both sides at P and Q, immediately after passing the contraction. The stream of water shooting from A will strike the opposite bank at G H, and will be reflected from it in the direction H S ; the effect will, therefore, be the same at H as if the current encountered an obstacle there similar to B A, and, consequent- ly, eddies will be repeated in the space near R. It follows, therefore, that a sudden contraction of the banks, succeeded by a widening, will not only produce eddies immediately adjacent to the contraction, but that these eddies will be continued for a certain space afterwards. Similar effects may be expected by inequalities in the bottom of a river ; but, instead of taking place as just described, in a direction parallel to the surface, they will be produced in a plane 142 A TREATISE O.\ HYDROSTATICS. CHAP. IX. perpendicular to it, and the eddies will be presented upwards like the curling on the crest of a wave. Let Jig. 71. represent the section of a river perpendicular to Ti' its surface, A K exhibiting the shape of the bottom. In the case of a gentle slope, such as ABC, let us first suppose the space A B C to be filled with water, which is quiescent, the stream of the river running upon its surface A C ; the motion of the river will be gradually communicated to the water below A C, so as to give it a motion from A towards C. The shape of the bottom ABC will cause it to be projected from C to- wards the surface, forming a vertical eddy which will frequently terminate in a curling wave. In this case B C acts in the same manner upwards as B A, in Jig. 70., did laterally. If the ex- tremities of the hollow be abrupt, as at D G, subaqueous eddies will be produced. All these effects may be exhibited experimentally, by causing water to flow through artificial channels with glass sides. It will be evident from all that has been stated, that irregu- larities in the bottom and sides of rivers must necessarily retard their currents ; the force which would otherwise carry the stream directly down its channel is here wasted in producing lateral and oblique motions. All the moving force of the water in an eddy must be originally derived from the precipitous de- scent of the stream, which is therefore robbed of all the power requisite for the maintenance of such effects. We, therefore, perceive why the velocity of rivers, in their descent to the ocean, is always much less than that which would be calculated upon mechanical principles, supposing them to flow in a perfectly even and regular channel. In fact, the effects of such inequal- ities partake, in a certain degree, of the nature of friction ; they are, as it were, friction on a large scale. It is also evident why rivers, the beds of which descend towards the sea with equal acclivities, yet may have very different velocities, the velocity being greater the more regular the channel. (105.) When a liquid in motion strikes a solid surface at rest, or when a solid surface in motion strikes a liquid at rest, the quiescent body deprives the moving one of a quantity of force equal to that which it receives ;* and this loss of force is said * Cab. Cyc. Mechanics, chap. lv CHAP. IX. RESISTANCE OF FLUIDS. 143 to arise from the resistance which the quiescent body offers to the body in motion. When a solid body is immersed in a liquid, the force necessary to move it with any given velocity is found to be greater than that which would be necessary to move it with the same velocity when not immersed : this excess of force arises Trom the resistance of the liquid to the solid, and it is a problem of great practical importance to establish the rules or theorems by which this resistance may be estimated, and by which its laws may be exhibited. The same rules precisely will be applicable to solid bodies, such as the float-boards of a water-wheel when struck by the water of a mill course. In the one case the force to be measured is called the resistance of the liquid, and in the other it is denominated the percussion of the liquid. In these, as in almost every other part of hydraulics, theory lends but feeble aid to practice. There are many effects attending the operation of the liquid, whether in resisting or communicating motion, which, from their nature, elude the grasp of theory, and appear to be incapable of being represent- ed by mathematical or arithmetical language or symbols : never- theless, there are a few general principles which may be re- garded as approximating within a certain degree of practical results, and sufficiently near them to impress upon the memory a general notion of the phenomena, if not to be useful in the actual calculations of the engineer. Indeed, the first steps in generalizing this class of effects are almost as obvious to the most common experience as their exact determination is difficult. For example, if a flat board of a foot square be moved in water with a certain velocity, so that its flat side shall be presented in the direction of its motion, a certain resistance is felt, and a certain force is necessary to keep it in motion ; but if the same board be moved in the direction of its edge, it is well known that a much less force will be found necessary to give it the same velocity as in the former case. When the boatman plies his oar, he keeps the flat part of the blade presented in the direction in which he pulls, at that part of the stroke at which the greatest effect is produced in impell- ing the boat ; but when he wishes to extricate the oar from the liquid, preparatory to another impulse, he turns the blade edge- ways towards the water, and the resistance, which before was powerful, becomes immediately insignificant. When the wings of a bird are spread for flight, the flat and broad part of their plumage is presented downwards, to give them support from the resistance of the air in that direction, while their edge is pre- sented forwards, to enable them to cleave the air with as little resistance as possible in that direction. These and like effects, which constantly fall under our ob- servation, indicate the general fact, that the broader the surface 144 A TP -ATISE ON HYDROSTATICS. CHAP. IX. presented in the direction of the motion, the greater will be the resistance. But it requires more accurate and philosophic examination, to decide whether the increase of resistance be always in the exact proportion of the increase of surface pre- sented towards the motion : both theory and experience decide this question in the affirmative. The resistance arises from the force which the moving body must expend in displacing the particles of fluid which lie in its way : all other things being the same, this force must obviously be proportional to the num- ber of particles to be displaced ; this number will evidently be determined by the magnitude of the surface. A flat board of the magnitude of one square foot displaces a certain quantity of liquid by its motion ; one of two square feet will displace twice that quantity ; and, therefore, will require twice the force to keep it in motion ; or, in other words, will suffer twice the resistance ; and the same will be true whatever be the magni- tude of the surface. We, therefore, conclude generally that "When a flat surface is moved perpendicularly against a fluid, the resistance which it suffers will increase or decrease in the -same proportion as the magnitude of the surface is in- creased or decreased." (106.) If, instead of being presented perpendicularly to the liquid, the surface be presented obliquely with respect to the direction of its motion, the resistance will be diminished on two accounts : first, The quantity of liquid displaced will be less ; and, secondly, The action of the surface in displacing it will have the mechanical advantage of an inclined plane, or wedge, so that, instead of driving the liquid forward, it will in some measure push it aside. Let A B,Jlg. 72., be the surface of a solid moving in a liquid Fig. 72. in the direction expressed by the arrow. It is evident that the quantity of liquid displaced by the surface A B is the same as that which would be displaced by the smaller surface A C mov- ing perpendicularly against the liquid. Let us suppose that A C is half the magnitude of A B ; it follows, therefore, that the quantity of liquid which would be displaced by A C is half CHAP. IX. RESISTANCE OF FLUIDS. 14& that which would be displaced by A B, if it moved perpendicu- larly against the liquid. Hence it may be inferred, that by reason of the oblique position of A B^ the quantity of liquid which it displaces is reduced one half. Again, this reduced quantity of liquid which is so displaced,' is not driven perpendicularly before the moving surface. The surface A B acts on each particle of the liquid as a wedge acts in cleaving a piece of timber ; and, by the principles of mechan- ics, it is established that a power acting against A C will over come a force on the face of the wedge greater than its own amount in the proportion of A B to A C ;* or, in the case already supposed, that of two to one. We, therefore, con- clude, that in the oblique position of the surface A B, com- pared with the same surface moving perpendicularly against the liquid, only half the quantity of liquid is displaced, and that quantity only offers half the resistance which the same quantity would offer to perpendicular motion of the surface A B. The conclusion is, that by the obliquity of the surface A B the resistance is reduced to one fourth of its amount. In like manner, if A C were a third of A B, the resistance would be reduced to one ninth of its amount. If A C were a fourth of A B, the resistance would be reduced to a sixteenth of its amount, and so on ; the resistance being always diminished in the proportion of the square of the back of the wedge, as compared with its face. In trigonometry, the number which expresses the proportion of A C to A B is called the sine of the angle at B ; and thus the resistance to a surface moving in a liquid is said to increase or decrease in proportion to the square of the sine of the angle which the direction of the surface makes with the direction in which it is moved. The resistance here determined is that which acts perpen- dicularly on the surface A B. The portion of it which acts in tiie direction of the motion may be found by the principles for the resolution of force. Let D E express the resistance per- pendicular to A B, and let E F be drawn perpendicular to the direction of the motion, D F will express that part of the resist- ance which acts against the motion. The proportion of D F to D E is the same as that of -A C to A B.f (107.) We have hitherto omitted the consideration of the effect produced upon the resistance of the fluid by any change in the velocity with which it strikes the solid, or with which the solid strikes it. If a flat board be moved perpendicularly against a liquid, it is quite evident that the greater the velocity with which it is moved, the greater will be the resistance which the liquid will offer to it ; and this effect may in part be ac- * Cab. Cyc. Mechanics, chap. xvi. t Ibid. chap. v. 13 *46 A TREATISE ON HYDROSTATICS. CHAP. IX. counted for very obviously. It has been already explained, that the resistance arises from the force which the solid loses in giving motion to the liquid which stands in its way. It is clear that the more rapid the motion of the solid is, the greater will be the velocity which it will communicate to the fluid, and, therefore, the greater the force with which the fluid will be propelled ; and, by consequence, the greater will be the resist- ance opposed to the solid. But the increase of resistance is not merely in proportion to the velocity. Each particle of the fluid which the solid strikes during one second of time, if it moves with a double speed, receives from it a double force, and therefore offers to it a double resistance. But, besides this the circumstance of the body moving with a double speed causes it to strike twice as many particles in a second ; each particle as just stated, being struck with a double force. It is, therefore apparent that a double speed will cause the body to impart a fourfold force to the liquid which it puts in motion. It will put double the quantity of liquid in motion with a double velocity it follows, therefore, that it will be opposed by a fourfold resistance. By like reasoning, it will be easy to prove that a threefold velocity will produce a ninefold resistance; that a fourfold velocity will cause the resistance to be increased sixteen times, and so on ; the resistance varying in proportion to the square of the velocity. (108.) In the preceding investigation we have explained how the quantity of resistance is varied by any change in the mag- nitude or figure of the solid, or in the velocity with which it is moved. But, in order to render these conclusions useful it will be necessary to show the actual amount of the resistance in some one particular case. If this be known, its amount in all other cases may be calculated by the theorems just explained, llius, if the absolute resistance produced by any particular velocity be known, the resistance which would be produced by any other velocity may be computed from the established prin- the vel ' resis tance varies in proportion to the square of Experiments were instituted by Bossut, with a view to de- ,ennme the absolute resistance sustained by a solid moved in a liquid. By these experiments it was found that if a flat board were moved perpendicularly against a liquid, it would suffer a resistance equal to the weight of a column of the fluid, the base JSfSs^iSff t0 l h \ board ' and the hei ght of which is equal to the height from which a body should fall, in order to acquire the velocity with which the board is moved against the liquid. It follows from this, that the resistance of different fluids Twill De different according to their specific gravities, for the heavier CHAP. IX. FORM OF BIRDS AND FISHES. 147 a column of the same height is, the greater in the same pro- portion will the resistance be. Thus the resistance of sea water is greater, in a slight degree, than that of fresh water ; and the resistance of mercury is many times greater than either. When a jet of liquid strikes a solid at rest, it is found that the absolute resistance is different, but that its variation depends upon the same laws. In this case the force sustained by the solid is equal to the weight of a column of the liquid, whose height is double the height from which a body should fall to acquire the velocity. Hence it follows, that a vein of liquid striking a solid with a certain velocity produces an effect amounting to double that which would be produced by moving the solid with the same velocity in a similar liquid at rest. (109.) The theorems just established constitute the only results in hydraulics which deserve the name of general princi- ples, and which approximate within a limit sufficiently close to the actual phenomena to be of any practical utility. But, even in the application of these, there are several circumstances which ought to be taken into consideration, in restricting and modifying the conclusions deduced from them. They are, how- over, attended with several consequences which experience fully verifies, and which are of considerable importance in the practical applications of the science. f The effect produced on the resistance of a liquid by the obli- quity of the surface of the solid which moves through it, forms a prominent element in the problem for determining, under dif- ferent conditions, the shape of the solid. This consideration must materially affect the shape to be given to vessels of all denominations, whether for navigating the seas, or for inland transport by canals and rivers. It is this principle which causes the length of the vessel to be presented in the direction of the motion, and which gives a sharp prow, where circumstances admit it, the advantage over a round one. The boats which ply on rivers, or other sheets of water not liable to much agita- tion, nor intended to carry considerable freight, are so con- structed, that every part of their bottom which encounters the liquid moves against it at an extremely oblique angle. The boats for the conveyance of persons to short distances on the Thames, and other rivers, afford obvious examples of this. Art in these cases only imitates nature. Animals, to whose existence or enjoyment a power of easy and rapid motion in fluids is necessary, have been created in a form which, with a due regard to their other functions, is the best adapted for this end. Birds, and especially those of rapid flight, are examples of this. The neck and breast tapering from before,- and in- creasing by slow degrees towards the thicker part of the body, A TREATISE ON HYDROSTATICS. CHAP. IX. | cause them to encounter the air with a degree of obliquity greatly diminishing the resistance, slight as it is, which that attenuated fluid opposes to their flight; but we find a more striking illustration of the same principle in the forms of fishes of every denomination. The reader must not, however be tempted to indulge in the supposition that nature has in these cases solved the celebrated problem, to find the form of the solid of least resistance. The solid contemplated in that prob- lem has no other function to discharge except to oppose the resistance of the fluid, and the question is one of a purely ab- stract nature, viz. What shape shall be given to ab^dy, so that while its volume and surface continue to be of the same mag- mtude, it will suffer the least possible resistance in moving through a fluid ? It will be apparent that many conditions must enter into the construction of an animal, corresponding to its various properties and functions, independently of those in vir- tue of which it impels itself through the deep, or cleaves the air. I he detection of verifications of the results of theory in e works of nature is in general so seductive, that writers are sometimes tempted to overlook the inevitable causes of discrep- ancy m their eagerness to seize upon analogies of this kind Without, however, seeking in natural objects the exact solution of a mathematical problem unencumbered by various conditions which nature has to fulfil, the examples which have been pro- duced give abundant manifestation of design in the works of liS^ T \ W ^ Ch i 8 ' r u^ t0 be ' the chief source of the delight which attends such illustrations. (110.) i The resistance arising from the quantity of fluid dis- placed by the moving body may, therefore, be always greatly diminished and m some cases rendered almost insignificant bv a proper adaptation of its shape.* The accumulated resistance arising from the increased speed of motion is, however, an im- pediment which no art can remove. The fact that the resist- ance of a liquid to a body moving in it increases in a prodi- giousjy rapid proportion in respect of the increase of velocity, s one which sets an impassable limit to the expedition of transport by vessels moving on the surface of water This property has long been well known ; but it has received greatly increased importance from the recent improvements in the ap- plication of steam. If a certain power be required to impel a vessel at the rate of five miles an hour, it might at first view be ought that double that power would cause it to move at the the hydrostauc pressure of the higher column at the anterior exSityS CHAP. IX. RAIL ROADS AND CANALS. 149 rate of ten miles an hour ; but from what has been already proved, it will be perceived that four times the power is neces- sary to produce this effect. In like manner, to cause the vessel to move at the rate of fifteen miles an hour, or to give it three times its original speed, nine times the original power is necessary. Thus it follows, that the expenditure of the moving principle, whether it be the power of a steam engine or the strength of animals, increases in a much larger ratio than the increase of useful effect. If a boat on a canal be carried three miles an hour by the strength of two horses, to carry it six miles an hour would require four times that number, or eight horses. Thus double the work would be executed at four times the expense. (111.) These considerations place in a conspicuous point of view the advantages which transport by steam engines on rail roads possesses over the means of carriage famished by in- land navigation. The moving power has in each case to over- come the inertia of the load ; but the resistance on the road, instead of increasing as in the canal in a faster proportion than the velocity, does not increase at all. The friction of a carriage on a rail road, moving sixty miles an hour, would not be greater than if it moved but one mile an hour, while the resistance in a river or canal, were such a motion possible, would be multiplied 3600 times. In propelling a carriage on a level rail road, the expenditure of power will not be in a greater ratio than that of the increase of speed, and therefore the cost will maintain a proportion with the useful effect, whereas in moving a boat on a canal or river, every increase of speed, or of useful effect, en- tails an enormously increased consumption of the moving prin- ciple. But we have here supposed that the same means may be re- sorted to for propelling boats on a canal, and carriages on a rail road. It does not, however, appear hitherto that this is prac- ticable. Impediments to the use of steam on canals have hith- erto, except in rare instances, impeded its application on them; and Ave are forced to resort to animal power to propel the boats. We have here another immense disadvantage to encounter. The expenditure of animal strength takes place in a far greater proportion than the increase of speed. Thus, if a horse of a certain strength is barely able to transport a given load ten miles a day for a continuance, two horses of the same strength will be altogether insufficient to transport the same load twenty miles a-day. To accomplish that, a much greater number of similar horses would be requisite. If a still greater speed be attempted,' the number 'of horses necessary to accomplish it would be increased in a prodigiously rapid proportion. This will be evident if the extreme case be" considered, viz. that 150 A TREATISE ON HYDROSTATICS. CHAP. X. there is a limit of speed which the horses under no circum- stances can exceed.* The astonishment which has been excited in the public mind, by the extraordinary results recently exhibited in propelling heavy carriages by steam engines on rail roads, will subside if these circumstances be duly considered. The moving power and the resistance are naturally compared with other moving powers and resistances to which our minds have been familiar. To the power of a steam engine there is, in fact, no practical limit ; the size of the machine and the strength of the materials excepted. This is compared with agents to whose powers na- ture has not only imposed a limit, but a narrow one. The strength of animals is circumscribed, and their power of speed still more so. Again, the resistance arising from friction on a road may be diminished by art without any assignable limit, nor does it sustain the least increase, to whatever extent the speed of the motion may be augmented ; on the contrary, the motion of a vessel through a canal has to encounter a resistance by increase of speed, which soon attains an amount which would defy even the force of steam itself, were it applicable, to overcome it with any useful effect. CHAP. X. OF HYDRAULIC MACHINES. WATER WHEELS. - OVERSHOT. -- UNDERSHOJ. -- BREAST. BARKER'S MILL. ARCHIMEDES' SCREW. SLUICE GOVERNOR. CHAIN PUMP. (112.) THE term " hydraulic machinery," in its general sense, is understood to comprise all machines in which the -force of water is used as a prime mover, and also those in which 'other powers are applied for the purpose of raising or impelling er itself. Many of these machines, however, owe their ef- ficacy to principles and properties, the investigation of which properly belongs to departments of physical science foreign to "that which forms the subject of the present treatise. We shall, therefore, here confine our observations to such machines, or ,t>arts of machines, as admit of explanation by the principles of a ydrostatical science, combined with the ordinary principles o/ 'mechanics. The most usual way in which water is applied as a ^-^.fc.. * Cab. Cyc. Mechanics, cliap. x*, CHAP. X. OVERSHOT WHEEL. 151 prime mover to machinery, is by causing it to act either by its impulse in motion, or by its weight on the circumference of a wheel, in a direction at right angles to the spokes or radii, and thus to make the wheel revolve and communicate motion to its axis. This motion is transmitted in the usual way, by wheel- work and other contrivances, to the machinery which it is re- quired to work. Water wheels vary in their construction, according to the way in which the force of the liquid is intended to be applied to them. The principal forms which they assume are denom- inated overshot, undershot, and breast wheels. Overshot Wheel. (114.) The most common form of the overshot wheel is rep- resented in Jig. 73. On the rim of the wheel a number of cav- Fig. 73. ities, called buckets, are constructed, which in the figure are exposed to view, by supposing one of the sides which enclose them to be removed. What may be called the mouths of the buckets are all presented in one direction in going round the wheel, and by this means the buckets on one side will always have their mouths presented upwards or nearly so, while those on the other side will have their mouths presented downwards. It follows, therefore, that the buckets on the side B are in such a position that all of them are capable of containing some water, and some of them of being kept filled, while those on the side D are incapable of retaining any liquid. Let us sup- pose a stream to flow from F into the bucket marked 1. The weight of the water which fills this bucket will cause the wheel to turn in the direction 1^23, &c., and the other buckets will successively come under the stream, and become filled ; and this 152 A TREATISE ON HYDROSTATICS. CHAP. X. continues until the range of buckets from A to B are filled. As the buckets approach B they begin slightly to lose the liquid by their change of position, and after passing B this loss is rapid, so that before they arrive at the lowest point C, they are empty, and in that state they ascend round C D to A, where they are again replenished. It appears, therefore, that there is a weight of water continually acting on one side of the wheel, distributed in the buckets from 3 to 8, and that this weight is not neutralized by any corresponding weight on the opposite side. The wheel is, therefore, kept continually revolving in the direction A B C D. A reference to the properties of the lever, or the wheel and axle, as explained in Mechanics,* will make it apparent that the water contained in the several buck- ets is not equally efficacious in giving motion to the wheel. The weight of the water which fills the bucket 1 has the same effect in turning the wheel as an equal weight acting down- wards at a would have in turning the lever D B on the centre O. In like manner the weight of the water in bucket 2 has the same effect in turning the wheel, as a similar weight acting at b would have in turning the same lever D B. Now if the weights be the same, the efficacy to turn the lever will be in- creased in the proportion of O a to O b. Although the contents of the bucket in passing from 1 to 2 may experience a slight diminution, yet this loss is perfectly insignificant compared with the advantage of the increased leverage O 6. In like manner the leverage continues to increase ; that of the bucket 3 being O c, of 4 being O d, and finally, the bucket 5 having the leverage of the whole radius. After passing below B the leverage begins, on the contrary, to decrease, and continues to decrease until it arrives at C. From these circumstances it is obvious that the efficacy of the wheel will, in a great degree, depend on giving the buckets such a form as will cause them to lose as little water as possible until they pass the point B, where they have the greatest mechanical advantage. As they approach C the circumstance of discharging their contents be- comes of less importance because of the decreasing leverage. Millwrights have expended much ingenuity in contriving forms for the buckets, calculated to retain the water in those parts of the circumference where its action is most efficacious, and to discharge it with facility and expedition. Details on this subject would, however, be misplaced in the present treatise. Numerous experiments have been made to determine the most advantageous size of overshot wheels, and the best veloci- ty at which they can be worked. Most authors are of opinion, * Cab. Cyc. Mechanics, chni>. xiv CHAP. X. BEST VELOCITY. 153 that the diameter of an overshot wheel should never exceed the height of the fall of water by which it is impelled ; but that it should be as nearly equal to this as is consistent with giving the water sufficient velocity on entering, the buckets. Some, however, think, that the diameter might with advantage even exceed the height of the fall. With respect to the velocity of the wheel, some maintain that the slower the motion the greater will be the effect ; while others hold that there is a certain velocity (of very small amount) which will give a maximum ef- fect, and assert that those who maintain the contrary opinion have not carried their experiments to a sufficient extent to es- tablish the principle. It requires little reflection to be able to perceive how the useful effect may be greatest when the wheel moves with a certain velocity, any increase or decrease of that velocity di- minishing the actual quantity of work done in a given time. The power of the wheel being the same, the velocity with which it moves will be less in proportion as its load is increased. Supposo a water wheel works a flour mill, in which, at different times, it has to move a different number of millstones, it is evi- dent that the greater the number it has to move, the slower will be the motion which it will, impart to each ; and, therefore, although the quantity of flour produced will be increased by increasing the number of stones, yet the quantity which each stone will produce will be diminished by the increased slowness of the motion. There is a certain velocity at which these ef- fects mutually neutralize each other, and at this velocity the useful effect is at its maximum. Suppose the power of the wheel is expended on moving the millstones without being fed with corn ; the velocity of the wheel will then evidently be greater than if the resistance of the grain were opposed to the power. The useful effect will, however, in this case be nothing ; the whole power being ex- pended on moving the unloaded machine. Let one pair of stones be now called into action ; the velocity will be immedi- ately diminished by the increased resistance, and the useful effect will be estimated by the quantity of flour produced by the single pair of stones in a given time, as one day. Let two pair of stones be now called into action ; the resistance being further increased, the velocity will sustain a corresponding diminution. The first pair of stones will produce a less quan- tity of flour in a day than they did before the second pair were called into action ; but this will be more than compensated for by the quantity of flour produced by the second pair, which before were unemployed. The same reason will be applicable if a third pair be called into action, and so on. Now it is evi- dent that the wheel may be required to move so many pairs of 154 A TREATISE ON HYDROSTATICS. CHAP. X. stones, that its whole power will be necessary barely to give them motion, none remaining to overcome the additional resist- ance offered by the corn with which they are fed. This resist- ance will then stop all motion, and no work will be done or useful effect produced. It is evident that as the machine gradually approaches this limiting state, the useful effect will diminish by degrees before it altogether vanishes ; and the point at which it commences so to diminish is that at which the machine has the velocity which produces the greatest use- ful effect. " Experience," says Smeaton, " proves that the velocity of three feet in a second is applicable to the highest overshot wheels as well as to the lowest ; and all other parts of the work, being properly adapted thereto, will produce very nearly the greatest effect possible. However, this also is certain from experience, that high wheels may deviate farther from this rule before they will lose their power by a given aliquot part of the whole, than low ones can be admitted to do. For a wheel of 24 feet high may move at the rate of 6 feet per second, with- out losing any considerable part of its power ; and, on the other hand, I have seen a wheel of 33 feet high, that has moved very steadily and well, with a velocity but little exceeding 2 feet per second." Undershot Wheel. (115.) An undershot water wheel is an ordinary wheel turn- ing on an axis, furnished with a number of flat boards placed at equal distances on its rim, and projecting from it in direc- tions diverging from its centre, and having their flat faces at right angles to the plane of the wheel. These boards are called float boards ; and such a wheel, of the most common construc- 'ion, is represented in Jig. 74. The edge of the wheel, at its Fig. 74. lowest point, is immersed in a stream called a mill-course, and CHAP. X. UNDERSHOT AND BREAST WHEELS. 155 the float boards are intended to receive the impulse of the water as it passes under the wheel. The wheel is thereby caused to revolve in the direction of the stream, with a force depending on the quantity and velocity of the water, and the number, form and position of the float boards. The mill-course is usually an artificial canal, carried from the river or other reservoir from which the wntor is supplied, and conducted, after it has passed the wheel, to some con- venient point, where it may be again discharged into the bed of the river. In order that the water may strike the wheel with the greatest possible force, no more inclination is given to the mill-course A B,/g". 75., than is sufficient to give motion Fig. 75. Ulllllllllllllllllllllll uiuuiiuuniiimii to the water in it, until it comes within a short distance of the wheel. There a fall B F is constructed, and the stream having acquired a velocity corresponding to the height of this fall rushes against the float boards, and puts the wheel in motion. The mill-course then has a further fall M V N to carry off the water, which would otherwise impede the advancing float board. It is found by experience advantageous that the float boards should not precisely converge to the centre of the wheel, but that instead of being perpendicular to the rim of the wheel they should present an acute angle towards the current. By this means force is gained, not merely by the impulse of the water, but in some degree by its weight. The experiments instituted to determine the best velocity of the wheel', and the best number of float boards, under given circumstances, do not appear to have led to any principles, suf- ficiently general and certain, to entitle them to notice here. Breast Wheel. (116.) A breast wheel partakes of the nature of the overshot and undershot wheels. Like the latter, it is furnished with float boards instead of buckets ; but, like the former, it is work- 156 A TREATISE ON HYDROSTATICS. CHAP. X. ed more by the weight of water than by its impulse. The water is delivered at a point M, Jig. 76., nearly on a level with the axis of the wheel, and the mill-course below that point is Fig. 76. accommodated to the shape of the wheel, so that the float boards turn nearly in contact with it. The spaces enclosed by the float boards and the mill-course thus serve the same pur- pose as buckets in the overshot wheel, and the water enclosed in them turns the wheel by its weight. Barker's Mill. (117.) The machine known by this name consists of a hollow upright tube of metal, A B )t %. 77., terminating in the upper end B in a funnel, and attached to an upright axis C D, on which a toothed wheel is fixed, from which motion may be communicated to any machinery. The hollow tube B A com- municates with a cross tube E F closed at the ends, and the upright tube A is closed at the lower end, and terminates in a point or pivot, which turns freely in a hollow cone adapted to receive it. The whole is enclosed in a frame and immersed in a reservoir. Let water be supposed to be supplied to the fun- nel B, from a pipe G, and let the upright and cross tubes be thus filled. The water standing at the level B, a pressure is excited on every part of the cross tube E F equal to the weight of a column of water whose height is A B. But since this pressure acts equally in every possible direction on the tube ii. F, it will keep the tube in equilibrium, and no motion will CHAP. X. BARKER'S MILL. 157 ensue. Let two holes be now pierced in opposite sides of the tube E F, and near the extremities, and let the water be sup- plied at G as fast as it flows from these holes, so that the level Fig. 77. B will be maintained. Those parts of the tube E F, from which the water issues, will thus be relieved from the pressure above mentioned, but the corresponding points on the opposite sides of the tube will still continue to sustain the same pressures. These pressures are, therefore, no longer counterbalanced, since they both tend to make the tube revolve in the same di- rection. The arms E F will, therefore, immediately commence to revolve, and will turn the upright tube round on the pivot, giving motion at the same time to the toothed wheel above. This motion may be communicated to any kind of machinery. In some elementary works on hydraulics, the operation of this machine is explained on totally wrong principles. The motion is said to be produced by the resistance of the air to the issuing water. It would be easy to refute this absurd no- tion upon theoretical principles ; but perhaps the argument 'most intelligible to those who give such an explanation, is to bid them try a model of Barker's mill in vacuo. The motion is produced on a principle precisely similar to that which causes a gun to recoil when discharged. Archimedes' Screw. (118.) This instrument is said to have been invented by Ar 14 158 A TREATISE ON HYDROSTATICS. CHAP. X. r ^ > . chimedes when in Egypt, for the purpose of enabling the in- habitants to clear the low grounds from the stagnant water which remained after the periodical overflowings of the Nile. It was also used instead of a pump to clear water from the holds of vessels ; and Athenseus states that the memory of Ar- chimedes was venerated by sailors for the benefit thus conferred on them. The instrument may be presented under different forms, which, however, all agree in principle. Suppose a leaden tube to be bent into a spiral form like a corkscrew, or the worm of a still, as represented in Jig. 78. Suppose A the extremity to be Pig. 78. open and presented upwards, and suppose the screw to be placed in an inclined position, as represented in the figure. From its peculiar form and position it is evident that commenc- ing at A, the screw will descend until we arrive at a certain point, B ; in proceeding from B to C it will ascend. Thus B is a point so situate that the parts of the screw on both sides of it are more elevated than it is, and therefore if any body were placed in the tube at B, it could not move in either direction B A or B C, without ascending. Again, the point C is so situ- ate, that the tube on each side of it descends ; and as we pro- ceed, we find another point, D, which like B, is so placed that the tube on each side of it ascends, and, therefore, that a body placed at D in the tube could not move in either direction without ascending. In like manner there are a series of points, F, H, &c., continued along the whole length of the spiral, which are circumstanced like B and D ; and another series, E, G, &c., which are circumstanced like C. Let us now suppose a ball, less in size than the bore of the tube, so as to be capable of moving freely in it, to be dropped in CHAP. x. ARCHIMEDES' SCREW. , 159 at A. As the tube descends from A to B the ball will descend by its weight, as it would down an inclined plane, until it ar- rive at B. The force Avhich it acquires in its descent will carry it beyond this point, and will cause it to ascend to a small dis- tance towards C ; but its weight soon destroys the force which it has retained by its inertia, and after a few oscillations on each side of B, its motion will altogether be destroyed by the friction of the tube, and it will remain at rest at that point. Now suppose the ball for a moment to be fastened or attached to the tube at B, so as to be incapable of moving in it ; and suppose the screw to be turned nearly half round, so that the end A shall be turned downwards, and the point B brought nearly to the highest point of the curve ABC. It is evident that the series of points B, D, &c., which were before situate so as to have ascending parts of the tube on each side of them, are now in the very contrary predicament, having interchanged situations with the points C, E, &c., as represented in Jig. 79. Fig. 79. The ball which we supposed attached to the tube, is now hang- ing as it were on the brow of an acclivity, immediately to the right of the highest point at B ; for we have supposed the point where the ball was placed to be brought nearly, but not exactly, to the highest point. If the ball be now disengaged or detach- ed, it will descend by its gravity from B to C, where it will ultimately rest. The point at which B was placed when the screw was in the position represented in Jig. 78., is marked b in Jig. 79. In fact, by turning the screw on its axis half round, it must be evident, upon the slightest attention, that no point of it can be really advanced in the direction of its length, and 160 A TREATISE ON HYDROSTATICS. CHAP. X. that no other effect can be produced than to cause every point to revolve in a circle round its axis. Thus the point B, Jig. 78., is transferred from the lowest part of the circle in which it re- volves, nearly to the highest, as represented in Jig. 79. : the ball, therefore, being no longer placed between two ascending parts of the screw, will no longer be prevented from moving in obe- dience to its gravity ; it will have an ascent on one side and a descent on the other, and towards the latter, of course, it must fall. The whole effect, therefore, of the half turn which we have supposed, is to transfer the ball from the point 6 to the point C, which is, in fact, equivalent to moving it up the inclined plane A C, 'Jig. 79., from b to C. Another half turn of the screw will be attended with similar effects. The ball being supposed to be attached to the tube at C, will, when the tube is restored to the position represented in Jig. 78., cause the ball to stand on the brow of an acclivity descending from C to D. If the ball, therefore, be again disen- gaged, it will fall to D, where it will again rest. By this means the ball is therefore carried up the inclined plane from c to D, as in Jig. 78., or, what is the same, from C to d in Jig. 79. It is clear that, by continuing this reasoning, we could show, that, under the circumstances supposed, the ball would be gradually transferred from the lowest point of the inclined plane to the highest as far as the screw extends. We have supposed the ball to remain attached to the screw at B until a half turn of the screw is nearly completed, and not until then to be detached. But suppose that the ball is detached when a very small part of a turn has been made : the point B will thus be brought into a situation a little above that at which it has an ascending branch of the screw on each side of it ; it will then have a descending part on that side from which it was moved ; if detached it will consequently descend in that direc- tion, and will cease to move when it arrives in that part of the screw where it will have an ascending branch at each side of it. Now suppose the ball not to be attached to the tube, but merely to lie in it, the motion which we have here supposed to be effected at intervals, and to be interrupted by the ball being occasionally attached to the tube so as to prevent it moving, will, in fact, take place continuously, and the ball will be car- ried up the inclined plane, not by distinct efforts separated by intervals, but by one uninterrupted and continuous motion. All that has been said of a ball in the tube would be equally true, if a drop or any quantity of a liquid were contained in the tube instead of the ball. Therefore, if the extremity of the screw were immersed in a well or reservoir of water, so that the water would by its weight or pressure be continually forced CHAP. x. ARCHIMEDES' SCREW. 161 into the extremity of the tube, it would, by turning the tube, be gradually carried along the spiral to any height to which it may extend. From the explanation given above it is clear, that it is essen- tial to the performance of this machine that the elevation of the spiral above the horizontal position should not exceed a certain limit. In fact, in each spire of the tube a certain point must be found, on either side of which the tube ascends. Now it is apparent that the tube may be so elevated in its position, that the part of the tube which proceeds towards the lower extremi- ty of the screw will descend in every part of the tube : this will be quite evident if the screw be supposed first to be placed in a perfectly upright position. Under such circumstances it is obvious, that if the ball were placed any where in the tube it would fall down to the lowest point ; a slight inclination from the vertical position will not prevent this from happening ; but if the screw receive such an inclination, that in each spire a point will be found so placed that the part proceeding towards the lower extremity shall ascend, then the ball placed at such a point will remain at rest ; and, if the screw be turned, will as- cend, as already explained. In practice, the spiral channel through which the water is carried is not in the form of a tube. A section of the instru- ment, as ased in practice, is represented in fig. 80. Fig. 80. The screw possesses an advantage over common pumps in being capable of raising water which is not pure, being mixed with gravel, weeds, or sand. The screw may be kept in a state of revolution by any of the usual moving powers. Dr. Brewster mentions that an excellent engine of this description was erected, in 1816, at Hurlet alum works, upon the water of Lev- ern near Paisley. This engine was moved by a water wheel, which communicated by a long shaft with the screw ; a beveled wheel was constructed on the screw, which worked in another 14* Mi;i A TI'.i.MI i: \ IIYIUMI-'I M [ JI beveled wheel on t.he f>:\ H-mity of the shn.f>. ; nnot.her bev:lod whccj on |J,< : .-,v|r: of t.he Wilt er- wheel, Worked ill a C01TepOll(I- intr wheel on t.he ot.he.r oxt.re.init.y of the <;h;i.ft.. The nerew WII.M HIM:: I'. '-pi. in r.on.Ht.niit. revolnfion by the Ihll of wnt.er which .sup- plied (.he reservoir, from wheneo t.he ;;;ime wu.t,er WII.H to be; rr.jsed by MM: :-.crew ilH<;lf. 7Vic Sluice Governor. fll!>.j In i-v|,|;iiriinrr f|,i- oj'-r:it.ioM of w.t.T wli::l>:, it. was rJiovvn ll,.-it lli<-,c w.r: :i - -rt:nn v-lorit.y ;.t, wliii-.li t.lnt useful i:f- fect resulting from them is a maximum. Any deviation from thin rate of motion, whether by increase or decrease, must ho attended by a corresponding loss of power : but, since the water in the mill-course must, from obvious natural causes, be subject f.o coni'.idcrnblr fliirl.iKit.ioiiH in it.n qimrit.it.y nwl forr.i:, tin: vHori- l.y which it WOUld Communicate tO tin; wheel would nmleiyo proportiormt.f: v/iriat.ioriH. It. i;;, therefore, nere:;:,;iry to j)f(ivn!- siome mi "MI ; of coiilj-ollinjf j.lic ,j i KID I it y of w;it.er, ri.iid me;i.::nrifi"; out. the |IOU I ), //. Hi., |;1 M. i-.l i nit. I') wln li li I I' li' -I , I'. Mini Dili wlll-l'l il K,|H- I I ilMH-il, V.'lil' II I IIIOVI 'I I' 1 / ii < 'MM |.'.M'lni" vvlicd 1 ji|;i< '! 'i. ill 111 III' mil' IMII' iy / , II ni'iV'l Ity Hi'- \vnld- v. li'-'-l. I' I', ;M'- I---, li-;ivy Imlh ntlrx li< d I') I <>'' , :> J'. Mil III I . 'Mi' ' ,i|i 'i,i, n < i'-'i i.y joini : Lh other rod ' ' i ' hi< ii nrfl i'.mi-'i MJ.'.M ii rin^ nl. I Tin ' : v/ii' i t li<< rnnii i I I (oil:, A |nl ii < I i -. i IM/M with', Ml " I'Hj^hl'iu y ) i i r :iv <:a,Uff(r Hi'- i in-/ lit'. I'.nit.-i ' I) |> I . - I ul I,:;. ;,l 'I'.Mllkrlul,),,., '. Mil \'> lilfii I;'-!'/ '.villiMi it. iipm. ,i j , ji HI ilo \ ||, i. / , ,l . ;,i,,,.,l wj1.li il T.- '-II'-' I. ' -cnl'-y the application of adequate mechanical force. It is neces- ? sary, however, nbt to confound compressibility with penetrabil- ity. So far from these qualities being identical, the one implies the absence of the other. A body is compressible when the forcible intrusion of another body into the space with- in which it is confined causes its particles to retreat, and to accommodate their arrangement to the more limited space within which they are compelled to exist. The very fact of their thus retreating before the intruding body is a distinct manifestation of their impenetrability. If they were penetra- ble, the body would enter the space in which they were confined, without driving them before it, or otherwise disturbing their arrangement. CHAP. III. ELASTICITY OF AIR. 181 CHAP. III. ELASTICITY OF AIR. ELASTIC AND COMPRESSING FORCES EQUAL. LIMITED HEIGHT OF THE ATMOSPHERE. ELASTICITY PROPORTIONAL TO THE DENSITY. EXPERIMENTAL PROOFS. INTERNAL AND EXTERNAL PRESSURE ON CLOSE VESSELS CONTAINING AIR. (131.) THE elasticity and compressibility of air have been already noticed. In the present chapter we propose to exam- ine and explain these qualities in more detail. It will be evident, upon the slightest reflection, that the elas- ticity of air must be equal to the force which is necessary to confine it within the space it occupies. Let us suppose that A B, Jig. 6., is a cylinder, having a piston P fitting air-tight at Fig. G. the top ; and let us imagine that this piston P is not acted upon by any external force, having a tendency to keep it in its place. If the cylinder below the piston be filled with air, this air will have a tendency, by virtue of its elasticity, to expand into a wider space ; and this tendency will be manifested by a pres- sure exerted by the air on all parts of the surfaces which con- fine it. The piston P will, therefore, be subject to a force tending to displace it and drive it from the cylinder, the amount of which will be the measure of the elasticity of the air beneath it. Now, if this piston be not subject to the action of a force directed inwards, exactly equal in amount to the pressure thus excited by the elastic force of the air, it cannot maintain its po- sition. If it be subject to an inward force of less amount than the elastic pressure, then the latter will prevail, and the piston be forced out. If it be subject to an inward force greater in 16 182 A TREATISE ON PNEUMATICS. CHAP. III. amount than the elastic pressure, then the former will prevail, and the piston will be forced in, the air being compelled to re- treat within a more confined space. In no case, therefore, can the piston maintain its position, except when it is subject to an inward pressure exactly equal to the elastic force of the ai* en- closed in the cylinder. The property of elasticity renders it necessary that, in what- ever state air exist, it shall be restrained by adequate forces of some definite amount, and which serve as antagonist principles to the unlimited power of dilatation which the elastic property implies. In all cases which fall under common observation, air is either restrained by the resistance of solid surfaces, or it is pressed by the incumbent weight of the mass of atmosphere placed above it. It may be asked, however, whether it will not follow from this, that the extent of our atmosphere is infinite ? for that, as we ascend in it, the weight of the superior mass of air must be gradually and unceasingly lessened ; and, therefore, the force which resists the expansive principle being removed by degrees, the fluid will spread through dimensions which are subject to no limitation. Although it is undoubtedly true that these considerations lead us justly to conclude that our atmos- phere extends to a very great distance from the surface, and that the higher strata of it are attenuated to a degree which not only exceeds the powers of art to imitate, but even out- strips the powers of imagination to conceive ; yet still the un- derstanding can suggest a definite limit to this expansion. Numerous physical analogies* favor the conclusion, that the divisibility of matter has a limit, or that all material substances consist of ultimate constituent particles or atoms, which admit of no further subdivision, and on the mutual relations of which the form and properties of the various species of bodies depend. Now, those ultimate particles of the air are endued with a certain definite weight, because it is the aggregate of their weights which forms the weight of any mass of air. It is a fact established by experiment, that in proportion as air expands, its elastic force is diminished ; and, therefore, if it continue to expand, it will at length attain a state of attenuation in which the disposition of its constituent particles to separate by their elasticity is so far diminished, as not to exceed the gravity of those constituent particles themselves. In this state the two forces will be in equilibrium, and the elastic force being neu- tralized, the particles will no longer be dilated. (132.) In these observations we have assumed a principle which is of the last importance in pneumatics, and which, in- deed, may be regarded as forming the basis of this part of * Cab. Cyc. Mechanics, chap. ii. CHAP. III. LIMITS OF THE ATMOSPHERE. 183 physical science, in the same manner as the power of transmit- ting pressure is the fundamental principle of hydrostatics. This latter principle, indeed, also extends to elastic fluids ; and all the consequences of the free transmission of pressure, which do not also involve the supposition of incompressibility, are ap- plicable to elastic fluids with as much truth as to liquids. But the principle to which we now more especially refer, and which may be looked upon as the chief characteristic of this form of body, and necessary to render definite the notion of their elas- ticity, may be announced as follows : " The elastic force of any given portion of air is augmented in exactly the same proportion as the space within which it is enclosed is diminished ; and its elastic force is diminished in exactly the same proportion as the space through which it is allowed to expand is augmented." To explain this, let A B C D, Jig. 7., be conceived to be a B cylinder, in which a piston A B moves air-tight and without friction ; and let us suppose the distance of the lower surface A B of the piston from the bottom D C of the cylinder to be 13 inches. Let air be imagined to be enclosed below the pis- ton, and let us suppose that the elastic force of this air is such as" to press the piston with a force of 16 ounces. From what 'has been already stated (131.), it is clear that to maintain the piston in its place, it is necessary that it should be pressed downwards with an equivalent force of 16 ounc*es. Now let the force upon the piston be doubled, or let the piston be loaded with a pressure of 32 ounces. The inward pressure prevailing over the elasticity, the piston will immediately be forced to- wards D C, but will cease to move at a certain distance A D, Jig. 8., from the bottom. Now, if this distance A D be meas- ured, it will be found to be exactly six inches. The air has, therefore, contracted itself into half its former dimensions. Since the piston is sustained in the position represented in 184 A TREATISE ON PNEUMATICS. CHAP. III. Jig. 8., it follows that the elasticity of the air beneath it is equivalent to the weight of the piston A B ; and, therefore, that the air included in the cylinder acquires double its original elasticity when it is compressed into half its or/ 'inal bulk. Fig. B. Let the piston be now loaded with three times its original weight, or 48 ounces ; it will be observed to descend into the cylinder, and further to compress the air, until its distance from the bottom is reduced to four inches. At that distance it will rest, being balanced by the increased elasticity of the air: this air is now compressed into one third of its original bulk, and it has three times its original elastic force. In the same manner, in whatever proportion the weight of the piston be augmented, in the same proportion will the dis- tance from the bottom at which it will rest in equilibrium be diminished ; and, consequently, the elastic force of the air is increased in the same proportion as the space into which it is compressed is diminished. Let us again suppose the piston to be loaded with sixteen ounces, and to be balanced, as in Jig. 7., by the resistance of the air at twelve inches from the bottom of "the cylinder. But let us also suppose the cylinder continued upwards to a height exceeding 24 inches ; let the weight upon the piston be now reduced to eight ounces. Since the elasticity of the air be- neath the piston was capable of supporting sixteen ounces, it will now prevail against the diminished pressure of eight ounces. The piston will continue to rise in the cylinder until the elasticity of the air is so far diminished by expansion, that it is capable of supporting no more than eight ounces ; the pis- ton will then remain in equilibrium. If the height of the piston above the bottom be now measured, it will be found to be 24 inches, that is, double its former height ; the air has, therefore, expanded to double its former dimensions, and is reduced to half its former elasticity. CHAP. III. ELASTICITY AS THE DENSITY. 185 Fig. 9. In like manner it may be shown, that, if the weight upon the piston were reduced to four ounces, or a fourth of its original amount, the piston would rise to four times its original height, or 48 inches, before it would be capable of balancing the re- duced elasticity of the air. Thus, by expanding to four times its primitive dimensions, the elasticity of the air is reduced to one fourth of its primitive amount. By like experiments, it is easy to see how the general law may be established. In whatever proportion the weight of the piston may be increased or diminished, in the same proportion exactly will the space filled by the air which balances it be di- minished or increased. (133.) The preceding illustration has been selected with a view rather to make the property itself intelligible, than as a practical experimental proof of it. The use of pistons movable in cylinders is attended with inconvenience in cases of this kind, arising from the effects of friction, and the difficulties of making due allowance for them. There is, however, another method of bringing the law to the test of experiment, which is not less direct, and is more satisfactory. Let ABC D,Jig. 9., be a glass tube curv ed at one end, B C, and having the short leg C D furnished with a stopcock at its extrem- ity : let the leg B A be more than 60 inches in length. The stopcock D being opened so as to allow a free communication with the air, and the mouth A of the longer leg being also open, let as much mercury be poured into the tube as will fill the curved part B C, and rise to a small height in each leg. By the principles of hydrostatics, the surfaces of the mercury E and F will stand at the same level. Let the stopcock D be now closed, the levels E F will still remain undisturbed. When the stopcock D was opened, the surface F sustained a pressure equal to the weight of a column of air con- tinued from F upwards as far as the atmos- phere extends. But the stopcock D being closed, the effect of the weight of all the air above that point is intercepted ; and, con- sequently, the surface F can sustain no pressure arising from weight, except the amount of the weight of the small quantity of air included be- tween F and D, which is altogether insignificant. But the air thus included presses on the surface F by its elasticity ; and the amount of this pressure is equal to the force which confined 186 A TREATISE ON PNEUMATICS. CHAP. III. the air within the space F D, before the stopcock was closed (131.) : but this force was the weight of the column of atmos- phere above D ; and hence it appears, that the elastic force of 'the air confined in the space D F is equal to the atmospheric pressure. Now the other surface E, the end A of the tube being open, is subject to the atmospheric pressure. Thus the two surfaces, F and E, of the mercury, are each subject to a pressure arising from a different quality of the atmosphere ; the one, F, being pressed by its elasticity, and the other, E, being pressed by its weight. These pressures being equal, the surfaces F and "E continue at the same level. The method of ascertaining, experimentally, the pressure arising from the weight of the atmosphere will be fully explain- ed hereafter ; meanwhile, it is necessary for our present pur- pose to assume this pressure as known. Let us suppose, then, that the atmospheric pressure acting upon the surface E is the same as would be produced by a column of mercury 30 inches in height resting on the surface E : the force with which the elasticity of the air confined in D F presses on the surface Fis therefore equal to the weight of a column of thirty inches of mercury. Tjie pressure of the atmosphere acting on the sur- face E is transmitted by the mercury to the surface F, and balances the elastic force just mentioned. Let the position of the surface F be marked upon the tube, and let mercury be poured into the longer leg at A. The increased pressure produced by the weight of this mer- cury will be transmitted to the surface F, and will prevail over the elasticity of the confined air : this surface will therefore rise towards D. compressing the air into a smaller space. Let the mercury continue to be poured in at A, until the surface F rise to F', Jiff. 10., the middle point between the end D of the tube, and its first position F. The air included is thus compressed into half its former dimensions, and its elasticity will be measured by the amount of the force with which the surface F 7 is pressed upwards against it : this force is the weight of the column of mercury in the leg B A, above the level of F', together with the weight of the atmosphere pressing on the top G- of the column. Let a horizontal line be drawn from the surface F' to the leg B A, and let the column G II be measured ; its Fig. 10. CHAP. III. DENSITY OF ATMOSPHERE. 187 length will be found to - be accurately 30 inches, and its weight is therefore equal to the atmospheric pressure. The force with which F' is pressed upwards is therefore equal to twice the atmospheric pressure, or to double the force with which F, in Jig. 9., was pressed upwards. Hence it appears, that the elasticity of the air confined in the space D F',Jig. 10., is double its former elasticity when filling the space D F, Jig. 9. Thus, when the air is compressed into half its volume, its elasticity is doubled. In like manner, if mercury be poured into the tube A, until the air included in the shorter leg is reduced to a third of its bulk, the compressing force will be found to be three times the atmospheric pressure, and so on. (134.) That the elasticity of the air which surrounds us is equal to the weight of the incumbent atmosphere, has been proved incidentally in the preceding experiment. Indeed, this is a proposition, the truth of which must appear evident upon the slightest consideration, and which is manifested by innu- merable familiar effects. If the elastic force of the air around us were less than the weight of the incumbent atmosphere, it would yield and suffer itself to be compressed until it acquired an elastic force equal to that weight. If it were greater in amount than the weight of the incumbent atmosphere, it would overcome that weight, and would press the atmosphere upwards, until, by expanding, its elasticity were reduced to equality with the weight of the atmosphere ; and these effects are continually going forward. The incumbent atmosphere is subject to con- tinual fluctuations, in weight, as will hereafter be proved ; and the lowest stratum of air which surrounds us is continually undergoing corresponding contractions and expansions, ever accommodating its elasticity to the pressure which it sustains. Also this stratum of air is itself subject to changes of elasticity, from vicissitudes of temperature proceeding from the earth to which it is contiguous. These changes produce a necessity for expansion and contraction in it, even while the weight of the incumbent atmosphere remains unchanged ; but the full developement of this last consideration belongs to the theory of heat rather than to our present subject. (135.) An open vessel, which is commonly said to be empty, is, in fact, filled with air ; and when any solid or liquid is placed in it, so much of the air is expelled as occupied the space into which the solid or liquid entered. If such a vessel be closed by a lid or stopper, the pressure, of the external atmosphere will act upon every part of the exterior surface with an intensity proportionate to its weight. The air which is enclosed in the vessel will, however, act on the interior surface with an inten- sity proportionate to its elasticity. According to what has been 188 A TREATISE OX PNEUMATICS. CHAP. IV. already explained, this elasticity is equal to the pressure ; and, therefore, there is a force tending to press the sides of the ves- sel outwards, exactly equal to the pressure acting on the exte- rior surface, and tending to press them inwards. These two forces neutralize each other, and the vessel is circumstanced exactly as if neither of them acted upon it. When the operation and properties of some pneumatical in- struments have been explained, we shall have occasion to notice many other effects of the elasticity of air. CHAP. IV. \ WEIGHT OF AIR. MAXIM OF THE ANCIENTS. ABHORRENCE OF A VACUUM. SUCTION. GALILEO'S INVESTIGATIONS. TORRICELLI DISCOVERS THE ATMOS- PHERIC PRESSURE. THE BAROMETER. PASCAL'S EXPERIMENT. REQUISITES FOR A GOOD BAROMETER. MEANS OF SECURING THEM. DIAGONAL BAROMETER. WHEEL BAROMETER. VERNIER. USES OF THE BAROMETER. VARIATION OF ATMOSPHERIC PRESSURE. WEATHER GLASS. RULES IN COMMON USE ABSURD. CORRECT RULES. MEASUREMENT OF HEIGHTS. PRESSURE ON BODIES, WHY NOT APPARENT. EFFECT OF A LEATHER SUCKER. HOW FLIES ADHERE TO CEILINGS, AND FISHES TO ROCKS. BREATHING. COM- MON BELLOWS. FORGE BELLOWS. VENT-PEG. TEA-POT. KETTLE. INK-BOTTLES. PNEUMATIC TROUGH. GUGGLING NOISE IN DE- CANTING WINE. (136.) IN the history of human discovery, there are few more impressive lessons of humility than that which is to be collected from the records of the progress by which the pressure of the atmosphere which surrounds us, and the manner in which it is instrumental in producing some most ordinary phenomena, be- came known. Looking back from the point to which we have now attained, and observing the numerous and obvious indica- tions of this effect which present themselves at all times, and on all occasions, nature seems almost to have courted the phi- losopher to the discovery. With every allowance for the feeble- ness of the human understanding, and for the disadvantages which the ancients labored under, as compared with more recent investigators ; still one is inclined to attribute the late- ness of the discovery of the atmospheric pressure and its effects not altogether to the weakness and inadequacy of the mental powers applied to the investigation. There seems to be some- thing of wilful perverseness and obstinacy instigating men to step aside from that course, and to turn their minds from those instances which Nature herself continually forces upon them. CHAP. IV. "NATURE ABHORS A VACUUM." ISO The ancient philosophers observed, that in the instances which commonly fell under their notice space was always filled by a material substance. The moment a solid or a liquid was by any means removed, immediately the surrounding air rushed in and filled the place which it deserted ; hence they adopted the physical dogma that nature abhors a vacuum. Such a prop- osition must be regarded as a figurative or poetical expression of a supposed law of physics, declaring it to be impossible that space could exist unoccupied by matter. Probably one of the first ways in which the atmospheric pressure presented itself was by the effect of suction with the mouth. One end of a tube being immersed in a liquid, and the other being placed between the lips, the air was drawn from the tube by the ordinary process of inhaling. The water was immediately observed to fill the tube as the air retreated. This phenomenon was accounted for by declaring that " Nature abhorred a vacuum," and that she therefore compelled the water to fill the space deserted by the air. The effects of suction by the mouth led, by a natural analogy, to suction by artificial means. If a cylinder be open at both ends, and a piston playing in it air-tight be moved to the lower end, upon immersing this lower end in water, and then drawing up the piston, an unoccupied space would remain between the piston and the water. " But nature abhors such a space," said the ancients, " and therefore the water will not allow such a space to remain unoccupied : we find accordingly that as the piston rises the water follows it." By such poetical reasoning pumps of various kinds were constructed. The antipathy entertained by nature against an empty space served the purposes of philosophy for a couple of thousand years, when it so happened that some engineers employed at Florence in sinking pumps had occasion to construct one to raise water from an unusually great depth. Upon working it they fouild that the water would rise no higher than about thirty-two feet above -the well. Galileo, the most celebrated philosopher of that day, was consulted in this difficulty ; and it is said that his answer was, that " Nature's abhorrence of a vacuum extended only to the height of thirty-two feet, but that beyond this her disinclination to an empty space did not extend." Some writers* deny the fact of his having given this answer ; others admit it,f but take it to have been ironical. It has been more generally taken as a solution seriously intended.:}: It appears, however, that Galileo, having his attention thus directed to the point, soon saw the absurdity of the maxim, that * Enc3'clop8edia Motropolitania, Pneumatics. f Biot, Traite de Physique, toino i. p. 69. j Montucla, Histoire do Mathematiques, tome ii. p. 203. 190 A TREATISE ON PNEUMATICS. CHAP. IV. " nature abhors a vacuum," and sought to account for the phe- nomenon in other ways. He attributed the elevation of the water to an attraction exerted upon that liquid by the piston. This attraction he conceived to have a determinate intensity, and when such a column of water was raised as was equal in weight to the whole amount of the attraction, then any further elevation of the water by the piston became impossible. At a very remote period air was known to possess the quality of weight. Aristotle and other ancient philosophers expressly speak of the weight of air. The process of respiration is attributed by an ancient writer to the pressure of the atmos- phere forcing air into the lungs. Galileo was, therefore, fully aware that the atmosphere l possessed this property ; and it is not a little surprising that when his attention was so immediately directed to one of the most striking effects of it, he was unable to perceive the connection. Some writers* affirm, we know not upon what authority, that Galileo, at the time he was interrogated respecting the limited elevation of water in a common pump, was aware of the true cause of the effect ; but that, not having thoroughly investigated the subject, he evaded the question of the engineers, with a view to conceal his knowledge of the principle, until he had carried his inquiry to a more satisfactory result. It does not, however, appear that he published his solution of the problem. After his death Torricelli, his pupil, directed his attention to the same problem. He argued that whatever be the cause which sustained a column of water in a common pump, the measure and the energy of that power must be the weight of the column of water, and, consequently, if another liquid be used, heavier or lighter, bulk for bulk, than water, then the same force must sustain a lesser or greater column of such liquid. By using a much heavier liquid, the column sustained would necessarily be much shorter, and the experiment in every way more man- ageable. He therefore selected for the experiment mercury, the heaviest known liquid. The weight of mercury, bulk for bulk, being about 13 times that of water, it follows that the height of a column of that liquid which would be sustained by a vacuum must be 13i times less than the height of a column of water thus sustained. Hence he computed that the height of the column of mercury would be about 28 inches. He procured a glass tube, A B (jig. 11.), more than 30 inches in length, open at one end A, and closed at the other end B. Placing this tube in an upright position, with the open end upwards, he filled it with mercury, and applying his finger to the end A, so as to * Biot, Traite de Physique, tome i. G9. Young's Natural Philosophy, voJ ii. p. 354. CHAP. IV. THE BAROMETER. 19. Fig. 11. prevent the escape of the mercury, he inverted the tube, plunging the end A into a cistern C D (Jig. 12.), containing mercury, the open end A being below the surface F of the mercury in the cistern, and no air having been allowed to communicate with it. Upon removing the finger, therefore, the mercury in the cistern came in immediate contact with the mercury in the tube. Immediately the mercury was observed to subside from the top of the tube, and its surface gradually to descend to the level E, about 28 inches above the mercury in the cistern. This result was what Torricelli anticipated, and clearly showed the absurdity of the supposition that nature's abhorrence of a vacuum extended to the height of 32 feet. Torri- celli soon perceived the true cause of this phenomenon. The atmospheric pressure acting upon the surface F, while the surface E was protected from this pressure by the closed end B of the tube, supported the weight of the column E F. This pressure was transmitted by the liquid mercury in the cistern from the external surface F to the base of the column contained in the tube. This experiment and its explanation soon became known to philosophers in every part of Europe, and among others, it attracted the notice of the celebrated Pascal. In order to subject the explanation of Torricelli to the most severe test, Pascal proposed to transport a tube of this kind to a great elevation upon a mountain, and argued that if the cause which sustained the column in the tube were the weight of the atmosphere acting upon the external surface of the mercury in the cistern, then it must be expected that if the tube was elevated, having a less and a less quantity of atmosphere above it, the column sustained by the weight of this incumbent atmosphere must suffer a corres- ponding diminution in height. He accordingly directed a friend residing in the neighborhood of a mountain, called Puys de Dome, near Auvergne, to ascend that mountain, carrying with him the apparatus already described. J D This was accordingly done, and the height of the column noted during the ascent. Con- formably to the principle explained by Torri- celli, the column was observed gradually to diminish in height, as the elevation of the 192 A TREATISE ON PNEUMATICS. CHAP. IV. apparatus was increased. The same experiment was repeated by Pascal himself, with similar success, upon a high tower in the city of Paris. Meanwhile other effects were manifested which not less unequivocally proved the truth of Torricelli's solution. The apparatus being kept for a length of time in a fixed position, the height of the column was observed to fluctuate from day to day between certain small limits. This effect was, of course, to be attributed to the variation of the weight of the incumbent atmosphere, arising from various meteorological causes. (137.) The apparatus which we have just described is, in fact, the common barometer. By the principle of hydrostatics it appears, that the height of the column E F, sustained by the atmospheric pressure, will be the same, whatever be the mag- nitude of the bore of the tube. If we suppose the section of the bore to be equal to a square inch, then the column E F will be pressed upwards, and held in equilibrium by the weight of a column of atmosphere pressing upon a square inch of the ex- ternal surface F ; consequently the weight of the column E F must be equal to the weight of a column of the atmosphere whose base is a square inch, and which extends from the surface of the mercury in the cistern to the top of the atmos- phere. If there be another tube whose bore is only half a square inch, then the pressure which will support the column in it will be that of a similar column of atmosphere, whose base is half a square inch ; such pressure then will only be half .the amount of the former, and, therefore, will only sustain half the weight of mercury. But a column of mercury of half the weight, having a base of half the magnitude, must necessarily have the same height. Hence it appears, that so long as the atmosphere presses upon a given magnitude of the surface F, with the same intensity, the column of mercury sus- tained in the tube will have the same height, whatever be the magnitude of its bore. In adapting such an apparatus as this to indicate minute changes in the pressure of the atmosphere, there are many circumstances to be attended to, which we propose to explain in the present chapter, so far as they are necessary to render intelligible the general principle and use of the barometer. It is, in the first place, necessary to have the means of meas- uring exactly the height of the column E F, fig. 12. : if the surface F were fixed, and the tube B A maintained in its posi- tion, it would be sufficient to mark a graduated scale upon the tube, indicating the number of inches and fractions of an inch of any part upon it, from the surface F. But it is obvious that this will not be the case when the pressure of the atmosphere is increased, as an additional quantity of mercury is forced into CHAP. IV. THE BAROMETER. 193 the tube, and consequently an equal quantity is forced out of the cistern. While the surface E rises towards B, the surface F therefore descends, and the distance of E from that surface is increased by both causes. A graduated scale marked upon the tube would then only indicate the change in the position of the surface E, but would not show the change in the length of the column E F, so far as that change is affected by the fall of the surface F. There are several ways in which this defect may be remedied. If the instrument be not required to give extremely accurate indications, it will be sufficient to use a tube the bore of which is small compared with the magnitude of the cistern. In this case a small change in the height of the column will make but a very inconsiderable change in the whole quantity of mercury in the cistern, and, therefore, will produce a very minute effect upon the position of the surface F. If such a change in the level F be so small as to affect the indications of the instrument in a degree which is unimportant for the purposes to which it is intended to be applied, the surface F may be regarded as fixed, and the whole change in the height of" the column may be taken to be represented by the change in the position of the level E. All ordinary barometers are constructed in this manner. But it is not difficult to adjust a scale upon a tube which will give with accuracy the actual variation in the length of the column by means of the change in the level of the surface E. Let us suppose that the cistern C D has a flat horizontal bottom and perpendicular sides, and that the magnitude of the bottom bears a certain known proportion to the bore of the tube. Sup- pose this proportion be that of one to a hundred. If the pres- sure of the atmosphere increase, so as to cause the column of mercury sustained in the tube to be increased in height by one inch, then as much mercury as fills one inch of the tube will be withdrawn from the cistern ; but as the base of the cistern is one hundred times greater than the bore of the tube, it is evi- dent that this inch of mercury in the tube would only cause a fall of the hundredth of an inch in depth of the mercury in the vessel:; consequently it follows that the increased elevation of an inch in the column produces a depression of a hundredth of an inch in the surface F. Thus it appears, that the increased length of the column E F is produced by the surface F falling through the one hundredth of an inch, while the surface E rises through 99 hundredth parts of an inch. The same will be true whatever change takes place in the height of the column. We may therefore infer, generally, that whatever variation may be produced in the surface E, the consequent variation produced in the height of the column is greater by a ninety-ninth part. 194 A TREATISE ON PNEUMATICS. CHAP. IV. If then the top be so graduated that a portion of it, the length of which is one hundredth part less than an inch, be marked as an inch, and all other divisions and subdivisions marked accord- ing to the same proportion, then the indications will be as accurate as if the surface F were fixed ; the tube being divided accurately into inches and parts of an inch. The barometer is represented mounted and fur- Fig. 13. nished with a scale, in Jig. 13. The glass tube is surrounded by one of brass, in which there is an aperture cut at D E, of such a length and at such a height above the cistern, as to include all that space through which the level of the mercury in the tube usually varies in the place in which the barometer is intended to be used. In these coun- tries the level of the mercury never falls below 28 inches, nor rises above 31 inches ; consequently a space somewhat exceeding these limits will be sufficient for the opening D E. The tube is per- manently connected with the cistern A B, and a scale is engraved upon the brass tube near the aperture D E, to indicate the fractions of the height of the mercury in the tube. There is another method of avoiding the diffi culty arising from the change in the level of the surface of the mercury in the cistern, used in the barometer here represented. The bottom of the cistern moves within it in such a manner as to pre- vent the mercury from escaping, and a screw is inserted at V, by turning which the bottom of the cylinder is slowly elevated or depressed. An ivory index is attached to the top of the cylinder, which is presented downwards and brought to a fine point, so as to mark a fixed level. When an observation is made with the barometer, the screw V is turned until the surface is brought accurately to the point of the index, by rais- ing or lowering the bottom according as the surface is below or above that point. It follows, therefore, that whenever an observation is made with this instrument, the surface of the mercury always stands at the same level, and therefore the di- visions upon the scale C F represent the actual change of height in the barometric column. Since the column of mercury sustained in the barometric tube is taken to represent the pressure of the atmosphere, it is clear that no air or other elastic fluid should occupy the part of the tube above the mercury. To avoid such a cause of error is not so easy or obvious as may at first appear. Mercury, as it CHAP. IV. THE BAROMETER. 195 exists in the ordinary state, frequently contains air or other elastic fluids combined with it, and which are maintained in it by the atmospheric pressure, to which it is usually subject. When it has subsided, however, in the barometric tube, it is relieved from that pressure, and the elastic force of such air as may be lodged in the mercury being relieved from the pressure which confined it there, it will make its escape and rise to the surface, finally occupying the upper part of the tube, and ex- erting a pressure upon the surface of the column by means of its elasticity. Such a pressure will then assist the weight of the column of mercury in balancing the atmospheric pressure, and consequently a column of less height will balance the atmosphere than if the upper part of the tube were free from air. To remove this cause of error it is necessary to adopt means of purifying the mercury used in the barometer from all elastic fluids which may be combined with it. The fact, that the application of heat gives energy to the elastic force of gases, enables us easily to accomplish this. For if the mercury be heated, the particles of air or other elas- tic fluids which are combined with it acquire such a degree of elasticity, that they dilate and rise to the surface, and there escape in bubbles. The same process of heating serves to expel any liquid impurities with which the mercury may be combined. These are converted into vapor, and escape at the surface. The presence of an elastic fluid at the top of the tube is thus removed so far as such fluid can proceed from the mercury. But it is also found that small particles of air and moisture are liable to adhere to the interior surface of the glass ; and when the mercury is introduced, and a vacuum produced at the top of the tube, these particles of air dilate, and, rising, lodge at the top, and vitiate the vacuum which ought to be there ; the particles of moisture also evaporate and rise likewise, both pro- ducing an aeriform fluid in the chamber above the surface of the mercury, which presses upon that surface with an elastic force, and produces a corresponding diminution in the height of the column of quicksilver sustained by the atmosphere, as already explained. This imperfection may be avoided by pre- viously heating the tube. The particles of air which adhere to its inner surface being thus expanded by heat, will fly off by their elastic force, and the particles of moisture will be con- verted into vapor, and likewise disengaged from the-surface. All the effects now explained may be produced by filling the tube with mercury in the first instance, and then boiling the liquid in it, which may be easily accomplished. The heat will not only expel all liquid and gaseous impurities from the mer- cury itself, bi.il abo .,111 disengage them from the inner surface 196 A TREATISE ON PNEUMATICS, GBAP. IV. of the tube. These precautions being taken, the column of mercury sustained in the tube will indicate by its weight the true amount of the atmospheric pressure. But in order to be able to compare the result of any one barometer with any other, it is necessary that the weights of equal bulks of the liquid mer- cury used in both cases should be the same ; and for this pur- pose we must be assured that the mercury used is pure, and not combined with other substances. We have just seen how- all substances in the liquid or gaseous form may be extracted from it. Impurities may still, however, be suspended in it in the solid form. To remove these it is only necessary to en- close the mercury in a small bag of chamois leather: upon pressing this bag the quicksilver will pass freely through its pores, and any minute solid impurities which may be contained in the mercury will remain in the bag. Pure and homogeneous mercury being thus obtained, we have advanced another step towards the certainty that the indications of diiferent barome- ters may correspond ; but there is still one other cause of dis- cordance to be attended to. Suppose a barometer to be used in Paris, and another in London, at a time when the pressure of the atmosphere in both places is the same, but the tempera- ture of the air at Paris is higher than the temperature of London. The mercury in the one barometer will have a higher tempera- ture than the mercury in the other. Now it is well known that when mercury or any other body is heated, its dimensions increase. In other words, bulk for bulk, it becomes- lighter. Consequently, of two columns equal in weight, that which has the higher temperature will have the greater altitude. Hence it appears, that under the circumstances supposed, at a time when the atmospheric pressure is the same in London as *t Paris, the barometer at the latter place will be higher than at the former. To guard against this source of error it is neces- sary, in making barometric observations, to note at the same time the contemporaneous indications of the thermometer. Tables are computed showing the changes in the height of the mercury corresponding to given differences of temperature. It is evident that in comparing the results of the same barometer observed at diiferent times, it is equally necessary to note the difference of temperature, and to allow for its effects. This, however, is a refinement of accuracy which is not attended to, except in observations made for philosophical purposes. (138.) One of the difficulties attending barometric observa- tions arises from the very minute changes produced in the height of the column by slight variations in the atmospheric pressure. The whole play of the upper surface of the column, in the most extreme cases, does not exceed three or four inches in a given place ; and mercury being a very heavy fluid, a vari- DIAGONAL BAROMETER. 1U7 ation in the pressure of the atmosphere, of sensible amount, may produce scarcely any perceptible change in the height of the column. One of the most obvious remedies, at first view, would seem to be the use of a fluid lighter than mercury. In the same proportion as the fluid is lighter will the change in the height of the column by a given change in the pressure of the atmosphere be greater ; but there are difficulties of a dif- ferent kind which altogether preclude the use of other fluids. The lighter liquids are much more susceptible of evaporation, and the surface of the liquid in the tube, being relieved from the atmospheric pressure, offers no resistance to the process of evaporation. The consequence is, that any liquid, except mer- cury, would produce a vapor, which, occupying the top of the tube, would press by its elastic force upon the surface, and co- operate with the weight of the suspended column in balancing the atmospheric pressure. Even from mercury we have reason to know that a vapor rises which is present in the upper part of the tube, but this pressure exerts no power which can introduce inaccuracy to any sensible extent into our conclu- sions. (139.) A form is sometimes adopted, called the diagonal barometer, for the purpose of increasing the range of the mer- cury in the tube. This is represented in Jig. 14., where A C B Fig. 14. represents the barometric tube. C is a point at a distance above the surface of the mercury in the cylinder less than the height of 28 inches. The space C D includes the range which the 198 A TREATISE ON PNEUMATICS. CHAP. IV. mercury would have if the tube were vertical ; but at C the tube is bent obliquely in the direction C B, having a sufficient length to bring the extremity B to the same level as D. The mercury which, had the tube been vertical, would range between C and D, will now have its play extended through the greater space C B ; consequently the magnitude of any part, however small, will be increased in the proportion of the line C D to the line C B. Thus, if C D be 4 inches, and C B 12 inches, then every change in the position of the surface of the mercury, produced by a change in the atmospheric pressure, will be three times as great in the diagonal barometer as it would be in the vertical one. (140.) Another contrivance for enlarging the scale, which is more frequently used, and for common domestic purposes at- tended with some convenience, is represented mfg. 15. This is called the wheel barometer. The barometric Fig. 15. tube is here bent at its lower extremity B, and turned upwards towards C. The atmospheric pressure acts upon the surface F, and sustains a column of mercury in the tube B A, which is above the level of F. The bore of the tube being in this case equal in every part of its length, it is clear that through whatever space the surface E falls, the surface F will rise, and vice versa- Hence it is obvious that the varia- tion in the height of the barometric column will always be double the change in the height of either surface E or F ; for if the surface F fall, the surface E must rise through the same space. They are thus receding from each other at the same rate, and therefore their mu- tual distance will be increased by the space through which each moves, or by double the space through which one of them moves. In the same manner, if F rise, E must fall, the two points mutually approaching each other at the same rate ; so that the distance between them will be diminished by the space through which each moves, or by double the space through which one of them moves. The change, there- fore, in the height of$ie barometric column will always be double the change in the position of the level F. Upon the surface at F there floats a small ball of iron, sus- pended by a string, which is carried over a pulley or small wheel at P, and counterpoised by the weight at W, less in amount than the weight of the iron ball. When the surface F rises, the iron ball, being buoyant, will be raised with it, and the CHAP. IT. WHEEL BAROMETER. 199 counterpoise W will fall ; and when the surface F falls, the weight of the iron ball, being greater than the weight of the counterpoise, will cause it to descend with the descending sur- face, and to draw the counterpoise W up. It is evident that, through whatever space the iron ball thus moves in ascending or descending, an equal length of the string will pass over the wheel P. Now this string rests in a groove of the wheel, in such a manner that, by its friction, it causes the wheel to re- volve, and, consequently, the revolution of this wheel indicates the length of the string which passes over its groove, which length is equal to the change in the level of the surface F. Upon the centre of this wheel P an index H is placed, which, like the hand of a watch, plays upon a graduated circular plate. Let us suppose that the circumference of the wheel P is two inches, then one complete revolution of this wheel will corre- spond to a change of 2 inches in the level F, and, therefore, to a change of 4 inches in the barometric column. But in one revolution of the wheel P the hand or index H moves complete- ly round the circle : hence the circumference of this circle corresponds to a change of 4 inches in the barometric column. Now, the circular plate may easily be made so that its cir- cumference shall measure 40 inches ; consequently 10 inches of this circumference will correspond to 1 inch of the column, and 1 inch of the circumference will correspond to the tenth of an inch of the column. In this way variations in the height of the column amounting to the tenth of an inch are indicated by a motion of the hand H over 1 inch of the circumference of the plate. By further subdivision a still greater accuracy may be obtained. In this form of the barometer it is evident that the prepon- derance of the iron ball assists the atmospheric pressure in sustaining the column. This cause of error, however, may be diminished almost indefinitely by making the preponderance of the ball over the counterpoise W barely sufficient to overcome the friction of the wheel P. Again, when the atmosphere is diminished in weight, and when the surface F has a tendency to rise, it is compelled to raise the ball ; and there is this ob- vious limit to the indications of the instrument, namely, that a change so slight that the difference of pressure will not ex- ceed the force necessary to elevate the ball will fail to be indicated. (141.) For scientific purposes, the vertical barometer is pref- erable to every other form of that instrument. In the oblique barometer the termination of the mercurial column is subject to some uncertainty arising from the level of the mercury not being perpendicular to the direction of the tube. In the wheel barometer there are several sources of error which, though so 4- 200 A TREATISE ON PNEUMATICS. CHAP. IV. small in amount as not to injure it for domestic or popular use, yet are such as to render it altogether unfit for scientific in- quiry. A contrivance called a Vernier, for noting extremely small changes, is usually applied to the vertical barometer, and supplies the place of an enlarged scale. It consists of a small graduated plate which is movable by a screw or otherwise, and which slides on the divided scale of the barometer. By means of this subsidiary scale, we are enabled to estimate magnitudes on the principal scale, amounting to very small fractions of its smallest divisions. The principle of the vernier is easily explained. Fig. 16. Let B A, Jig. 16., represent the scale of the barometer . extending through three inches, and divided to tenths of an inch. Let C D be the sliding scale of the ver- nier, equal in length to eleven divisions of the principal scale, and divided into ten equal parts. Thus each division of the vernier will be the tenth of eleven divisions of the instrument ; that is, it will be the tenth part of 11 tenths of an inch ; but 11 tenths of an inch is the same as 110 hundredths, and the tenth part of this is 11 hundredths. Thus it appears that one division on the vernier is in this case 11 hundredth parts of an inch. Now one division on the instrument being a tenth of an inch, or 10 hundredths of an inch, it is evident that a division on the vernier will exceed a division on the instrument by the hun- dredth part of an inch ; for if we take 10 hundredths from 11 hundredths, the remainder will be 1 hun- dredth. Let us suppose that the vernier is placed so that its 3 lowest division, marked 10, shall coincide with the lowest division on the instrument marked 28 ; then the first division of the vernier marked will coincide with the division of the instrument next above the 29th. The division marked 1 on the vernier will then be a little below the division marked 29 on the scale, and _ the distance between these will be the hundredth of an inch, as already explained. The division marked 2 of the vernier will be a little below the division marked 9 on the scale, and the distance below it will be 2 hun- dredth parts of an inch ; because two divisions of the vernier exceed two divisions of the scale by that amount. In like manner, the division marked 3 on the vernier will be below the division marked 8 on the scale by 3 hundredths of an inch, and so on. Let us suppose that the mercury is observed to stand at a height greater than 29 inches and 5 tenths, but less than 29 CHAP. IV. VERNIER. 201 inches and 6 tenths. Its level being expressed by the dotted line M, Jig. 17., let the vernier now be moved on Fig- 17. the scale until its highest division exactly coin- cides with the level of the mercury. On compar- ing the several divisions of the vernier with those of the instrument, let us suppose that we find that the division marked 4 on the vernier coincides with that marked 1 on the instrument ; then the dis- tance from the level of the mercury M to the next division below it, marked 5, will be 4 hundredth parts of an inch ; for the distance of the division marked 3 on the vernier above the division marked 2 on the instrument is 1 hundredth of an inch, be- cause it is the difference between a division of the vernier and a division of the instrument. Again, the distance of the division of the vernier, marked 2 above the division of the instrument marked 3, is 2 hundredths of an inch, and the distance of the division of the vernier marked 1 above the division of the instrument marked 4, is 3 hundredths of an inch. In like manner the division of the vernier marked is distant from the division of the instru- ment marked 5 by 4 hundredths of an inch. This will be manifest by considering what has been ~ILl_ 10 already explained. In general we are to observe r what division of the vernier coincides most nearly with any division of the instrument, and the figure which marks that division of the vernier will ex- press the number of hundredths of an inch in the distance of the level of the mercury from the next division of the instrument below it. (142.) The most immediate use of the barometer for scientific purposes ;s to indicate the amount and variation of the at- mospheric pressure. These variations, being compared with other meteorological phenomena, form the scientific data from which various atmospheric appearances and effects are to be deduced. The fluctuations in the pressure of the atmosphere being ob- served in connection with changes in the state of the weather, a general correspondence is supposed to prevail between these effects. Hence the barometer has been called a weather glass. Rules are attempted to be established, by which, from the height of the mercury, the coming state of the weather may be predicted, and we accordingly find the words " Rain," " Fair," " Changeable," " Frost," &c., engraved on the scale attached to common domestic barometers ; as if, when the mercury stands at the heigld marked by these words, the weather is always A TREATISE ON PNEUMATICS. CHAP IV Hi ' ta abha, , ef The variation in the altitude of the barometer in a cri, that when the mercury is very low, and therefore the at phere very hght, hi f h winds and sto'rms may be expected * at least to of fei TeTthi te th S ?fi f the p merCUry indicates the weather? ff f Jt Sh WS the a PP roach of unll?Ty b r e efe X r P r!nl ne to dST vfi ^{J ^^ considerations j which will bo os p hcro , which CHAP. IV. WEATHER GLASS. JJUtf 2. In sultry weather, the fall of the mercury indicates coming thunder. In winter, the rise of the mercury indicates frost. In frost, its fall indicates thaw ; and its rise indicates snow. 3. Whatever change of weather suddenly follows a change in the barometer may be expected to last but a short time. Thus, if fair weather follow immediately the rise of the mercu- ry, there Avill be very little of it ; and, in the same way, if foul weather follow the fall of the mercury, it will last but a short time. 4. If fair weather continue for several days, during which the mercury continually falls, a long succession of foul weather will probably ensue ; and again, if foul weather continue for several days, while the mercury continually rises, a long suc- cession of fair weather will probably succeed. 5. A fluctuating and unsettled state in the mercurial column indicates changeable weather. The domestic barometer would become a much more useful instrument, if, instead of the words usually engraved on the plate, a short list of the best established rules, such as the above, accompanied it, which might be either engraved on the plate, or printed on a card. It would be right, however, to ex- press the rules only with that degree of probability which ob- servation of past phenomena has justified. There is no rule respecting these effects which will hold good with perfect cer- tainty in every case. (143.) One of the most important scientific uses to which the barometer has been applied is the measuring of heights. If the atmosphere, like a liquid, were incompressible, this prob- lem would be very simple. The pressure on the mercury in the cistern would be equally diminished in ascending through equal heights. Thus, if the pressure produced by an ascent of 10 feet were equivalent to the weight of one inch of mercury, then the column would fall one inch in ascending that height. It would fall two inches in ascending 20 feet, three in ascend- ing 30 feet, and so on. To find, therefore, the perpendicular height of the barometer at any time above its position at any val between its inceptive and maximum velocity. We have supposed the size of the drop and the density of the air to remain the same. The increasing density of the medium retards the velocity of the drop, and causes it to press the air with a force a little superior to its own weight during this retardation, from the time it begins till the descent is completed, when the air is relieved from this pressure. If the foregoing views are correct, the atmospheric pressure will be affected, though in different ways, by the quantity of aqueous vapor in the atmosphere, by the quantity of that which, either in the form of clouds, rain, snow, or hail, is de- scending without having yet attained its maximum velocity, and by the quantity which has already attained this velocity. Hence the mercury of the barometer may be depressed in consequence of the descent of drops in their first stage, long before they reach the earth ; and this effect will be modified by the different por- tions in the subsequent stages, as well aa by other causes which affect the atmos- pheric pressure. AM. ED. 204 A TREATISE ON PNEUMATICS. CHAP. IV. other time, it would be only necessary to observe the differ- ence between the altitude ofthe mercury in both cases, and to allow 10 feet for every inch of mercury in that difference ; and a similar process would be applicable if an inch of mercury cor- responded to any other number of feet. But this explanation proceeds on the supposition, that in ascending through equal heights, the barometer leaves equal weights of air below it. Suppose in ascending 10 feet the mercury is observed to fall the hundredth of an inch, then it follows, that the air left below the barometer in such an ascent has a weight equal to the one hundredth of an inch of mercury. Now, in ascending the next 10 feet, the air which occupies that space, having a less weight above it, will be less compressed, and consequently within that height of 10 feet there will be contained a less quantity of air than was contained in the first 10 feet immediately below it. In this second ascent the mer- cury will, therefore, fall, not the hundredth of an inch, but a quantity as much less than the hundredth of an inch as the quantity of air contained in the second 10 feet of height is less than the quantity of air that is contained in the first 10 feet of height. In like manner in ascending the next 10 feet a still less quantity of air will be left below the instrument, and the mercury will fall in a proportionally less degree. If the only cause affecting density of the air were the com- pression produced by the weight of the incumbent atmosphere, it would be easy to find the rule by which a change of altitude might be inferred from an observed change of pressure. Such a rule has been determined, and is capable of being expressed in the language of mathematics, although it is not of a nature which admits of explanation in a more elementary and popular form. But there are other causes affecting the relation of the pressure to the altitude which must be taken into account. The density of any stratum of air is not only affected by the weight of the incumbent atmosphere, but also by the tempera- ture of the stratum itself. If any cause increase this tempera- ture, the stratum will expand, and with a less density will support the same incumbent pressure. If, on the contrary, any cause produce a diminution of temperature, the stratum will contract and acquire a greater density under the same pressure. In the one case, therefore, a change of elevation, which would be necessary to produce a given change in the height of the barometer would be greater than that computed on theoretical principles, and in the other case the change would be less. The temperature, therefore, forms an essential element in the calcu- lation of heights by the barometer. A rule or formulary has been deduced, partly from established theory, and partly from observed effects, by which the change. CHAP. IV. ATMOSPHERIC PRESSURE. 205 of elevation may be deduced from observations made on the barometer and thermometer. To apply that rule, it is necessary to know, 1st, the latitude of the place of observation ; 2dly, the height of the barometer and thermometer at the lower station ; and, 3dly, the height of the barometer and thermometer at the higher station. By arithmetical computation the difference of the levels of the two stations may then e calculated. The formulary does not admit of being explained without the use of mathematical language. (144.) It has been already stated, that the atmospheric pres- sure at the surface of the earth is capable of supporting a column of water 34 feet in height. It follows, therefore, that if our atmosphere were condensed to such a degree that its specific gravity would be equal to that of water, its height would be 34 feet. Now the specific gravity of a stratum of atmosphere con- tiguous to the surface is about 840 times less than the specific gravity of water ; that is, a cubic inch of water weighs 840 times more than a cubic inch of air. If as we ascend in the atmosphere it continued to have the same density, then its height would be evidently 840 times the height of 34 feet, which would amount to 28,560 feet, or 5 miles and a quarter. It is obvious, therefore, that since even at a small elevation the density of the atmosphere is reduced to half its density at the surface, the whole height must be many times greater than this. The barometer in the balloon in which De Luc ascended fell to the height of 12 inches. Supposing the barometer at the sur- face to have stood at that time at 30 inches, it follows that he must have left three fifths of the whole atmosphere below him. His elevation was upwards of 20,000 feet. (145.) A column of pure mercury, whose base is a square inch, and whose height is 30 inches, weighs about 15 Ibs. avoir- dupois. It follows, therefore, that when the barometer stands at 30 inches the atmosphere exerts a pressure on each square inch of the surface of the mercury in the cistern amounting to 15 Ibs. Now it is the nature of a fluid to transmit pressure equally in every direction ; and if the surface on which the atmosphere acts were presented to it laterally, obliquely, or downwards, still the pressure would be the same. Taking, therefore, the medium height of the barometric column at 30 inches, it follows that all bodies which exist at the surface of the earth exposed to our atmosphere are continually under this pressure, and that every square inch on their surface constantly sustains a force of about 15 pounds. Thus, the body of a man, the surface of which amounts to 2000 square inches, will sus- tain a pressure from the surrounding air to the enormous amount of 30,000 pounds. It might at first view be expected that this great force to 18 206 A TREATISE ON PNEUMATICS. CHAP. IV. which all bodies are subject would produce manifest effects, so as 'to crush, compress, or break them, whereas we find bodies of most delicate texture unaffected by it. Thus a close bag, made of the finest silver paper, and partially filled with air, is apparently subject to no external force. Its sides do not collapse. This arises partly from the circumstance of the pres- sure on every side, and in every direction being equal, and, therefore, producing mechanical equilibrium. It is obvious that a body which is driven in every possible direction upwards and downwards, laterally and obliquely, with equal forces, will not move in any one direction ; for to suppose such a motion would be to assume that the quantity of pressure in that direction exceeds the quantity of pressure in other directions. But still, though a body may not be driven in any direction by the atmos- pheric pressure, it may happen that its parts are crushed and compressed. We do not, however, find this to happen. This arises from the fact, that the elastic force of the air is equal to its pressure ; and since the internal cavities of a body, such as the thin bag above mentioned, are filled with air, which is con- fined within them, that air has precisely the same tendency to swell the bag, and to keep the parts asunder, as the external pressure of the atmosphere has to make them collapse. In the same manner we may account for the fact that animals move freely in the air without being sensible of the enormous pressure to which their bodies are subject. The internal parts of their bodies are filled with fluids, both in the liquid and gaseous states, which offer a pressure from within exactly equivalent to the external pressure of the air. This may be easily rendered manifest by applying to the skin the mouth of a close vessel, to which an exhausting syringe is attached. By this instrument, which will be described hereafter, the air may be rarefied in the vessel, and the atmospheric pressure conse- quently partially removed from the skin. Immediately the force of the fluid from within will swell the skin, and cause it to be sucked into the glass. This experiment may be perform- ed by the mouth on the flesh of the hand or arm. If the lips be applied to the flesh, and the breath drawn in so as to produce a partial vacuum in the mouth, the skin will be draM'n or sucked into the mouth. This effect is owing, not to any force resident in the lips or the mouth drawing the skin in, but to the fact that the usual external pressure is removed, and that the pressure from within is suffered to prevail. (146.) All cases of that class of effects which are commonly expressed by the word suction are accounted for in the same manner. If a flat piece of moist leather be put in close contact with a heavy body, as a stone, it will be found to adhere to it with CHAP. IV. SUCTION. BREATHING. 207 considerable force, and if a cord of sufficient length be attach- ed to the centre of the leather, the stone may be raised by the cord. This effect arises from the exclusion of the air between the leather and the stone. The weight of the atmosphere presses their surfaces together with a force amounting to 15 pounds on every square inch of those surfaces in contact. If the weight of the stone be less than the number of pounds which would be expressed by multiplying the number of square inches in the surfaces of contact by 15, then the stone may be raised by the leather ; but if the stone exceed this weight, it will not suffer itself to be elevated by these means. The power of flies and other insects to walk on ceilings and surfaces presented downwards, or upon smooth panes of glass in an upright position, is said to depend on the formation of their feet. This is such that they act in the manner above described respecting the leather attached to a stone ; the feet, in fact, act as suckers, excluding the air between them and the surface with which they are in contact, and the atmospheric pressure keeps the animal in its position. In the same manner the hydrostatic pressure attaches fishes to rocks. The pressure and elasticity of the air are both exercised in the act of breathing. When we draw in the breath we first make an enlarged space in the chest. The pressure of the ex- ternal atmosphere then forces air into this space so as to fill it. By a muscular action the lungs are next compressed so as to give this air a greater elasticity than the pressure of the exter- nal atmosphere. By the excess of this elasticity it is propelled, and escapes by the mouth and nose. It is obvious, therefore, that the air enters the lungs not by any direct act of these upon it, but by the weight of the atmosphere forcing it into an empty space, and that it is expired by the action of the lungs in com- pressing it.* The action of common bellows is precisely similar, except that the aperture at which the air is draAvn in is different from that at which it is expelled. In the lower board of the bellows * There are tv.-o sets of cavities concerned in respiration, one within the other. The air is admitted only into the interior cavities or those of the lungs, an organ contained in the chest. Neglecting the actual division of the chest into two cav- ities, as well as the cellular structure of the lungs, we may illustrate the pneu- matic principles of respiration by considering the lungs as a distensible and elastic bag, and the chest as a firm, yet dilatable box, in which it is contained, and by which its outer surface is alternately pressed and relieved from pressure. There is no empty space in the lungs, as but a small proportion of the air is expelled ; and I should prefer considering the elasticity of the portion which remains, rather than the atmospheric pressure, as the cause whic'-i directly produces the expansion of the lungs when the dilatation of the chest by the action of its muscles removes the pressure from the surface of the lungs. The diminished elasticity of the air which results from its expansion, allows the atmospheric pressure to preponderate, and force into the lungs new portions of air continually as long as they are dilating. Next, by a muscular action of the chest, assisted by the elasticity of certain parts, the air of the lungs ia compressed and partly expelled. AM. ED. 208 A TREATISE ON PNEUMATICS. CHAP. IV. is a hole covered by a valve, consisting of a flat piece of stiff leather, movable on a hinge, and which lies on the hole, but is capable of being raised by a slight pressure. When the upper board of the bellows is raised, the internal cavity is suddenly enlarged, and the air contained in it is considerably rarefied. The pressure of the atmosphere forces in air at the nozle ; but this being too small to allow its admission with sufficient ease and speed, the valve covering the hole is acted upon by the atmosphere, and raised, and air rushes in through the large aperture under it. When the space between the boards is filled with air in its common state, the upper board is depressed, and the air confined in the bellows is suddenly condensed. The valve covering the hole is thus kept firmly closed, and the air has no escape except through the nozle, from which it issues with a force proportional to the pressure exerted on the upper board. A bellows, such as that in common domestic use, thus simply constructed, has an intermitting action, and blows by fits, its action being suspended while the upper board is being raised. In forges and large factories, in which fires are exten- sively used, it is found necessary to command a constant and unremitting stream of air, which may be conducted through the fuel so as to keep it in vivid combustion. This is effected by bellows with three boards, the centre board being fixed and furnished with a valve opening upwards, the lower board being movable with a valve also opening upwards, and the upper board being under a continual pressure by weights acting upon it. When the lower board is let down, so that the chamber between it and the middle board is enlarged, the air 'included between these boards being rarefied, the external pressure of the atmos- phere will open the valve in the lower board, and the chamber between the lower and middle boards will be filled with air in its common state. The lower board is now raised by the power which works the bellows, and the air between it and the middle board is condensed. It cannot escape through the lower valve, because it opens upwards. It acts, therefore, with a pressure proportional to the working power on the valve in the middle board, and it forces open this valve, which opens upwards. The air is thus driven from between the lower and middle boards into the chamber between the middle and upper boards. It cannot return from this chamber, because the valve in the mid- dle board opens upwards. The upper board being loaded with weights, it will be condensed while included in this chamber, and will issue from the nozle with a force proportionate to the weights. While the air is thus rushing from the nozle, the lower board is let down and again drawn up, and a fresh supply of air is brought into the chamber between the upper and mid- dle board. This air is introduced between the middle and CHAP. IV. VENT-PEG. TEA-KETTLE, &/C. 209 upper board before the former supply has been exhausted, and by working the bellows with sufficient speed a large quantity of air will be collected in the upper chamber, so that the weights on the upper board will force a continual stream of air through the nozle. The effect produced by a vent-peg in a cask of liquid depends on the atmospheric pressure. If the vent-peg stop the hole in the top while the liquid is discharged by the cock below, a space will remain at the top of the barrel in which the air originally confined is allowed to expand and become rarefied : its pressure on the surface of the liquid above will, therefore, be less than the atmospheric pressure resisting the escape of the liquid at the cock ; but still the weight of the liquid itself, pressing down- wards towards the cock, will cause the discharge to continue until the rarefaction of the air becomes so great, that the excess of the atmospheric pressure is more than sufficient to resist the escape of the liquid ; the flow from the cock will therefore be stopped. If the vent-peg be now removed from the hole, air will be heard to rush in with considerable force and fill the space above the liquid. The atmospheric pressure on the surface above and on the mouth of the cock being now equal, the liquid will escape from the cock by the effect of the pressure of the superior column, according to the principles established in hydrostatics. If the vent-peg be again placed in the hole'; the flow from the cock will be gradually diminished, and will at length cease. Upon the removal of the vent-peg, the same effect will be ob- served as before. If the lid of a tea-pot be perfectly close,. and fit the mouth air-tight, or if the interstices, as frequently happens, be stopped by the liquid which lies round the edge of the mouth, then all communication between the surface of the liquid in the vessel and the external air is cut off. If we now attempt to pour liquid from the tea-pot, it will flow at first, but will immediately cease. In this case the air under the lid becomes rarefied, and the pressure on the surface of the liquid in the tea-pot is so far diminished, that the atmospheric pressure resists its discharge at the spout. To remedy this inconvenience, it is usual to make a small hole somewhere in the lid of the tea-pot for the admission of air ; this hole serves the same purpose as the hole for the vent-peg in the cask. Although it is not usually practised, a small hole should be made in the lid of a kettle, but for a different reason. If the lid of a kettle fit it closely, so as to stop all communication be- tween the external air and the interior of the vessel, when the water contained in it becomes heated, team will rise from its surface, and the air enclosed in the space between the surface 18* 210 A TREATISE ON PNEUMATICS. CHAP. IV. and the lid being heated, will acquire an increased elastic force. From these causes, the pressure which acts on the surface of the water in the kettle will continually increase, so long as the lid maintains its position : this pressure, transmitted by the water in the kettle, will overcome the pressure of the atmos- phere acting on the water in the spout, and the effect will be that the water will be raised in the spout and flow from it ; or, if the lid be not firmly enough fixed to withstand the pressure of the steam, it will be blown off the kettle. Such effects fall within every one's experience. If a small hole were made in the lid these effects would be prevented. Ink bottles, constructed so as to prevent the inconvenience of the ink thickening and drying, owe their efficacy to the atmospheric pressure. The quantity of evaporation which takes place in the liquid, other circumstances being the same, is proportional to the quantity of surface exposed to the external air. To diminish this quantity of surface, without inconvenient- ly diminishing the quantity of ink in the bottle, bottles have been constructed of the shape represented in/g\ 18. A B is a Fig. 1C. close glass vessel, from the bottom of which a short tube B proceeds, from which another short tube rises perpendicularly. The depth of the tube C is such as will be sufficient for the immersion of a pen. When ink is poured in at C, the bottle, being placed in an inclined position, is gradually filled up to the knob A : if the bottle be now placed in the position repre- sented in the figure, the chamber A B being filled with the liquid, the air will be excluded from it, and the pressure tend- ing to force the ink upwards in the short tube C will be equal to the weight of the column of ink, the height of which is equal to the depth of the ink in the bottle A B, and the base of which is equal to the section of the tube C. This will be manifest from the properties of hydrostatic pressure established in Hy- drostatics, chap. iii. Now the atmospheric pressure acts on the surface C with a force which would be capable of sustaining a column of ink many times the height of the bottle A B ; conse- CHAP. IV. PNEUMATIC TROUGH. 211 quently, this pressure will effectually resist the escape of the ink from the mouth C, and will keep it suspended in the bottle A B. In this case the whole surface, which is exposed to the effect of evaporation, is the surface of liquid in the tube C ; and, consequently, an ink bottle of this kind may be left many months in a warm room, and no perceptible diminution in the quantity of ink, or change in its quality, will take place. As the ink in the short tube C is consumed by use, its surface will fall to a level with the tube B. A small bubble of air will then insinuate itself through the tube B, and will rise to the top of the bottle A B ; there it will exert an elastic pressure, which will cause the surface in C to rise a little higher, and this effect will be continually repeated until all the ink in the bottle has been used. The only inconvenience which has been attributed to these ink bottles arises from sudden changes in the temperature to which they are exposed. When the external air, having been previously warm, becomes suddenly cool, the small quantity of air which is included in the bottle A, not being cooled BO fast as the external air, will exert an elastic pressure which will cause the ink. to overflow at C. This is an effect, however, which we have never observed, although we have seen these bottles much used.* If such an ink bottle be placed upon a marble chimney-piece, or any other surface heated beyond the temperature of the air in the room, the air confined in the bottle will then become heated, and acquire increased elastic force, and, in this case, the ink will overflow. The fountains for supplying water to bird cages are con- structed upon the same principle. The pneumatic trough used in the chemical laboratory, and the gas holders, or gasometers, used in gas works, depend on the atmospheric pressure. A vessel, having its mouth upwards, is completely filled with a liquid. The mouth is then stopped, a flat piece of glass, or a smooth plate of metal, pressed against it, and the vessel is inverted, the mouth being plunged in a cistern filled with the same liquid. If the height of the vessel in this case be less than the height of the column of the liquid which the atmospheric pressure would support, the vessel will continue to be completely filled with the liquid, even after the plate is removed from its mouth ; for the atmospheric pressure acting on the surface of the liquid in the cistern will prevent the liquid contained in the vessel from falling out of it. Any one may satisfy himself of this fact. Take a wine glass, and * If any inconvenience arise, it would be from an increase in the temperature, and consequently the elasticity, of the included air, or from a diminution of tho at- mospheric pressure. AM. ED. 212 A TREATISE OX PNEUMATICS. CHAP. IV. fill it with water, and then, having applied a piece of card to its mouth so as to prevent the water from escaping, invert it, and plunge the mouth downwards in a basin of water. Let the card be then removed, and let the glass be raised above the surface, still, however, keeping the edge of its mouth below the surface. It will be observed that the glass will still remain completely filled with water. Take a small quill, or a hollow piece of straw, and insert one end in the water, so that it will be imme- diately below the mouth of the glass, and at the same time blow gently through the other end, so as to introduce air in small quantities into the water immediately under the mouth of the glass. This air will ascend in bubbles, and will find its way to the highest part of the glass, and, remaining there, will expel the water from it ; and this will continue so long as air is supplied, until all the water contained in the glass is expelled from it, and the glass is filled with air. If the process be further continued, tho air will begin to escape under the edge of the glass, and rise in bubbles to the surface. The pneumatic trough is a large cistern filled with mercury, in which is placed, below the surface of the liquid, a shelf to support a receiver. By plunging any vessel in the deeper part of the trough, it may be filled with mercury, and if it be slowly raised, keeping its mouth still below the surface of the liquid, it will still remain filled with mercury by the pressure of the atmosphere acting on the surface of the mercury in the trough. The mouth of the vessel may then be placed on the shelf, while the vessel itself is above the surface of the mercury. The trough is represented infg. 19. at A B. The shelf is placed .in Fig. 19. it at C ; a receiver R is placed on the shelf, with its mouth downwards, over an aperture D, which communicates with a CHAP. IV. NOISE IN DECANTING WINE. 213 tube, by which gas may be introduced. The gas passing through the tube rises in bubbles through the mercury in the receiver, and lodges at the top ; and, by continuing this process, the whole of the mercury will at length be expelled from the receiver, and its place filled with the gas. In this manner gases of various kinds may be preserved out of contact with the at- mosphere, and the same shelf may be furnished with several holes, and may support a number of different jars. The gasometer used in gas works is constructed on the same principles, only on a different scale. When used for great sup- plies of gas, such as are necessary for the illumination of towns, these vessels are constructed of a very large size, and are im- mersed in pits lined with cast iron, and filled with water. It is clear that all which has been just explained will be equally applicable, whatever be the liquid used in the cistern ; and for different gases it is necessary to use different liquids, since the contact with particular liquids will frequently affect the quality of the gas. The peculiar guggling noise which is produced in decanting wine, arises from the pressure of the atmosphere forcing air into the interior of the bottle. In the first instance, the neck of the bottle is completely filled with liquid, so as to stop the admis- sion of air. When a part of the wine has flowed out, and an empty space is formed within the bottle, the atmospheric pres- sure forces in a bubble of air through the liquid in the neck, which, by rushing suddenly into the interior of the bottle, pro- duces the sound alluded to. This effect is continually repeated so long as the neck of the bottle continues to be choked with the liquid. But as the contents of the bottle are discharged, the liquid, in flowing out, only partially fills the neck, and while a stream of wine passes out through the lower half of the neck, a stream of air passes in through the upper part. The flow in this case being continual and uninterrupted, no sound takes place. The atmospheric pressure acting on the surface of liquids maintains air combined with them in a greater or lesser quan- tity, according to the nature of the liquid. If an open vessel, containing a liquid, be placed under a receiver, and the air be exhausted, the air combined with the liquid will be immediately set free, and will be observed to rise in bubbles to the top. This effect will be very perceptible if water be used, but still more so in the case of beer or ale. When liquor is bottled, the air confined under the cork is condensed, and exerts upon the surface a pressure greater than that of the atmosphere. This has the effect of holding in com- bination with the liquor air, which under the atmospheric pres- sure only would escape. If any air rise from the liquor after 214 A TREATISE ON PNEUMATICS. CHAP. V. being bottled, it causes a still greater condensation, and an in- creased pressure above its surface. If the nature of the liquor be such as to produce air in con- siderable quantity, this condensation will at length become so great as to force out the cork ; or, failing to do that, break the bottle. This is found to happen frequently with beer, ale or porter. The corks in such cases are tied down by cord or wire. When the cork is drawn from a bottle containing liquor of this kind, the fixed air being relieved from the pressure of the air which was condensed under the cork instantly makes its escape, and, rising in bubbles, produces effervescence and froth. Hence the head observed on porter and similar liquors, and the sparkling of champagne or cider. CHAP. V. RAREFACTION AND CONDENSATION OF AIR. EXHAUSTING SYRINGE. RATE OF EXHAUSTION. IMPOSSIBLE TO PRO- DUCE A PERFECT VACUUM. MECHANICAL DEFECTS. THE AIR PUMP. BAROMETER GAUGE. SYPHON GAUGE. VARIOUS FORMS OF AIR PUMP. PUMP WITHOUT SUCTION VALVE. EXPERIMENTS WITH AIR PUMP. BLADDER BURST BY ATMOSPHERIC PRESSURE. BLADDER BURST BY ELASTICITY OF AIR. DRIED FRUIT INFLATED BY FIXED AIR. FLACCID BLADDER SWELLS BY EXPANSION. WATER RAISED BY ELASTIC FORCE. A PUMP CANNOT ACT IN THE ABSENCE OF AT- MOSPHERIC PRESSURE. SUCTION CEASES WHEN THIS PRESSURE IS REMOVED. THE MAGDEBURG HEMISPHERES. GUINEA AND FEATH- ER EXPERIMENT. CUPPING. EFFERVESCING LIQUORS. SPARK- LING OF CHAMPAGNE, ETC. PRESENCE OF AIR NECESSARY FOR THE TRANSMISSION OF SOUND. THE CONDENSING SYRINGE. THE CON- DENSER. (147.) WHEN a part of the air enclosed in any vessel is with- drawn, that which remains, expanding by its elastic property, fills the dimensions of the vessel as effectually as before. Un- der these circumstances, however, it is obvious, that any given space within the vessel contains a less quantity of air than it did previously, inasmuch as, while the whole dimensions of a vessel remain the same, tlje total quantity of air diffused through them is diminished. When the same quantity of air in this manner is caused^to expand into a greater space, it is said to be rarefied. But on the other hand, when a vessel containing any quantity of air is caused to receive an increased quantity, by additional CHAP. V. EXHAUSTING SYRINGE. 215 Fig. 20. J\. air being forced into it, then any given portion of its dimen- sions will contain a proportionally greater quantity of air than it did before tho additional air had been forced in. Under these circumstances, the air contained in the vessel is said to be con- densed, and it is our purpose in the present chapter to describe the mechanical instruments by which these processes of rare- faction and condensation are practically effected. The Exhausting Syringe. (148.) The most sirnplo form of instrument for producing the rarefaction of air is that which is called the exhausting syr- inge. In order to comprehend the construction and operation of this instrument, let us suppose AB,Jig. 2(X, a cylinder, or barrel, furnished with a stopcock C, inserted in a small aperture in the bottom. Let the end of this tube be screwed upon the vessel R, in which the rarefaction is to be made. From the side of the barrel, near the bot- tom, let another tube D proceed, also fur- nished with a stopcock. Let us suppose the piston P at the bottom of the barrel, both stopcocks being closed. Let the pis- ton P be now drawn from the bottom to the top, as represented in Jig. 21., this piston being supposed to move air-tight in the barrel. A vacuum will remain between the piston P and the bottom B. If the stopcock C be opened, the air contained in the vessel R will, by its elastic force, rush through the open stopcock C, and expand so as to fill tho barrel. Thus the air which previously occupied the dimensions of the ves3el R has HOAV expanded through the dimensions of R and A B. Let the stop- cock C be now closed, and the stopcock D opened, and let the piston P be pressed to the bottom of the barrel. The air contained in the barrel will thus be forced out at the open stopcock D, and driven into external atmosphere. Let the stopcock D be next closed, and the piston again ele- vated, as in fig. 21. A vacuum will once more be produced in the barrel ; and, on opening the stopcock C, the air in R will ugain expand into the barrel, occupying the extended dimensions as before. Let the stopcock C be again closed, and the stop- cock D opened. If the piston be pressed to the bottom of the b:.rrcl as before, the air contained in the cylinder Avill again be 216 A TREATISE ON PNEUMATICS. CHAP. V. Fig. 21. expelled through the stopcock D. By continuing this process, alternately opening and closing the two stopcocks, and elevat- ing and depressing the piston, a quantity of air will rush from the vessel R on each ascent of the piston, and the same quantity will be expelled through the tube D on each descent of the piston. It is evident that this process may be con- tinued so long as the air Avhich remains in R is capable of expanding, by its elasticity, through the open tube C into the barrel above. A slight degree of attention only is neces- sary to perceive that the quantity of air ex- pelled from R at each ascent of the piston is continually diminished ; and it will not be difficult even to explain the exact rate at which this diminution proceeds. Let us sup- pose the magnitude of the barrel A B to have any given proportion to the dimensions of the vessel R ; suppose, for example, that the di- mensions of the barrel are the ninth part of those of the vessel. "When the piston is first raised from the bottom to the top, the air which previously occupied the vessel expands so as to occupy the dimensions of the vessel and barrel together. The barrel, therefore, will contain a tenth part of the whole of the enclosed air ; for since the vessel R contains nine times as much as the barrel, the vessel and barrel together contain ten times as much as the barrel. Consequently the air enclosed in the barrel will necessarily be a tenth of the whole. On de- pressing the piston, this tenth part is expelled through the tube D. On elevating the piston, the air remaining in the vessel R, which is nine tenths of the original quantity, now expands through the vessel and barrel, and, for the reason already as- signed, the barrel will contain a tenth part of this remaining 9 tenths ; that is, it will contain 9 hundredth parts of the original quantity. On the second descent of the piston, this 9 hundredth parts will be expelled. The 9 tenths which remain in the cyl- inder after the first stroke of the piston, have now lost 9 hun- dredth parts of the whole ; and, since 9 tenths is the same as 90 hundredths, 9 hundredths being deducted from that leave a remainder of 81 hundredths. This, therefore, is the proportion of the original quantity which now remains in the vessel R. When the piston is next raised, this portion will expand, as before, into the enlarged CHAP. V. EXHAUSTING SVR1NGE. 217 space, and the tenth part of it will rise into the barrel. But a tenth part of 81 hundredths is 81 thousandths. Accordingly, on the next descent, this 81 thousandths will be expelled. The 81 hundredths which remained in the vessel R before this dim inution are thus diminished by 81 thousandths. This 81 hun dredths are equivalent to 810 thousandths, and, therefore, the quantity remaining in the vessel R will be found by subtracting 81 thousandths from 810 thousandths. The remainder will, therefore, be 729 thousandths, which will be the proportion of the original quantity of air which remains in the vessel after tho third stroke of the piston. It will not be difficult to continue this reasoning further, and to discover not only the quantity of air expelled at each successive stroke, but also the quantity remaining in the vessel R ; and we may, without difficulty, compute the following table : Number of Strokes. Proportion of the original quantity of air expelled at each stroke. Proportion of the original quantity of air remaining after each stroke. Total quantity of air expelled. 1 10 9 10 i 10 2 9 Too 81 100 19 100 3 81 1,000 729 1,000 27J 1,000 4 729 10,000 6,561 10,000 3,439 10,000 5 6,561 100,000 59,0-19 100,000 , 40,951 100,000 59,049 531,441 468,559 6 1,000,000 1,000,000 1,000,000 7 531,441 10,000.000 4,782,969 10,000,000 5,217,031 10,000,000 To make this table more intelligible, let us suppose that the vessel R contains, in the first instance, 10,000,000 grains of air. The first stroke of the piston expels a tenth part of this quanti- ty, that is, 1,000,000 grains. There remain in the vessel R 9,000,000 grains. The tenth part of this 9,000,000 is expelled by the second stroke, that is, 900,000 grains of air. There now remain in the vessel, 8,100,000 grains. Of this again a tenth 19 218 A TREATISE ON PNEUMATICS. CHAP. V. part is expelled by the third stroke, that is, 810,000 grains. The quantity remaining in the receiver will then be 7,290,000 grains. The tenth part of this is expelled by the fourth stroke, that is, 729,000 grains, and there remain in the vessel 6,561,000 grains. The fifth stroke expels a tenth part of this, or 656,100 grains, and there then remain in the vessel, 5,904,900 grains. A tenth part of this again is expelled by the sixth stroke, that is, 590,490 grains, and the remainder in the vessel is 5,314,410 f rains. A tenth of this again, or 531,441 grains, is expelled y the seventh stroke. The following table exhibits these results : Number of Strokes. Grains expelled at each stroke. Grains remaining under pressure. Total number of grains expelled. 1 1,000,000 9,000,000 1,000,000 2 900,000 8,100,000 1,900 ; 000 3 810,000 7,290,000 2,710,000 4 729,000 6,561,000 3,439,000 5 656,100 5,095,900 4,095,100 6 590,490 5,314,410 4,685,599 7 531,441 4,782,969 5,217,031 By attending to the numbers in the third column of the above table, it will be perceived, that each succeeding number is nine tenths of the preceding one. It follows, therefore, that after each stroke of the piston, the quantity of air which re- mains in the vessel R will be nine tenths of the quantity which it contained before the stroke. From a due consideration of this circumstance, it will be perceived that, however long the process of rarefaction be continued, the vessel R can never be completely exhausted of air ; for, a determinate quantity being contained in it, nine tenths of this will remain after the first stroke. After the second stroke, nine tenths of this again will CHAP. V EXHAUSTING SYRINGE. 219 remain, and, however long the operation be continued, still a determinate quantity will remain after every succeeding stroke of the .piston, this quantity being nine tenths of what the vessel R contained after the preceding stroke. But although a per- fect exhaustion can never be attained by these means, yet if the instrument ROAV described could be constructed as perfect in practice as it is in theory, there would be no limit whatever to the degree to which the air in the vessel-R might be rarefied. Thus, by a determinate and finite number of descents of the piston, it might be reduced in weight to the millionth part of a grain, or even to a quantity millions of times less than this. Still, however small the quantity which may remain in the vessel R, so long as the elastic force by which the particles repel each other exceeds the weight of the final or ultimate particles of the air, so long that repulsive energy will cause it to expand through the tube C into the cylinder A B.* The exhausting syringe used in practice differs in some particulars from that which we have here described with a view to illustrate the principle of its operation. The stopcocks C and D, which would require constant ma- nipulation while the process of rarefaction is going forward, are dispensed with in practice, and the elastic pressure of the air itself is made to act upon valves which serve the pur- poses of these cocks. Let A B, Jig. 22., rep- resent an exhausting syringe, having a tube and stopcock C proceeding from the lower part as already described. The tube C is screwed to a very small aperture in the bottom of the barrel. Across this aperture is stretched a small piece of oiled silk, which is impervious to air. It is extended across the aperture so loosely, that a slight pressure from below will produce an open space between it and the sur- face of the bottom near the aperture, capable of admitting air from below, and yet so tight that a pressure from above will cause it to lie close against the bottom, round the aperture, BO as to stop the passage of air from above. By this arrangement it is possible for air pressed with a sufficient force to enter the barrel through the * If the quantity of air in the vessel R at the commencement of the process be expressed by 1, then the quantity after one stroke of the piston will be (- 9 ?7 ), after tico strokes 2 2 , after ** strokes ami after n stroke*! 220 A TREATISE ON PNEUMATICS. CHAP. V. valve V, when the stopcock C is opened; but it is impossible, the other hand, for air pressing above the valve to escape through it, since the pressure of the air only serves to render more close the contact between the valve and the surface sur- rounding the aperture which it covers. A small hole is pierced irough the piston, extending from the lower to the upper surface, and this hole at the upper surface is covered with an oiled silk valve V, in the same manner as the aperture V in the bottom. For the reasons already assigned it is, therefore, pos- s tor air to pass up through this hole in the piston, and escape at the upper surface ; but it is impossible for air, by any pressure to pass m the contrary direction, since such pressure only renders the contact of the valve more intimate, and, conse- quently, causes it to be more impervious to air. Let us suppose an instrument thus constructed to be attached to a vessel R, m which the rarefaction is to be produced, and the stopcock C to be opened. On raising the piston P a vacu- um will be produced between it and the valve V. The piston valve V' will now be pressed downwards by the weight of the atmosphere, and will be subject to no pressure from below ecause of the absence of air beneath it. It will then stop ie admission of air from above the aperture, and will maintain .e vacuum below. The elastic force of the air contained in me vessel K now acting upwards against the exhausting valve V will raise it, and the air will escape through the space be- ST^Sn'V 11 !? the surface surrounding the aperture, and will the barrel above ; but the air having expanded into an Teased space will have an elastic force less than that of the 3rnal air, and consequently the piston valve V' will be press- d down by a greater force than it is pressed up, and will therefore remain closed. Let the piston be now depressed : as iscends the air enclosed in the cylinder acquires increased force, and pressing upon the exhausting valve V causes close, so as to intercept the air in the cylinder from the I K. When the piston has descended in the barrel throuo-h icn a space as to condense the air beneath it, so as to give it a greater elastic force than the external atmosphere, it will press the piston valve V upwards, with a greater force than the external air presses it downwards. Consequently the valve V will be opened, and the air confined beneath the piston will begin to escape through it. When the piston has arrived at the bottom of the barrel, the whole of the air will thus be ex- pelled. This process is repeated whenever the piston is raised depressed ; and thus the valves, which in the form adopted tor explanation required constant manipulation, acquire a self- ctmg property. This form of the instrument, which is that mmonly used, is attended with an obvious limit to its opera- CHAP. V. EXHAUSTING SYRINGE. 221 tion, which does not exist in the theoretical form represented in Jig. 20. It is evident that the operation of the valves depends upon the presence of air of a certain determinate elastic force in the vessel R, which elastic force it is the purpose of the in- strument to reduce indefinitely. When the elastic force of the air contained in R is so far diminished that it is only equal to the force required to raise the valve V, the action of the ma- chine must stop, for any further diminution would render the air confined in R unable to open the valve, and therefore no more air could pass into the barrel A B. This is a practical limit of the power of the exhausting syringe. The degree of perfection of which the instrument is susceptible, therefore, depends upon making the valve V offer as little resistance to being raised as is consistent with its being perfectly air-tight when closed. But we have another limit to the operation of this instrument, arising from the piston valve V. This valve is closed not only by its own tension, but also by the weight of the incumbent atmosphere above it. When the piston is depressed, the air included in the barrel must first attain a degree of elastic force by condensation equal to the pressure of the atmosphere, before it can open the valve V. But this is not sufficient : it must acquire a further increased elastic force equal to the tension of the valve V over the aperture, in order to raise that valve and escape, and therefore the perfection of this valve also depends on having as little tension as is consistent with being perfectly air-tight from above. The efficiency of the instrument will also depend upon the accuracy with which the piston fits the bottom and sides of the barrel. When the piston is depressed to the bottom, it is con- sidered in theory to be in absolute contact, so as to exclude every particle of air from the space between it and the bottom. But in practice this perfection can never be obtained. It may, however, be very accurately fitted, and the air retained between it and the bottom may be reduced almost without limit. The small hole which passes from the valve V' to the bottom of the piston will still remain, however, and will continue to be a re- ceptacle for air, even when the piston is in close contact with the bottom. This space, therefore, produces a defect in the machine which is not removed.* If we suppose the magnitude * It is owing to this, and to the want of accuracy in the mechanical construc- tion of the piston and barrel, that the limitatior^mentioned in the preceding para- graph can exist. However small the quantity of air remaining, if it could be pent up in a space infinitely small, its elasticity wouJJ overcome the resistance of the piston valve and that of tho atmospheric pressure. On the contrary, there is nothing to overcome tho resistance of the exhausting valve but the enfeebled energy of rarefied air. This renders some mechanical _ method of opening tho ex- hausting valvo mo-e mrc^sary to tho perfection oi't'ie instrument. AM. ED. A TREATISE ON PNEUMATICS. CHAP. V. of this hole, together with whatever space may remain unfilled between the lower surface of the piston and the bottom of the barrel to be the ten thousandth part of a solid inch, then the valve V' will cease to act when the air which fills the barrel e piston being at the top, is such that, if condensed into the thousandth part of an inch, its elastic force will exceed the atmospheric pressure by a quantity less than the force required to open the valve V'. This source of imperfection will evidently be diminished by diminishing the depth of the aperture below the valve V and by increasing the size of the cylinder ; for if the air in the'bar- i be as many times rarer than the external atmosphere, as the magnitude of the barrel is greater than the magnitude of the space below the valve V, then this air, when condensed into that space, will exert a pressure equal to that of the atmos- here. Suppose the barrel contains ten cubic inches ~of air nd that the magnitude of the hole is the hundredth part of a cubic inch, then the magnitude of the cylinder will be 1000 times the magnitude of the space which remains between the valve and the bottom of the barrel, when the piston is pressed ) the bottom. Consequently the process of rarefaction would deduced until the air in the receiver would be rendered 1000 times rarer than the external atmosphere. The vessel R being connected with a tube furnished with a stopcock C may be detached from the syringe together with the stopcock by unscrewing the tube C ; and if the stopcock be mously closed, the interior of the vessel will continue to contain the rarefied air. In various branches of physical science inquiries continually arise respecting qualities and effects , of material substances, which are subject to considerable modification by the pressure or other qualities of the air which surrounds them ; and it is ten necessary m such investigations to discover what these qualities and effects may be, if the substances were not exposed te mechanical pressure or other effects consequent upon the resence of the atmosphere. Although we do not possess any means of removing altogether the presence of this fluid, yet rom what has been already stated it is plain that it may be so attenuated m an enclosed chamber, such as the vessel R, that these effects may be diminished in intensity to any degree which experimental inquiry may demand. With these views it is necessary, however, not only to be to introduce the substances which are submitted to exper- imental investigation into the chamber in which the rarefaction 3 been accomplished, but also to be able to observe them when so situated. The latter purpose could be accomplished by constructing the receptacle R of ghss ; but still it would be CHAP. V. AIR PUMP. 223 necessary to have access to the interior, and to construct it of a convenient form to receive the subjects of experiment, and even in many cases to be able to manipulate or produce changes of position on the object thus enclosed. For these purposes the form of the vessel R, and the mode of connecting it with the syringe, must be somewhat changed, and the arrangement which is given in order to adapt them thus to all the exigencies of experimental investigation is called THE AIR PUMP, an instrument which we will now proceed to explain. The Air Pump. (149.) The vessel in which the rarefaction is produced by an air pump is called a Receiver, and is usually constructed of glass, in a cylindrical form, with an arched or round top, furnished with a ball as a convenient handle. A section R of this is rep- resented in Jig. 23. The mouth or lower part is open, and it is Fig. 23. ground to a perfectly smooth and flat edge. A circular brass plate is constructed, also ground truly plane and perfectly smooth, and its magnitude is accommodated to the size of the largest receiver intended to be used ; a section of this plate is represented at S S. When the receiver is placed on the plate with its mouth downwards, the edge of the mouth and the surface of the plate should be so truly plane and smooth, that they may rest in air- tight contact. This may always be insured by smearing the 224 A TREATISE CX PNEUMATICS. CHAP. V ground edge of the receiver with a little lard or unctuous mat- ter. Wheji the receiver is thus laid on the plate it becomes an enclosed chamber, similar to R, Jig. 22., but with this con- venience, that any substance or object to be submitted to experiment may be previously placed under it, and observed through it after the air has been rarefied. In the centre of the plate S S a small aperture O communicates with a tube T, analogous to the tube inserted in the bottom of the syringe in fg. 22. This tube is furnished with a stopcock at C, which when closed cuts off all communication between the receiver and the syringe, and -when open allows the syringe to act en the receiver as already described. The syringe B furnished with a piston P is fixed on a firm stand, and the tube T is carried in such a direction as to open a communication with the valve V in the bottom of the syringe. To facilitate the operation, it is usual to raise and depress the piston, not by the hand applied at the extremity of the piston rod as formerly described, but by a winch D, which turns a toothed wheel W, working in corresponding teeth, formed on the edge cf the piston rod E. It is not necessary again to describe the operation of the syringe, since it is exactly what has been already explained with reference to Jig. 22. The piston P is elevated and depressed by alternately turning the wheel W in opposite directions, and the piston valve \ T/ and the exhausting valve V have the property and work in the manner already described. This instrument and that represented in fig. 22. differ in noth- ing except the length and shape of the communicating tube T, the shape of the receiver R, and the mechanical method of working the piston. To expedite the process of rarefaction, it is usual to provide two syringes worked by the same wheel as represented in the figure, each being drawn up while the other is depressed. By these means a given degree of rarefaction is produced in half the time which would be required with a single syringe. In using this instrument it is always desirable, and frequently necessary, to ascertain the degree of rarefaction whicli has oeen accomplished within the receiver. This is indicated, with great precision, by an apparatus called a barometric gauge, repre- sented at H G. This consists of a glass tube II G, the upper end H of which has free communication with the receiver or rather with the tube T at some point above the stopcock C. The" tube H G is more than 30 inches in length, and its lower extremity is plunged in a small cistern of mercury. As the rarefaction proceeds in tho receiver, the elastic force of the air pressing upon the mercury in the tube H G is diminished, and immediately becomes less than the pressure of the external CHAP. V. SIPHON GAUGE. 225 atmosphere on the surface of the mercury in the cistern M ; consequently this external pressure prevails, and forces mercury up to a certain height in the tube G H. As the rarefaction of the air in the receiver increases, its elastic force being dimin- ished, the atmospheric pressure will prevail with increased effect, and will cause the column sustained in the tube to rise. The weight of this column, combined with the elastic pressure of the air remaining in the receiver, is equal to the atmospheric pressure, because they are balanced by it, and it is therefore apparent that the elastic pressure of the air in the receiver must be equal to the excess of the atmospheric pressure above the weight of the mercurial column in the tube. Let us suppose that the common barometer stands at 30 inches, and that the column in the gauge measures 27 inches, the difference between these, namely, 3 inches of mercury, will express the elastic force of the rarefied air in the receiver ; for the column of 30 inches in the barometer measures the atmospheric pressure, and the column of 27 inches in the gauge must be added to the pressure of the rarefied air, in order to obtain the force which balances this pressure ; therefore the force of the rarefied air must be equivalent to the pressure of 3 inches, by which the barometric column exceeds the mercurial column suspended in the gauge. In small pumps, which are used on the table, gauges of this form are rejected in consequence of their inconvenient dimen- sions. An instrument called a siphon gauge is then used, the principle of which is easily understood. A small glass tube, of 8 or 10 inches in length, is bent into the form A B C D, repre- sented in Jig. 24. The extremity A is closed, and the extremity D opened and furnished with a screw, by which it may be attached to a tube con- nected with the tube T, Jig. 23., above the stop- cock C. Pure mercury is poured into the tube A B C D, Jig. 24., until the leg A B is completely filled, and the mercury rises to S about half an inch above the inflection B. The pressure of the atmosphere communicating freely with the sur- face S through D C will maintain the mercury in the space S B A, and will prevent the surface S from rising towards C by the pressure of the column B A. When D is screwed to the pump, and put in communication with the exhausting tube T, Jig. 23., above the stopcock C, then the surface S will be pressed by the elastic force of the air in the receiver R, with which it communicates. So long as that elastic force is capable of sustaining the column of mercury in the leg B above the level of the surface S, this instrument will give no indica- Fig. 24. 220 . A TREATISE ON PNEUMATICS. CHAP. V tion of the degree of rarefaction ; but when, by the operation of the syringe, the air in the receiver is so far exhausted that its elastic force is unable to sustain the mercurial column in B A above the level S, then the mercury will begin to fall in the leg B A, and the surface S will rise in the leg B C. The column suspended in the leg B A, above the level S, will now be the exact measure of the elastic force of the air in the receiver which sustains it. In this respect the siphon gauge must be regarded as a more direct measure of the elastic force of the air in the receiver than the barometer gauge. The lat- ter, in fact, measures, not the elastic force of the air in the receiver, but the difference between that elastic force and the pressure of the atmosphere. To obtain the elastic force of the air in the receiver it is necessary also to ascertain the indica- tions of the barometer. The siphon gauge, however, gives at once the pressure of the air in the receiver. (150.) The air pump has been constructed from time to time in a great variety of forms, the details of which it would not be proper to introduce into the present treatise. The general principle in all is the same : they differ from each other chiefly in the construction of the piston and valves. In the form which has been above described, the air effects its escape from the receiver at each stroke of the piston by opening the suction valve V, fg. 23. Now in whatever way this valve is constructed it must require some determinate force to raise it ; and this force, in the case already described, is the elastic force of the rarefied air remaining in the receiver. Thus the operation of the machine is accomplished by the presence in the receiver of the very agent which it is the object of the machine itself to remove, and from the very construction of the instrument it must cease to act while yet air of a determinate pressure remains in the receiver. This defect has been sometimes attempted to be removed by causing the suction valve to open, not by the pressure of the rarefied air, but by some mechanical means acted upon by the piston. Such contrivances, however, are found to be attended with peculiar inconveniences which more than outweigh their advantages. Probably the most simple and the best contrivance is one in which the suction valve is altogether dispensed with, and the air passes freely through the open tubes from the receiver to the pump barrel. Let T,fg. 25., be the exhausting tube which is carried from the receiver, and enters the pump barrel at a point distant from the bottom of the barrel by a space equal to the thickness of the piston. The piston P is a solid plug, which moves air-tight in the barrel, and is propelled by a polished cylindrical rod which slides in an air-tight collar C in the top of the cylinder, which in this case is closed. A valve is ;HAP. v. AIR PUMP. 227 placed in the top of the cylinder, which opens outwards, and which may be constructed in the same manner as the silk valves already described. When the piston descends, it leaves a vacuum above it, the external air not being allowed admission Fig. 25 through the valve at the top ; and when the piston arrives at the bottom of the barrel, it has passed the mouth of the exhaust- ing tube T, and fills the space below it. The air in the receiver then expands into the empty pump barrel, and when the piston is raised, having passed the mouth of the tube T, the air which has expanded into the barrel is confined between the piston and the top, where, as the piston rises, it is condensed. When it acquires sufficient elastic force, it opens the valve at the top, and is discharged into the atmosphere. The valve in the top of the barrel is in this case continually under the atmospheric pressure, and therefore the air confined in the pump can never be driven through it, until it is condensed b . the piston, so that its force shall be greater than that of the r mosphere. From the causes already explained, arising from inaccuracy of mechanical construction, some small space must inevitably remain between the piston and the top of the barrel, even when the piston is drawn upwards as far as possible. This small space will contain condensed air, and the valve at C will cease to act, when the air which occupies this space exceeds the atmospheric pressure by a force less than the tension of the valve. When the piston is pressed to the bottom, a small space will 228 A TREATISE ON PNEUMATICS. CHAP. V. likewise remain between the piston and the bottom, which will be occupied by air, but at each ascent of the piston this air ex- pands, and is subject to constant diminution as the working of the pump is continued. The principal source of imperfection in such an instrument, independently of that which arises from the mechanical inac- curacy of its construction, depends on the tension of the valve in the top, and the pressure of the atmosphere upon it. To diminish this imperfection, the valve in the top is sometimes made to communicate by a pipe with a small subsidiary ex- hausting syringe, by which the pressure of the atmosphere on the valve may be partially withdrawn, so that a less force acting under the valve may open it. A perspective view of an air pump, with all its accompani- ments, constructed upon this principle, is exhibited in Jig. 26., where the several parts of the machine are marked with the same letters as the corresponding part in the sectional diagram, Jig. 23. The subsidiary syringe just alluded to is also repre- sented at Q,. It is worked by a handle H. Experiments with the Air Pump. (151.) The pressure and elasticity of air are capable of being strikingly illustrated in various ways by experiments with the air pump. If a glass receiver, open at both ends, have a strong bladder tied upon one end, so as to be air-tight, and be placed upon the open end on the plate of an air pump, when the air is exhausted from the receiver, the pressure of the external atmosphere on the bladder will immediately cause its upper surface to be con- cave, and when the air is sufficiently rarefied within the receiver, the pressure on the bladder will burst it, producing a loud noise like the discharge of a pistol. Again, if a large glass bowl, having a bladder tied firmly on its mouth so as to be perfectly air-tight, be pkced under the receiver of the air pump, on withdrawing the air, the elastic force of the air confined in the bowl being still undiminished, and being no longer balanced by the atmospheric pressure on the outside, the bladder will be blown into a convex form ; and when the air in the receiver is so rarefied that the elasticity of the air confined in the bowl suffers little resistance, the bladder will burst, and the air confined in the bowl will expand through the receiver. (152.) Fruit when dried and shriveled contains within it par- ticles of air, which are held in its pores by the pressure of the external atmosphere. If, therefore, this pressure be removed, we may expect that the air thus confined will expand, and if CHAP. V. EXPERIMENTS ON AIR. Fig.M. 229 there is no aperture in the skin of the fruit for its escape, it will distend the skin. Fruit in this case placed under a receiver will assume the appearance of ripeness by exhausting the air ; for the expansion of the air contained in the fruit, by inflating the skin, will give it a fresh, ripe appearance. Thus a shriveled apple will appear to grow suddenly ripe and fresh ; and a bunch of raisins will be converted into a bunch of ripe grapes. (153.) A flaccid bladder closed so as to be air-tight at the mouth contains within it a small portion of air. This air presses, by its elasticity, on the inner surface, which is resisted by the atmospheric pressure from without. If such a bladder be placed under the receiver of a pump, and the air exhausted, the external pressure being thus removed, the elasticity of the air included will cause the bladder to swell, and it will take all the 20 230 A TREATISE ON PNEUMATICS. CHAP. V. appearance of being fully inflated. Such a bladder placed under several heavy weights will raise them by the expansion of the air. (154.) Let a close glass vessel A B,/g-. 27. be partially filled with water, and let the tube C D be inserted through its neck, the end D being below the surface of the water ; the air above the surface will thus be confined. If such a vessel be placed under a receiver, and the air be withdrawn, t^e elastic force of the air confined in A B above the surface of the water will press the water up in the tube D C, from which it will issue in a stream at C, when the pressure of the atmosphere is sufficiently removed by rarefaction. (155.) By means of an air pump we are enabled to demonstrate that the power which causes water to follow the piston in a pump is the atmospheric pressure, by showing that the water will not follow the piston when that atmospheric pressure ia removed. Let a small exhausting syringe, with its lower end in a vessel of water, be placed on the plate of the air pump, and let a glass receiver, open at the top, be placed over it. On the top of this receiver let a brass cap fitting it air-tight be placed, through a hole in the centre of which a metal rod ter- minating in a hook passes air-tight. Let the hook be attached to the end of the piston rod, so that by drawing the rod up through the air-tight collar, the piston may be drawn from the bottom of the cylinder towards the top. If this be done before the air has been exhausted from the receiver, the water will be found to rise after the piston as in the common pump ; but as soon as the air in the receiver has been highly rarefied, it will be found that although the piston may be drawn up in the syringe the water will not follow it. This effect may be ren- dered visible by constructing the barrel of the pump or syringe of glass, through which the water will be seen to rise in the one case and not in the other. (156.) If an air-tight piston be placed in close contact with the bottom of a syringe not furnished with a valve, any attempt to draw it up will be resisted by the atmospheric pressure ; and if it be forced to the top of the cylinder and there discharged, it will be immediately urged with considerable force to the bot- tom. The atmospheric pressure above the piston, acting with a force of about 15 pounds on the square inch, produces this effect ; for the space between the piston and the bottom of the cylinder not containing ay air, this pressure is unresisted. Now if this piston be introduced under the receiver of an air CHAP. V. EXPERIMENTS ON AIR. 231 Fig. 28. pump, and be drawn up as already described, it will be found that in proportion as the air is withdrawn from the receiver, less and less force will be required to produce the effect ; and, at length, the rarefaction will become so great, that the pres- sure of the remaining air is incapable of overcoming the friction of the piston with the cylinder, and it will, when drawn to the top, remain there, without returning to the bottom. In this state, let the air be re-admitted to the receiver ; the piston will then be immediately pressed to the bottom of the cylinder. (157.) The celebrated experiment of the Magdeburgh hem- ispheres may be performed by means of an air pump. Two hollow hemispheres, constructed of brass, as represented in fig. 28., are so formed that when placed mouth to mouth they shall be in air-tight contact. They are furnished with handles, one of which may be screwed off. In the neck to which this handle is screwed is a tube furnished with a stopcock. The handle being screwed off, let the hem- isphere be screwed on the pump plate, and the other hemisphere being placed over it, let the stopcock be opened so as to leave a free communication between the interior of. the sphere and the exhausting tube of the air pump. The pump being now worked, the interior of the sphere will form the receiver from which all communication with the ex- ternal air is cut off, and rarefaction will be produced in it to any degree which may be desired. This being effected, let the stop- cock be closed ; and let the sphere be detached from the pump plate, and the handle screwed upon it. If then the two handles be drawn in opposite directions, so as to pull the hemispheres from one another, it will be found that they will resist with considerable force. If the diameter of the sphere be 6 inches, its section through the centre will be about 28 square inches. The hemispheres will be pressed together by a force amounting to 15 pounds for every square inch in the section. If 28 be multiplied by 15, we shall obtain 420, which is the amount of the force wi1 which the hemispheres will be held together. If one of the handles be placed on a strong hook, and a weight of 400 pounds be suspended from the other, the weight will be supported by the pressure of the atmosphere. This was one of the earliest experiments in which the effects of atmospheric pressure were exhibited. Otto Guericke, the inventor of the air pu""np, constructed in 1654, a pair of such hemispheres one f.-ct in diameter. The section through the 232 A TREATISE ON PNEUMATICS. CHAP. V. Fig. 29. centre of these was about 113 square inches, which, multiplied by 15, gjves a pressure amounting to about 1700 pounds. If the exhaustion were complete, the hemispheres would be held together by this force ; but, even though incomplete, they were still able to resist a prodigious force tending to draw them asunder. j (158.) It is a consequence of the general theory of gravita- tion, that under the same circumstances, bodies are attracted in proportion to their mass ; and hence it would follow, that all bodies, whatever be their masses, should fall at the same rate. Now the instances which most commonly come under our ob- servation seem to contradict this inference ; for we find a piece of metal and a piece of paper fall at very different rates, and still more different is the rate at which a piece of metal and a feather would fall. The cause of this circumstance, however, is easily explained. The resistance offered by the air is pro- portional to the quantity of surface which the body presents in the direction of its motion. Now the metal may present a considerably less surface than the feather, while the force which it exerts to overcome the resist- ance is many times greater, because of , its greater weight. Hence it follows, that the resistance of the air produces a differ- ent effect on the metal compared with the effect which it produces on the feather ; but all doubt will be removed if the feath- er and the metal are allowed to fall in a chamber from which the air has been withdrawn. A glass receiver is repre- sented in Jig. 29., which may be placed on the plate of an air pump, and on the top is placed a brass cover, which is air- tight. Under this several brass stages are attached, constructed in the manner of trap doors on the hinges, and supported by small pins, which project from the sides of a metal rod, passing through an air- tight collar in the brass cover. By turn- ing this metal rod the pins may be removed from under the trap doors, and they will fall, disengaging whatever may be placed upon them. Suppose a piece of coin and a feather be placed upon one of these stages, supported by a projecting pin. This arrangement being made, let the brass cover be placed on the receiver, so as to be air-tight, and let the receiver be then exhausted by the pump. When a CHAP. V. PRODUCTION OF SOUND. 233 high degree of rarefaction has been produced, let the rod be turned by the handle at the top, so as to remove the pin from under the stage ; the coin and the feather will be immediately let fall, and it will be observed that they will both descend at exactly the same rate, and strike the bottom at the same in- stant. This is the experiment commonly known by the name of " the guinea and feather experiment." (159.) The surgical process called cupping, consists in re- moving the atmospheric pressure from the part of the body submitted to the operation. A vessel with an open mouth is connected with an exhausting syringe. The mouth is applied in air-tight contact with the skin, and, by working the syringe, 14 part of the air is withdrawn from the vessel, and, conse- quently, the skin within the mouth of the vessel is relieved from its pressure. All the other parts of the body, however, being still subject to the atmospheric pressure, and the elastic force of the fluids contained in the body having an equal de- gree of tension, that part of the skin which is thus relieved from the pressure will be swelled out, and will have the ap- pearance of being sucked into the cupping glass. If the skin be punctured by lancets, the blood will thus be drawn from it in a peculiar manner. (160.) That the presence of air is necessary for the trans- mission of sound may be strikingly illustrated by the air pump. A small apparatus,^ 1 . 30., which, by being drawn upwards and Fig. 30. 20 234 A TREATISE ON PNEUMATICS. CHAP. V. downwards alternately, causes a bell to ring, is placed on the pump plate, and covered by a receiver with an open top. A brass cover, furnished with a sliding rod, is placed upon this. The sliding rod is terminated in a hook, which catches the ap- paratus, and by which it may be alternately raised and lowered, without allowing any air to pass into the receiver. The appa- ratus being thus suspended in the receiver by a silken thread, so that it shall not touch the bottom or sides, let the air be exhausted by the pump. When the rarefaction has been carried to a sufficient extent, let the rod be alternately raised and lowered, so that the bell shall ring. It will be found to be inaudible. If the air be now gradually admitted, the sound will at first be barely audible, but will become louder by degrees, until the receiver is again filled with air, in the same state as the exter- nal atmosphere. In this experiment care must be taken not to let the sounding apparatus rest on the pump plate, for it will then communicate a vibration to that, which will finally affect the external air, and produce a sound. The Condensing Syringe. condensing syringe is an instrument by which a greater quantity of air may be forced into a vessel than that vessel contains when it has a free communication with the external at- mosphere. Let A B, Jig. 31., be a cylinder furnished with a piston P, which moves air-tight in it. Let C be a tube proceeding from the bottom, and furnished with a stopcock. Let us sup- pose this tube to communicate with the re- ceiver or vessel R, in which it is intended to condense the air. Let another tube D pro- ceed from the cylinder, also furnished with a stopcock. Let the piston be now drawn to 3 the top of the cylinder, both stopcocks being open. The receiver R being in free com- munication with the atmosphere, will contain air of the same density and pressure as the external atmosphere. Let 'the stopcock D be now closed, and let the piston be pressed to the bottom of the cylinder ; the air confined in the cylinder below the piston will thus be forced through the tube C into the vessel R, while the piston is pressed against the bottom B. Let the stopcock C be closed, so as to CHAP. V. CONDENSING SYRINGE. 235 prevent the escape of the air from the vessel R, and let the stopcock D be opened, so as to allow a free communication between the cylinder A B and the external atmosphere. Let the piston be again drawn to the top of the cylinder. The cylinder will then be filled with atmospheric air of the same density as the external atmosphere. Let the stopcock D be closed and C opened, and let the piston be once more forced to the bottom of the cylinder; the contents of the cylinder will be thus again discharged, and forced into the receiver R. Let the stopcock C be again closed, and let the process be repeated. It is evident that at each stroke of the piston a volume of at- mospheric air vrill be forced into the receiver equal to the dimensions of the cylinder A B ; and there is no limit to the degree of condensation, except that which depends on the strength of the receiver R, and the cylinder and tubes, and on the power by which the piston is urged. After each stroke of the piston, the density of the air in R is increased by the admission of as much atmospheric air as fills the cylinder A B, and therefore the density, as the process ad- vances, receives equal increments at each stroke of the piston. Let us suppose that the receiver R has ten times the capacity of the cylinder A B, and let us suppose that the elastic pressure of the air in R at the commencement of the Fig. 32. . operation is expressed by the number 10. After the first stroke this pressure will be expressed by the number II, inasmuch as the quantity of air in R has been increased by one tenth part of its volume. After the second stroke the pressure will be express- ed by the number 12 ; after the third by the number 13, and so on. In the form given in practice to the con- densing syringe, the necessity for manipu- lating by the stopcocks here represented is removed. A silk valve, such as that de- scribed in the exhausting syringe is placed in the tube C, jig. 32., but opening down- wards. The neck of the receiver R is fur- nished with a stopcock and a tube, which terminates in a screw. This screw is con- nected with a corresponding one proceeding from the bottom of the syringe. By this arrangement, the air is capable of passing through the silk valve from the syringe to the receiver, but not in a contrary direction. A small hole is made through the piston, extending from the upper to the lower sur- 236 A TREATISE ON PNEUMATICS. CHAP. V. face, and the silk valve is extended across this hole on the lower surface, so that air is capable of passing through this valve to the cylinder below it, but not in a contrary direction. Now let us suppose that the air in the receiver has the same pressure and density as the external atmosphere, and let the piston P be at the top of the cylinder, the air in the cylinder A B also having the same pressure and density as the external air. By pressing the piston towards the bottom of the cylinder, the air enclosed will become condensed, and by its increased pressure will open the valve V, and as the piston descends will be forced into the receiver R. When the piston has arrived at the bottom, all the air contained in the cylinder will be trans- ferred into the receiver. It will be retained there, because the valve V, opening downwards, will not permit its return. If the piston be now drawn up, it will leave a vacuum below it when it begins to ascend, but the pressure of the atmosphere above will open the valve V , and the air rushing through will fill the cylinder as the piston ascends ; and when the piston has arrived at the top of the cylinder, the space below it will again be filled with atmospheric air. By the next descent of the piston this air is forced into the receiver R as before, and so the pro- cess is continued. It should be observed, that when the piston P is drawn to the top of the cylinder, the air which has passed into A B has not quite so great a pressure as the external atmosphere. This arises from the valve V requiring some definite force, however small, to open it. When the air which has passed into the chamber A B acquires a pressure which is less than the atmos- pheric pressure by an amount equr.l to the tension of the valve V', then the excess of the pressure of the atmosphere over the resistance of the air contained in A B will be insufficient to open the valve V, and no more air can pass into the cylinder. It should also be observed, that the valve V, being pressed up- wards by the elastic force of the air condensed in the receiver, requires a still greater pressure than this to open it, and there- fore before the valve V can be opened, the air enclosed below the piston P must always be condensed by the pressure of the piston in a higher degree than the air is condensed in the re- ceiver. The observations which have been made respecting the limit of the operation of the exhausting syringe, arising from mechanical imperfections and other causes, will also be applicable here. However nicely the piston P, and the cylin- der in which it plays, may be constructed, there will still be some small space remaining between it and the silk valve V, when it is pressed to the bottom of the cylinder. Into this space the air contained in the cylinder may, finally, be con- densed ; and when the pressure of the air contained in the CHAP. V. THE CONDENSER. 237 receiver becomes equal to the pressure of the air condensed into the space between the piston at the bottom of the cylinder and the silk valve, the operation of the instrument must neces- sarily cease ; for then the utmost degree of condensation which can be produced above the silk valve V will be insufficient to open the valve, and therefore the syringe cannot introduce more air into the receiver. The Condenser. (163.) The condenser has the same relation to the apparatus just described, as the air pump has to the exhausting syringe. The condenser consists of a receiver firmly and conveniently fixed, communicating by a tube with one or two condensing syringes, which may be worked in the same manner as the ex- hausting syringe described in the air pump. In the use of such an instrument, it is convenient to possess the means of indicating the degree of condensation which has been effected. For this purpose a mercurial gauge is used, analogous to that which is applied to the air pump. A bent Fig. 33. tube, ABC, fig. 33., contains a small quantity of mercury, S, B, S', in the curved part. When the ends of the tube are open, and in free com- munication with the atmosphere, the surfaces, S, S', will stand at the same level. The ex- tremity C is furnished with a stopcock, by which a communication with the atmosphere may be permitted or intercepted. The extrem- ity A communicates by a tube with the receiver in which the air is to be condensed. At the commencement of the process, before any con- densation has taken place, the stopcock C is closed, and the air included between it and the surface S' has then the same pressure as the external atmosphere. The'air in the receiver having also that pressure, the two surfaces S and S' necessarily stand at the same level. When the condensation of air in the receiver commences, the pressure on the surface S is increased ; therefore that surface falls, and the surface S' rises. The pressure of the air con- densed in the receiver will thus be balanced by the weight of the column of mercury between the levels S and S', together with the pressure of the air enclosed between S' and C. But by what has been proved in (133.) it follows, that the pressure of the air enclosed in S' C is increased in the same proportion as the space S' C has been diminished. Now, as the original pressure of the c.::- contained in this space was equal to the 238 A TREATISE ON PNEUMATICS. CHAP. VI. pressure of the atmosphere, it is always easy to find the pres- sure of the air reduced in bulk by increasing the amount of atmospheric pressure in the same proportion as the space S' C has been diminished. Thus, if the air enclosed in the tube be reduced to half its original bulk, then the pressure it exerts will be double the atmospheric pressure. If it is reduced to two thirds of its bulk, then the pressure of the enclosed air will be to the atmospheric pressure in the proportion of three to two, and so on. The pressure thus computed being added to the pressure arising from the column of mercury between the levels of the surfaces S and S', will give the whole pressure of the air condensed in the receiver. Although the condenser is not without its use in experiment- al physics, yet it is an instrument far less important than the air pump to which it is so analogous. The cases are innumer- able in which it is necessary to inquire what effect would take place in the absence of the atmosphere ; but they are com- paratively few in which it is necessary to investigate what effects would be produced under increased atmospheric pressure. We do not, therefore, think it necessary, in a treatise of this nature, to enter into further details concerning the condenser. CHAP. VI. MACHINES FOR RAISING WATER. THE LIFTING PUMP. PUMP WITHOUT FKICTION. THE SUCTION PUMP. THE FORCING PUMP. THE SAME WITH AIR VESSEL."- THE SAME WITH A SOLID PLUNGER. DOUBLE FORCING PUMP. THE FIRE EN- GINE. SIPHONS. THE WURTEMBURG SIPHON. (164.) MACHINES of a great variety of forms, and constructed upon various principles, derived from mechanics, hydrostatics, and pneumatics, have been applied to the purposes of raising water above its natural level. These machines generally are called Pumps. The most simple machine of this description is that which is called The Lifting Pump. (165.) Let A B D C,fig. 34., be a short cylinder submerged in the well or reservoir from which the water is to be raised. This cylinder communicates by a valve x, with a tube or pipe CHAP. VI. LIFTING PUMP. 239 Fig, 34. C E, which is carried upwards to whatever height it is required to raise the water. A piston moves water-tight in the cylinder A D, and is worked by a rod or frame- work, as represented in the figure. This piston is furnished with a valve v, which opens upwards. When the piston descends, the pres- sure of the water opens the valve i>, and the cylinder between the two valves is filled with water. When the piston is raised, the water between the valves being pressed against the yalve x opens it, and is driven into the tube C E, from which its return is intercepted by the valve x. The water follows the piston in its ascent by the hydrostatical pressure of the water in the reservoir outside the cylinder ; and on the next descent of the piston, water will again pass through the valve t>, which will be driven through the valve r, on its next ascent. The use of the valve x is evidently to relieve the valve v during the de- scent of the piston from the pressure of the column of water in the tube C E. If the valve v were subject to that pressure, it would fail to be opened during the descent of the piston by the pressure of the water in the well, because the level of that water is necessarily below the level of the water in the pipe C E. The use of the valve v is to prevent the return of the water through the piston during its ascent. In drawing up the piston a force will be necessary sufficient to support the entire column of water from the valve v to the surface of the water in the tube C E. The actual amount of this force is the weight of a column of water, whose base is equal to the horizontal section of the piston, and whose height is equal to the height of the surface of the water in the tube C E above the valve v. It is evident that after each stroke of the pump, the pressure on the piston, and the force necessary to raise it, will be increased by the weight of a column of water whose base is the horizontal section of the piston, and whose height is equal to the increase which the elevation of the column in C E receives from' the water driven through the valve x. (166.) The ingenious form of pump represented in fig. 35. acts upon the principle of the lifting pump, though very differ- ent from it in appearance. It is recommended by the circum- 240 TREATISE ON PNEUMATICS. CHAP. VI. Fig. 35. stance of being free from friction, or nearly so, and by being capable of being worked by the weight of an animal walking up an inclined plane, one of th most advantageous ways in which animal power can be applied. Let A B C D be a wooden tube of any shape, round or square, which descends to a depth in the well or reservoir equal to the height above the surface of the reservoir to which the water is required to be raised. Thus if A H be the height to which the water is to be raised above the level of the well, then the depth G B must be at least equal to AH. L M is a heavy beam or plunger, sus- pended from a chain, and capable of descend- ing by its own weight in water. A valve v covers an opening placed at the bottom of the tube or barrel. By the hydrostatic pressure the water will enter the valve v, and fill the barrel to the level of the water in the cistern. G I is a short tube proceeding from the side of the barrel, at the surface of the water, and communicating with the vertical tube A H by a valve H, which opens upwards. K is the spout of discharge. The plunger L M hangs loosely in the tube, so that it moves upwards and downwards perfectly free from friction. When this plunger is allowed to descend by its weight into the water which fills the lower part of the tube, the valve v is closed, and the water displaced by the plunger is forced through the valve H into the tube A H. When the plunger is raised, the valve H is closed, and the water thus forced into the tube A H cannot return. The water from the cistern then flows through the valve v, and rises in the tube to the level G. The next descent of the piston propels more water into the tube A H, and this is continued so long as the piston is worked. The manner in which such an apparatus is worked by the weight of a man is represented in Jig. 36. Two pumps are used, such as that just described, and when the plunger de- scends in one it rises in the other. The two pumps communi- cate with one vertical pipe, which therefore receives a continual supply of water ; for while the action of one pump is suspend- ed, the other is in progress. A man walks from one end of an inclined plane to the other, and, by his weight upon one side or the other of the fulcrum, causes the plungers alternately to rise and fall. CHAP. VI, 241 The Suction Pump. (167.) The common suction pump is a large syringe, which is connected with a tube, the lower extremity of which is plunged in a well, from which water is to be raised. This tube is called a suction pipe. Let W,^T. 37., represent the well or reservoir from which the water is to be elevated, and let S O represent the suction tube. The lower end O of this tube being pierced with holes acts as a strainer, and prevents the admission of solid impurities into the pipe which might choke the pump and impede its action. At the upper end of the suction tube a valve x is placed which opens upwards, and at this point the tube is connected with the great syringe B C, furnished with a piston, in which there is another valve v, which also opens upwards, as already described in the exhausting syringe. The piston is worked alternately upwards and downwards in common pumps by a lever, called the brake, but may also be worked in many other ways. At the commencement of the operation, the level of the water in the suction tube coincides with the level of the exter- nal water in the well, because both are subject to the same atmospheric pressure ; but when the syringe B C is worked, it will rarefy the air in the tube S O. on the principle and in the manner explained in (148.). The pressure of the air in S O on the surface of the water within it being thus diminished, and 242 A TREATISE ON PNEUMATICS. CHAP. Yl. Fig. 37. rendered less than the pressure of the atmosphere on the exte- rior surface of the water in the well, a column of water will be forced in the tube S O by the excess of the atmospheric pres- sure. In proportion as the rarefaction of the air between the surface of the column suspended in the tube S O and the valve x is increased, in the same proportion will its pressure on the surface of the column be diminished, and so long as this dimi- nution is continued the height of the column will increase. There is, however, a limit to this height. If the air could be altogether withdrawn from the tube S O, and an absolute vacuum produced beneath the valve x, like that which exists above the mercury in the barometer, then the atmospheric pres- sure, acting with undiminished effect on the surface of the water in the well, would sustain a column of water in the tube S O, the weight of which would be equal to a column of mer- cury with the same base, and having the height of the mercury in the barometer. Now the specific gravity of water is about 13i times less than that of mercury, and consequently a force which could sustain a column of 30 inches of mercury would CHAP. VI. SUCTION PUMP. 243 support a column of water 13^ times greater in height. If the barometer, therefore, be considered to stand at 30 inches, the atmospheric pressure would support a column of water of about 405 inches, or 34 feet. From this consideration it will appear that if the operation of the syringe were perfect, and that an absolute vacuum could be produced below the valve #, still the water could never ascend through that valve by the atmospheric pressure, if its height above the level of the water in the cistern exceeded 13^ times the height of the barometric column. In these countries the barometric column varies between 28 and 31 inches in height, and therefore the valve x ought not to be more than 30 feet above the level of the water in the well. But it is still to be observed, that the construction and opera- tion of the great syringe B C is subject to inevitable imperfec- tions, which are always greater the larger the scale on which the instrument is made. Even in small syringes accurately constructed, a degree of imperfection exists, which has been already noticed in the explanation of the exhausting syringe ; but such defects are greatly increased in a larger syringe, such as that used in common water pumps, where a common and less expensive mode of construction must be used. From these causes, a column of water, which can be raised in the tube S O, will be less than even 30 feet in height. It is obvious, however, that within this limit the length of the tube S O must be determined by the degree of excellence attained in the construction of the syringe C B. When the rarefaction has been carried to a sufficient extent, the tube S O being adjusted to a proper length, the column of t r ater will rise until part of it pass through the valve x, and it will ascend to a level in the syringe B C, the height of which above the water in the well will be determined by the excess of the atmospheric pressure above the pressure which continues to act on the surface of the water in C B. The water which is thus drawn into the syringe presses by its weight on the valve x, and cannot return into the suction tube. When the piston is now pressed down, it will act on tKe water which has been raised above the valve x in the manner of the lifting pump already described, and the remainder of the process in raising the water will be in all respects the same as that which has been explained in reference to the lifting pump. In this case the water raised through the suction pipe, and deposited above the valve x in the syringe, serves as a well to the syringe, con- sidered as a lifting pump. It is evident that, according as the water is elevated above the piston, the ^atmospheric pressure acting on the surface of the water in the well will force more water through the valve x. In this way the process is contin- ued ; during every ascent of the piston water being raised 244 A TREATISE ON PNEUMATICS. CHAP. VI. through the valve a:, and during each descent of the piston the same quantity of water passing through the valve v. As the water accumulates above the piston, as described in the lifting pump, it at length reaches the spout from which it is dis- charged. Fig. 37. Such is the construction and operation of the common house- hold pump. It may appear, at first view, that the pressure of the atmosphere sustaining the column of water in the suction tube furnishes an aid to the power which works the pump. This, however, is not the case ; at least not so in the sense in which it is commonly understood. To make this intelligible, it will be necessary to consider somewhat in detail the forces which are in operation during the process. There are some forces which are directed downwards from the top of the syringe towards the bottom of the well, and others which are directed upwards. Now it is evident that the mechanical power applied to draw the piston up will have to overcome all that excess by which the forces downwards exceed the forces upwards. Let CHAP. VI. SUCTION PUMP. 245 us suppose a column of water resting on the piston, after having passed through the valve v. The upper surface of this column is pressed upon by the weight of the atmosphere ; the piston has, therefore, this weight to sustain. It has also to sustain the weight of the water which is above it. The atmospheric pressure acting also on the water in the well, is transmitted by the quality of liquids explained in Hydrostatics, chap, ii., to the bottom of the piston ; but this effect is diminished by the weight of the column of water between the surface of the water in the well and the bottom of the piston, for the atmospheric pressure must, in the first place, sustain that column, and can only act upon the bottom of the piston in the upward direction with that amount of force by which it exceeds the weight of the column of water between the piston and the well. The effect, therefore, on the piston is the same as if it were pressed down- wards by the Aveight of the column of water between the piston and the well, and at the same time pressed upwards by the atmospheric pressure. Thus the piston may, in fact, be regard- ed as being urged downwards by the following forces, the atmospheric pressure, the weight of the water above the piston, and the weight of the water between the piston and the well ; that is to say, in fact, by the atmospheric pressure, together with the weight of all the water which has been raised from the well. At the same time, it is pressed upwards by the atmos- pheric pressure transmitted from the surface of the water in the well. .This upward pressure will neutralize or destroy the effect of the same atmospheric pressure acting downwards on the surface of the water above the piston, and the effective downward force will be the weight of all the water which is contained in the pump. By this reasoning, it appears that the pump must be worked with as much force as is equal to the weight of all the water which is in it at any time, and, therefore, that the atmospheric pressure affords no aid to the working power. Since the action of the pump in raising water is subject to intermission, the stream discharged from the spout will neces- sarily flow by fits and irregularly, if some means be not adopted to prevent this. At the top of the pump a cistern may be con- structed, with a view to remove this inconvenience. If the pump be worked, in the first instance, so as to raise more water in a given time than is discharged at the spout, the column of water will necessarily accumulate in the barrel of the pump above the spout. The cistern M N will, therefore, be filled, and this will continue until the elevation of the surface of the water in the cistern above the spout will produce such a pres- sure, that the velocity of discharge from the spout will be equal to the velocity with which the water is raised bv the piston. 21* 246 A TREATISE ON PNEUMATICS. CHAP. VI. The level of the water in the cistern will therefore cease to rise. This level, however, will be subject to a small variation as the piston rises ; for while the piston is descending, the water is flowing from the spout, and no water is raised by the piston ; consequently the level of the water in the cistern falls. When the piston rises, water is raised, and the quantity in the cistern is increased faster than it flows from the spout ; conse- quently the level of the water in the cistern rises, and thus this level alternately rises and falls with the piston. But if the magnitude of the cistern be much greater than the section of the pump barrel, then this variation in the surface will be pro- portionally small, for the quantity of water which fills a part of the barrel, equal to the play of the piston, will produce a very slight change in the surface of the water in the cistern. The flow, therefore, from the spout S will be uniform, or nearly so. The Forcing Pump. (168.) The forcing pump is an instrument which combines the principles of the suction and the lifting pump. In Jig. 38., Fig. 38. C E is a suction pipe which descends into the well, at the top of which is the suction valve V opening upwards. The pump barrel A B C D is furnished with a solid piston without a valve, and from the side of this barrel, just above the suction valve, there proceeds a pipe which communicates with an upright cylinder G H, which is carried to the height to which the water is intended to be raised. In the bottom cf this cylinder is CHAP. VI. FORCING 1'UMP. 247 placed a valve V, which opens upwards. In the commence- ment of the process, the suction pipe C E, and the chamber between the piston and valves, are filled with air. When the piston is depressed to the valve V, the air enclosed in the latter chamber becomes condensed, and, opening the valve V', a part of it escapes. On raising the piston the air below it becomes rarafied, and the air in the suction pipe, opening the valve V by its superior pressure, expands into the upper chamber : a part of it is expelled through the valve V 7 , when the piston next descends. During this process, it is evident that the pump acts as an air pump or exhausting syringe, and is in all respects equivalent to the instrument described in (148.). When the air becomes sufficiently rarefied by this process, the atmospheric pressure forces water from the well through the suction pipe and the valve V into the chamber between the piston and the valves. When the piston now descends, it presses on the sur- face of the water, and the valve V opening upwards prevents the return of the water into the suction pipe ; while the pres- sure of the piston, being transmitted by the water to the valve V, opens it, and, as the piston descends, the water passes into the force pipe G H. The next ascent of the piston allows more water to pass through the valve V, and the next descent forces this water through the valve V into the force pipe. By contin- uing this process, the quantity of water in the force pipe con- tinually increases, receiving equal additions at each descent of the piston. It is evident that the force pipe may be placed in any posi- tion, whether perpendicularly, obliquely, or horizontally, and that, in every case, the action of the piston will propel the water through it. When the piston is pressed downwards, and the valve V' is opened, it is necessary that the force which works the piston should balance the weight of the column of water in the force pipe, for this weight is transmitted by the water between the piston and force pipe to the bottom of the piston ; consequently, the height of the column of water in the force pipe will measure the intensity of the pressure against the base of the piston when the valve V is open. A column of water about 34 feet in height, suspended in the force pipe, will press on the base of the piston with a force of about 15 pounds on each square inch, and the pressure at other heights will be proportional to this. The force necessary to urge the piston downwards may, there- fore, always be calculated. In drawing the piston up, the valve V' is closed, and relieves the piston from the weight of the incumbent column ; if the valve V is opened, the piston is sub- ject to the same pressure as in the suction pump. This pres- sure has been already proved to be equal to the weight of the 248 A TREATISE ON PNEUMATICS. CHAP. VI. column of water raised above the level of the water in the well. It follows from this, that if the height of the force pipe be equal to the length of the suction pipe, then the piston must be pressed upwards and downwards with the same force ; but if the height of the force pipe be greater or less than the length of the suction pipe, then the downward pressure must be greater or less, in the same proportion, than the force which draws the piston up. In fact, the force which draws the piston up in this pump, after the water has been raised to the valve, is uniform ; while the force with which the piston must be urged down- wards is continually increasing, until the water in the force pipe reaches its point of discharge, and until the discharge becomes equal to the supply. The supply of water by the force pipe through the valve V', is evidently intermitting, being suspended during the ascent of the piston ; it follows, therefore, that the flow from the point of discharge will be liable to the same intermission, if means be not adapted to counteract this effect. A cistern placed at the top of the force pipe, as already described in the suction pump, may serve the purpose, but it is generally more convenient to use an apparatus called an air vessel, which is represented in Jig. 39. Immediately above the valve V a short tube commu- nicates with a strong, close vessel of sufficient capacity ; through the top of this vessel the force pipe G H passes, and descends to a point near the bottom. By the action of the pump the water is forced into the vessel M N, and when its surface rises above the mouth H of the force pipe, the air in the vessel M N is confined above the water ; and as the water is gradually forced in, this air is compressed, and acts with increased elastic CHAP. VI. AIR VESSEL.- 249 force on the surface of the water : this pressure forces a column of water into the pipe H G, and maintains that column at an elevation proportional to the elastic force of the condensed air. When the air in the vessel M is reduced to half its original bulk, it will act. on the surface of the water with double the atmospheric pressure ; meanwhile, the water in the force pipe being subject only to once the atmospheric pressure, there is an unresisted upward force equal to the atmospheric pressure which sustains the column of water in the tube : a column will then be sustained about 34 feet in height. When the air is reduced to one third of its original bulk, the height of the col- umn which it can sustain is 68 feet, and so on. If the force pipe terminate in a ball pierced with small holes, so as to form a. jet d'eau, the elastic pressure of the air on the surface will cause the water to spout from the holes. It is of great importance in the forcing pump that the piston should be truly water-tight in the cylinder, and in practice this is not always very easily accomplished. The arrangement represented in Jig. 40. is better adapted to insure the perfect Fig. 40. action of the pump than the form of piston already represented. In this case a polished cylindrical metal plunger P passes through a collar of leathers A B, which exactly fits it ; and it is maintained perfectly air-tight and water-tight by being lubri- cated with oil or tallow. When the plunger is raised, the space it deserts is replaced by the water which rises through tho 250 A TREATISE ON PNEUMATICS. CHAP. VI. valve V ; and when it descends, the water which filled the space into which it advances is driven before it, through the valve V, into the force pipe. If the forcing pump, represented in Jig. 38., be attentively considered, it will be perceived that the principles on which the piston acts in its ascent and descent are perfectly distinct. In its ascent it is employed in drawing the water from the suc- tion pipe into the pump barrel, and in its descent it is employed in forcing that water from the pump barrel into the force pipe. Now the piston being solid, and not furnished with any valve, there is no reason why its upper surface should not be employ- ed in raising or propelling water, as well as the lower. While the lower surface is employed in drawing water from the suc- tion pipe, the upper surface might be employed in propelling water into the force pipe ; and, on the other hand, in the de- scent of the piston, when the lower surface is employed in pro- pelling water into the force pipe, the upper surface might be engaged in drawing water from the suction pipe. To accom- plish this, it is only necessary that the top of the cylinder should be closed, and that the piston rod should play through an air- tight collar, the top of the cylinder communicating with force pipe and the suction pipe, as well as the Such an arrangement is represented in Jig. Fig. 41. piston ascends, the suction valve F is opened, and water is drawn into the pump barrel below the piston ; and when the CHAP. VI. FIRE ENGINE. 251 piston descends, the suction valve F is closed, and the pressure of the piston on the water below it opens the valve C, and pro- pels the water into the force pipe C G. Also, while the piston is descending, water rises through the suction valve E into the barrel above the piston ; and when the piston ascends, the water being pressed upwards keeps the valve E closed, and opens the valve D, and is thus propelled into the force pipe. By this arrangement the force pipe receives a continual supply of water from the pump barrel without any intermission ; and in like manner the pump barrel receives an unremitting flow from the suction pipe. This will be distinctly seen, if it is con- sidered that either of the two suction valves E or F must be always open. If the piston descends, the valve E is open and F is closed ; and if the piston ascends, the valve E is closed and the valve F is open: a stream, therefore, continually flows through the one valve or the other into the pump barrel. In like manner, whether the piston ascends or descends, one of the valves C or D must be open ; if it descends, the valve D is closed and C is open ; if it ascends, the valve D is open and C is closed. The Fire Engine. (109.) The fire engine is subject to a variety of different forms, which all, however, agree in one principle. It generally consists of a double forcing pump communicating with the same air vessel, and instead of a force pipe a flexible leather hose is used, through which the water is driven by the pressure of the condensed air in the air vessel. A section of the ap paratus is represented in fig. 42. T is a pipe which descends into the receiver, or to any vessel containing the supply of water. This pipe communicates with two suction valves V, which open into the pump barrels of two forcing pumps A B, in which solid pistons P are placed. The piston rods of these are connected with a working beam, so arranged that a number of different persons may act on both sides of it. Force pipes proceed from the sides of the pump barrel above the valves V, and they communicate with an air vessel M, by means of valves V', which also open upwards. The pipe descends into the air vessel near the bottom, as already described in jig. 39. This pipe is connected with the flexible leathern hose L, the length of which is adapted to the purposes to which the machine is to be applied. The extremity of the hose may be carried in any direction, and may be introduced through the doors or windows of buildings. By the alternate action of the pistons, water is drawn through the suction valve, and propelled through the forcing valves V, until the air in the top of the vessel M be- 25* A TREATISE ON PNEUMATICS. CHAP. VI. Fig. 42. comes highly compressed. This pressure acts continually on the surface of the water in the vessel, and forces it through the leathern hose, so as to spout from its extremity with a force depending partly on the degree of condensation, and partly on the elevation of the extremity of the hose above the level of the engine. It is to be considered that the pressure of the condensed air has, in the first instance, to support a column of water, the height of which is equal to the level of the end of the tube above the level of the water in the air vessel ; and until the pressure of the condensed air exceeds what is neces- sary for this purpose, no water can spout from the end of the hose ; and, subsequently, the force with which it will so spout will be proportional to the excess of the pressure of the con- densed air above the weight of the column of water, whose height is equal to the elevation of the end of the hose above the level of the water in the air vessel.* The, Siphon. (170.) The siphon is a contrivance by which a liquid may be conducted from one vessel to another through an intermediate channel or pipe, which rises above the natural level of the liquid. Let D,fg. 43., be a cistern containing a liquid, and let B be the height over which it is necessary to conduct that liquid. * The resistance of atmospheric pressure is not here considered. AM. ED CHAP. VI. SIPHONS. 253 Let A B C be a bent tube open at both ends, and let the leg B A be immersed in the liquid which it is required to transfer, and let the end C be directed into the vessel to which it is in- Fig. 4-3. tended to remove it. Let the air which fills the tube D B C be drawn from it by the mouth applied at C, or by an exhausting syringe. The atmospheric pressure immediately taking effect on the surface D of the water' in the cistern will press the water into the tube A B, towards the point B ; and if the point B be not at a greater height above the level of the cistern than 34 feet, then the water will rise to the highest point B, and will flow so as to fill the entire tube to the mouth C. To comprehend the principle upon which the siphon acts, let us suppose the water at the point B acted upon by two pres- sures, one towards C, and the other towards D. It will move in the one direction or in the other according as the one or the other pressure prevails. The atmospheric pressure acting on the surface D supports the column in the siphon between the surface and the point B, and it presses the water at B towards C with a pressure equal to the amount by which the atmos- pheric pressure exceeds the weight of the column D B, which it sustains in the siphon. The atmospheric pressure also acts at the mouth C of the siphon, and is resisted by the weight of . the column C B. It exerts a pressure on the water at B, amounting to the excess of the atmospheric pressure above the weight of the column C B. Thus it appears that the water at B is urged towards C by a force equal to that pressure by which the atmospheric pressure exceeds the weight of the water in B D, and this force is resisted by a force equal to that by which the same atmospheric pressure exceeds the weight of the water in C B. Now, since the atmospheric pressure exceeds the weight of the water in D B by a greater quantity 22 254 A TREATISE ON PNEUMATICS. CHAP. VI. it exceeds the weight of the water in B C, it follows that B will be urged towards C with a greater force than it is urged towards D, and, therefore, that it will move towards C. It is Fig. 43. evident that the excess of the force which urges it towards C above the force which urges it towards D will be equal to the weight of the column of water C which is contained in the longer leg of the siphon below the level of the water in the cistern D. If the leg of the siphon terminate at D', the forces which would act on the water at B would be equal, for the one would >e the atmospheric pressure diminished by the weight of the water in B D, and the other would be the atmospheric pressure diminished by the weight of the water in B D' ; but the weight of the water in BD and BD' being equal, the forces which act on the water at B will also be equal; therefore no water will flow from the siphon. If the leg of the siphon terminate above D', as at E, then the pressure on the water at B, the siphon being supposed to be filled, will be greater in the direction at B D than in the direction at B C, and, therefore, the water will flow back into the cistern, and the siphon will be useless Let F G be a vessel to which the liquid is to be transferred When it rises in this vessel above the mouth C to anv higher le M^ a l^' thei ! * h \ wei & ht of th e ^ater in the leg below L will be balanced by the pressure of the water in the vessel F G and, therefore, the efficient leg of the siphon will be B L Thus' as the surface of the water rises in the vessel F G the actual leg of the siphon is shortened. When the surface L has risen towards the level of the surface D, then the legs of the siphon become equal, and, by what has been already stated, its action must cease. CHAP. VI. SIPHONS. 255 It thus appears that the siphon is merely an instrument used in decanting a liquid, but that it does not perform the office of a pump in raising it above the level which it held in the vessel from which it is drawn. The process of exhausting the syringe by suction, or other- wise, is frequently difficult and always inconvenient. But this may be avoided by presenting the legs of the siphon upwards in the first instance, and having stopped the shorter leg with the hand, filling the siphon through the longer leg C B. Both ends of the tube being then stopped, let them be pressed down- wards, the shorter leg being introduced below the water in the cistern, and the longer leg being carried over the vessel in which the liquid is to be decanted. The process of exhaustion is sometimes facilitated in the following manner : A small tube proceeds from the longer leg near its extremity at D, fig. 44. The extremity A being immersed in the liquid, and the extremity C being stopped by the hand, the mouth applied at the extremity E of the subsid- iary tube will exhaust the siphon and cause the water to rise in it. When the siphon is constructed upon a very large scale this process is impracticable. In that case both ends of the tube A and C may be first plugged, and a hole being made at the highest part B, the instrument may be filled with liquid. The hole through which it is filled being then plugged, and the extremities opened, the instrument will act. A siphon of any magnitude may thus be constructed, and water may be carried over a hill, the perpendicular height of the top of the siphon not exceeding 34 feet above the level of the reservoir from 256 A TREATISE ON PNEUMATICS. CHAP. VI. which the water is to be drawn ; but it is obvious, also, that the basin into which it is discharged must not be higher than the level of the receiver from which it is drawn. The Wurtemburg siphon has the convenience, when once filled, of always remaining so, the waste by evaporation only being supplied. This instrument is represented in Jig. 45 Fig. 45. When not in use, it may be hung up upon a hook or nail by the curved part B. The ends D and E will then be presented upwards, the liquid being retained in the siphon by the atmos- pheric pressure acting on both surfaces at D and E. When the leg B C D is immersed in a vessel of liquid, the surface D is pressed clown by the weight of the incumbent liquid, and also by the atmospheric pressure acting above that. This pressure is transmitted to E, where it is resisted by the atmos- pheric pressure only ; consequently the Avater will be driven from E with a force equivalent to the hydrostatic pressure on the surface D. CHAP. VII. AIR GUN AIR BALLOON. 257 CHAP. VII. THE AIR GUN, AIR BALLOON, AND DIVING BELL. THE AIR GUN. FIRST ATTEMPTS AT BALLOONS. LANA'S BALLOON OF RAREFIED AIR, FIRE BALLOONS. MONTGQLFIER's BALLOON. FIRST ASCENT. BALLOONS INFLATED WITH HYDROGEN. PARA' CHUTE. BLANCHARD'S EXPERIMENT. CAUSES OF THE EFFICACY OF THE PARACHUTE. ASCENT OF GAY LUSSAC AND BIOT. APPEAR- ANCES IN THE HIGHER REGIONS OF THE ATMOSPHERE. THE DIVING BELL. The Jtir Gun. (171.) THE air gun is an instrument for projecting balls or other missiles by the elastic force of condensed air. A strong *metal ball is constructed, furnished with a small hole, and a valve opening inwards : in this ball air may be condensed to any degree which its strength is capable of bearing, by means of a condensing syringe screwed into the hole. When this condensation has been accomplished, the ball is detached from the syringe and screwed at the breech of a gun, constructed so that a trigger is capable of opening the valve. The ball being placed in the barfel near the breech, and fitting the barrel so as to be air-tight, is exposed to the pressure of the condensed air the moment the valve is opened : this pres- sure propels it along the barrel, and continues to act upon it so long as the valve -is opened. It is thus projected from the gun in the same manner as that in which a ball is urged by the expansive force of exploded gunpowder. The force of projec- tion obviously depends on the degree of condensation which in given to the air in the ball. The stock of the gun may contain a magazine of balls, and be furnished with a simple mechanism by which these balls may be transferred in succession into the barrel, so that the gun is easily and quickly loaded after each discharge. The magazine of condensed air may receive different shapes and be differently arranged ; but that which is now described is one of the best forms for it. The Mr Balloon. (172.) The physical conditions under which a solid body im- mersed in a liquid will rise to the surface, sink to the bottom, 22* 258 A TREATISE ON PNEUMATICS. CHAP. VII. or remain suspended, have been fully detailed in a former part of this volume. (Hydrostatics, chap, v.) If a body be heavier than the quantity of liquid, the place of which it occupies, it will sink by that preponderance. If it be equal in weight to the liquid it displaces, it will remain sus- pended, as the liquid itself would ; but if it be lighter than the liquid which is displaced, the superior weight of the surround- ing liquid will press it upwards, and will cause it to ascend to the surface. Liquids being incompressible, all their strata have the same density, or nearly so ; and, consequently, a solid which at one depth is lighter than the liquid which it displaces, will also be lighter at every depth. Consequently, if a solid has a tendency to rise towards the surface at any depth, it will continue so to rise until it reach the surface. If, however, the strata of liquid approaching the surface had gradually decreased in density, then the solid, which was lighter, bulk for bulk, than an inferior stratum, might be equal in weight, bulk for bulk, to a superior one, and heavier, bulk for bulk, than others nearer to the sur- face. Thus, such a body would rise at certain depths, but at other lesser depths it would sink ; and at the depth of a certain stratum it would remain suspended. The property of liquids, which is the cause of these phe- nomena, is their power of freely transmitting pressure. This will be plainly perceived by referring to (55.), where it is shown that the solid rises to the surface by the pressure of the column of the liquid whose base is contiguous to it, and rests on the same level, and which pressure is transferred to the base of the solid by the inferior strata of liquid. Now this property of transmitting pressure is common to elastic fluids, and we are, therefore, warranted in the inference, that a solid suspended in a gaseous fluid, which is lighter, bulk for bulk, than the fluid, will rise ; that if it be heavier, bulk for bulk, it will fall ; and if it be equal in weight, bulk for bulk, it will remain suspended. That a solid, therefore, may rise in the atmosphere with any given force, it 13 only necessary lhat its weight should be less than the weight of the air which it displaces by the amount of that force. Upon this principle BALLOONS are constructed. The method of constructing a balloon, which naturally first suggests itself, is to exhaust a large chamber of the air which it contains, so as to render it a vacuum, or nearly so : it v, ill then continue to displace the same quantity of atmosphere as before, but its weight will be diminished by the weight of the air with- drawn from the chamber, and it will have a disposition to rise in the atmosphere proportionate to the difference between the actual weight of the materials which form the chamber and the weight of the air whose place it occupies. This was, accord- CHAP. vii. LANA'S BALLOON. 259 ingly, the method adopted in the earliest attempts on record to construct balloons. About the middle of the seventeenth century, a Jesuit named Francis Lana constructed four hollow spheres of copper, each twenty feet in diameter, and so thin that the total weight of the copper composing them was less than the weight of the air which they would displace. He proposed to attach these spheres to a boat furnished with a sail, as represented in Jig. 46., by which means he hoped to traverse the clouds. Fig. 46. The method of exhaustion which Lana possessed was insuf- ficient to accomplish his purpose ; but even had.it been other- wise, the atmospheric pressure acting on the external surface of the attenuated metal globes would have crushed them, and proved the project to be impracticable. It may be stated gen- erally, that no known solid possesses sufficient strength to enable a globe, or any other vessel formed of it, to resist the atmospheric pressure from without, when that pressure is not balanced by a corresponding pressure from within, unless it be made of so great a thickness that its weight will very much exceed the weight of the air which it displaces. To give sufficient buoyancy to a large hollow body, and at the same time to secure it from the effect of atmospheric pres- sure, it will be therefore necessary to fill it with some elastic fluid which will, by its elasticity, balance the effect of the ex- 260 A TREATISE ON PNEUMATICS. CHAP. VII. ternal air, and, by its small specific weight, produce a degree of buoyancy sufficient to raise the materials of which it is constructed. In this case, as the forces which act on the bal- loon are held in a state of equilibrium, or nearly so, no extraor- dinary degree of strength is required, and any extremely light and flexible substance impervious to air or gas may be used. The most obvious contrivance which is suggested by these considerations is atmospheric air rarefied by heat ; for in this case, the expansion produced by the heat gives the same degree of elasticity with a much less quantity of atmospheric "air. To explain this, let a glass bulb A be furnished with a tube T, which, rising from it to the extremity at which it is curved, descends into a vessel V, fig. 47., containing water or other Fig. 47. liquid : the air is thus enclosed in the tube in the common state of the external atmosphere. Let a spirit lamp, or any other source of heat, be now applied to the bulb at A ; the air in the bulb, receiving increased elasticity from the heat, will press the water towards the mouth of the tube, and, rising in bubbles, will escape at the surface of the water. This will continue until the air in the tube is highly rarefied ; still, however, retaining a degree of elasticity sufficient to balance the atmos- pheric pressure acting on the surface of the water in the vessel, and transmitted by it to the surface of the water in the tube. That the air in the tube is highly rarefied, may be veri- fied by removing the lamp from the bulb : as the tube cools, the air will contract itself into its former dimensions, and the pressure of the atmosphere will force the liquid through the CHAP. VII. FIRE BALLOON. 261 mouth of the tube and over the curved part into the bulb. It will bo found, that in this way the bulb and tube will be filled, with the exception of a very small bubble of air, which will remain suspended at the highest point of the tube : this bubble will have the same temperature as the external air, and the same pressure ; and it is obvious, that this is as many times lighter than the air which originally filled the tube and bulb, as its present magnitude is less than the whole contents of the bulb and tube. If, instead of a glass bulb, we take a large spherical bag con- structed of any light substance, and having in one part a circular opening or hole, this bag may be distended by blowing into it common air. If the hole be then presented downwards, and a lamp suspended beneath it, the flame of the lamp will gradually increase the temperature of the air contained in the bag : it will thus acquire increased elastic force, by which a part will be expelled at the hole under which the lamp is suspended. This process of rarefaction will be continued so long as the air contained in the bag receives increased temperature from the heat of the lamp ; but throughout the whole process the elastic force of the rarefied air will be equal to the external pressure of the atmosphere, and the bag will be subject to no force tend- ing either to burst it or to crush it. Such a bag, if constructed of sufficient magnitude, may by these means be rendered lighter than the air which it displaces. It will thus have a corresponding buoyancy, and will ascend in the atmosphere with a force equal to the difference between its own weight and the weight of the air which it displaces. The application of these principles forms the first successful attempt in aeronautics. In the year 1782, two paper-makers, named Montgolfier, residing at Annonai, in France, constructed a bag of silk, in the form of a square box, containing about 40 solid feet when filled. In the bottom of this was placed an aperture, under which burning paper was applied : it ascended to nearly 100 feet in the air. The experiment was immediately instituted on a larger scale. A balloon, constructed of a capaci- ty exceeding 700 solid feet, rose in the same manner to an elevation of more than 600 feet. A balloon in the spherical form, but on a scale still larger, was next constructed ; it con- tained 23,000 feet, and had a buoyancy capable of raising 500 pounds. It ascended in the atmosphere to a height of about 6000 feet. Hitherto the experiments were confined to the object of ascertaining, the mere possibility of ascending in the atmos- phere ; and, in some cases, the effects produced on animal life at great elevations were tried, by sending up various ani A TREATISE ON PNEUMATICS. CHAP. VII. f wicker - work suspended from the At length, in the latter end of the year 1783, a balloon was t^' Wlth a Vlew to trans P rt one or more pe> the higher regions of the atmosphere. This machine 3 ! f ^ f^ ^ 74 *<* in height and 48 in Immediately under an aperture in the bottom of the on SPen ? ed ^r 11 gmte Wlthin reach of the aer onaut! Son w?h' Wa tl P f if the bUrning fuel to maintain the rare ^c- abourSOOO ft h MP'I An / s ' ent was de to a height of bout 3000 feet by M. Pilatre de Rozier and the marquis d'Ar- landes. After this experiment various others succeeded in balloons constructed in the same manner maThinP^xlf -T C i t0r f theS6 balloons conceived that the machine owed its buoyancy to the gas produced by the fire, and which with an elastic pressure equal to the air was sped?' M^& ; S 6 mechanical P finci P le of the ascenrwas The step from fire balloons to balloons filled with gas specif- ically hghter than atmospheric air, of the same preL^wi now easy and obvious. The gas at present denominated hydrogen was submitted to a series of experiments, by which t was found that its specific gravity was only one seventh of it ot common atmospheric air. It was obvious, therefore, that a balloon filled with this gas would have considerable oyaney. Balloons were accordingly constructed and inflated . tnis gas, and various ascents have since been made the particulars of which would not be suitable to the limHs of the present treatiss The density of each stratum of air being proportional to the pressure under which it is placed, it followsthat in ascending i the atmosphere the strata will have less and less specifif t g hP In 7 ' f f M'I fcerefore, containing gas which balances the lower strata, will, if it be completely filled, have a tendency st when it has ascended into the higher strata : for the gas, not having room to expand, will maintain its original elastic ce whi e the atmospheric pressure, being diminished in the ascent will cease to balance this elastic force of the confined There will then be a bursting pressure equivalent to the ess of the atmospheric pressure of the lower strata over the aosphenc pressure in the strata to which the balloon has ascended. tfe^T eff ^ ct \ ma j be Provided against by imperfectly filling the balloon in the first instance, so that as it ascends, the ga? which it contains will have room to expand, and thus, while the sure of the atmosphere is diminished, the elastic pressure CHAP. VII. HYDROGEN BALLOONS. of the gas in the balloon will be diminished in the same propor- fhS'dp lon ^ a \ the atmospheric pressure is not diminished to that degree which would cause the gas enclosed in the balloon buSh h S li aS t0 com P let & inflate ^ no force tending to burst the balloon can exist ; but should the ascent be continued to a greater height, then a bursting pressure will be called into action by the pressure of the atmosphere being diminished in a greater degree than the elastic force of the g!s in the balloon In this case the danger may be removed by the provision of a valve opening in some convenient part of the balloon, by which a part of the gas may be allowed to escape. Such a valve is also necessary in order to enable the aeronaut to descend at pleasure. Without it he would be compelled to remain in the atmosphere as long as the balloon continued to retain the gas with which it was inflated ; but provided with such a valve, he ^m ^n^f'rf ^ gaS ^ esca P^ and thereby diminish ie magnitude of the balloon, and consequently produce a cor- responding decrease in its buoyancy. By analogy we should infer that the power of ascending at p easure would be obtained by being able to supply an increased quantity of gas to the balloon; but this would not be easily obtain^ h 5 ' accordin ^' the power of ascending has been obtained by carrying up sand-bags, or other weights called ballast, by throwing out which the machine is lightened, and fonnH t fT '"I 5 7 lf fr m any acciden tal cause it should be found to fall with dangerous precipitancy, its rate of descent may be retarded by throwing out this ballast. nJEff!S C T e f d ?? ger attendin aeronautical experi- ments arises from the accidental escape of the gas from the balloon; and it has consequently been a desirable object to itrive means, m such cases, for rendering the fall of the aeronaut less liable to dangerous effects. With this view an apparatus has been contrived, called a parachute. It is usually formed like a large umbrella, which spreads above the car with its concave side presented downwards. The effect of this acting against the air below is to break the descent, and after a short time the rate of descent becomes uniform, instead of y r 1G8 enerall y are > accelerated. The magni- tude of the parachute may be such, that the rate of descent shall >e so slow that no danger is to be apprehended from the con- cussion attending the fall. If, therefore, the aeronaut descend on land, his safety is insured. The subjects of the first experiments with the parachute were naturally inferior animals. M. Blanchard dropped a dog sus- pended from a parachute, from the altitude of 6000 feet above the surface of the earth. A whirlwind interrupted its descent, and carried it above the clouds. The aeronaut soon after met 264 A TREATISE ON PNEUMATICS. CHAP. VII. the parachute again ; the dog recognized its master, and express- ed his uneasiness and solicitude by barking ; another current of air, however, carried him off, and he was lost sight of. The parachute with the dog descended soon after the aeronaut in safety. Ten years after this, M. Garnerin made several suc- cessful experiments with the parachute. He placed it half expanded between the balloon and the car, so as to spread like an umbrella above him. At the height of about 2000 feet he had the intrepidity to cut off the parachute and car from the balloon. He descended slowly, the parachute gradually unfold- ing itself, and finally reached the ground in safety. The same experiment was several times repeated with similar success. In one case he descended from the perpendicular height of 8000 feet. As the balloon derives its efficacy from the weight of the atmosphere, the parachute depends on the inertia of that fluid. In descending, the broad concave surface of the parachute must drive before it the column of air extending from its surface to the ground ; but the circumstance on which its principal excel- lence depends is, that the resistance arising from this inertia increases in a more rapid proportion than the velocity of descent. A double velocity in the parachute would produce a fourfold resistance in the ait ; a threefold velocity would pro- duce a ninefold resistance ; a fourfold velocity a sixteenfold resistance ; and so on. The law of this resistance has been already fully explained respecting liquids in (107.) ; and it may be explained in the case of the atmosphere in exactly the same words ; but in the case of the descent of the parachute from great elevations, there is an obvious cause which makes the resistance increase even in a more rapid proportion than is indicated by this law. The increase of the resistance in the proportion of the square of the velocity arises from the suppo- sition that the resisting fluid through which the body moves continues to be of the same density. Now this is not the case with the atmospheric air through which the parachute falls ; each stratum into which it enters has a density greater than that from which it descends, and consequently, on that account alone, will offer a proportionally increased resistance. This cause, added to the former, will very speedily compel the para- chute to descend with a uniform velocity. This velocity will be small in the same proportion as the parachute is large, and as the weight of the car and its contents is small. As the gas by which a balloon is inflated is lighter than the atmosphere, the valve provided for its escape, when the aero- naut wishes to descend, is placed usually in the top of the balloon. If it were placed in the bottom, even although it were open, the gas would not escape ; at least not in any considera- CHAP. VII. PARACHUTES. 265 ble quantity, nor with any degree of certainty. The superior pressure of the atmosphere, and the natural levity of the gas itself, would prevent its escape ; but when the valve is placed in the top, the gas will issue from it on the same principle as a lighter fluid rises in a heavier. The car which bears the aero- naut is usually supported by a net-work, which extends over the balloon and which is connected with it by a number of ropes and strings, as represented in Jig. 48. Fig. 48. The total impracticability of guiding or governing balloons in their course through the air, has hitherto prevented them from being applied to any purpose of extensive utility. Scien- tific men have, on some occasions, ascended in the atmosphere, with a view of observing at great elevations the effect of tem- perature, pressure, electricity, and other phenomena connected with meteorology. In 1804, M. Gay Lussac and M. Biot made an ascent from Paris, furnished with various meteorological apparatus, to a height of upwards of 13,000 feet. Soon after- wards, M. Gay Lussac ascended alone, to a height of 23,000 feet above Paris. In 1807, M. Garnerin ascended at ten o'clock at night from Paris, and, rising with unusual rapidity, soon attained an immense elevation above the clouds. By some neglect, the apparatus for discharging the gas from the balloon 266 A TREATISE ON PNEUMATICS. CHAP. Vlt. was found to be unmanageable, and the high degree of rare- faction at so great an elevation produced in the balloon such a tendency to burst, that the aeronaut was obliged to cut a hole in the silk to allow the escape of the air. The .balloon then descended with such rapidity, that he was obliged to counteract its motion by casting out all his ballast. The balloon thus continued alternately rising and sinking for nearly eight hours, during which he experienced the effects of a thunder storm, by which he was finally dashed against the mountains. He landed at Mont Tonnere, at a distance of 300 miles from Paris. The effects produced on the aeronaut by the rarefaction of the atmosphere at great elevations, are sensibly manifested in respiration ; the pulse is rendered more rapid, the head unusu- ally swelled, and the throat parched. The intense cold which also necessarily accompanies rare- faction produces great inconveniences, and an irresistible disposition to sleep is felt It has been found also that storms and currents in the atmos- phere are local, and that while one stratum is thus agitated, other strata inferior or superior to it will be calm. By man- aging his ascent or descent, the aeronaut may thus transfer him- self from wind to stillness, from a storm to a calm, or from one current of wind to another in a different direction. The veloci- ty with which balloons are sometimes transported through the air amounts to eighty miles an hour. The appearance of the clouds from great heights is said to resemble a plain of snow, or a sea of white cotton. Those which are charged with elec- tricity are said to resemble the smoke of ordnance. Clouds containing hail or snow are often encountered, in which the car becomes almost filled with these substances. Clouds of mist or rain frequently drench the aeronaut. When birds are allow- ed to escape from the balloon at a great height, they fall almost perpendicularly downwards, the attenuated air not having suffi- cient inertia to offer resistance to their wings.* Attempts have been made to render balloons useful in mili- tary operations, by viewing from an elevated position the dispo- sition and movements of an hostile army. An academy, with this object, was actually established at Neudon, near Paris, during the late war, where a corps of aeronauts was trained to the service. A balloon was kept constantly inflated^ and secured to the ground by a rope, which allowed it to ascend to a height of about twenty-five yards. At this institution military balloons were prepared for the different divisions of the French army and on one occasion an ascent was made by a French general, at the battle of Fleury, to a height of nearly 500 yards, * The Edinburgh Encyclopaedia, article Aeronautics. CHAP. VII. DIVING BELL. 267 from which he reconnoitred the hostile armies. It is said that the signals which were made to general Jourdan on this occa- sion decided the fate of the engagement. The project, however, has long since been abandoned, not being found generally available. It has been proposed to render balloons useful in geographi- cal surveys, both as a means of raising the observer to great elevations, and of transmitting signals to great distances. The Diving Bdl (173.) The spirit of inquiry which so strongly characterizes the human mind, and which stimulates man to undertakings in which life itself is imminently risked, has not only prompted him to ascend into the regions of the air, but has also carried him to the depths of the sea. The practice of diving is of very early origin, and was first probably adopted for the recovery of articles of value dropped into the water at small depths. Instances are recorded of per- sons having acquired by practice the habit of enduring submer- sion for a length of time which in many cases seems astonishing, and in others altogether incredible. Indeed, the circumstances attending most of these narrations bear unequivocal marks of fiction. The gratification of a taste for the marvellous does not tempt us to allow a space in our pages for a description of the feats of the Sicilian diver, whose chest was so capacious that by one inspiration he could draw in sufficient air to last him a whole day, during which time he would sojourn at the bottom of the sea, and who became so inured to the water, that it was almost a matter of indifference to him whether he walked on dry land or swam in the deep, remaining often for five days in the sea living upon the fish which he caught ! Various attempts were made to assist the diver by enabling him to carrv down a supply of air ; and after a long period and gradual improvements, suggested by experience, the present diving bell was produced. This machine depends for its efficacy on that quality in air which is common to all material substances, impenetrability ; that is, the total exclusion of all other bodies from the space in which it is present. The diving bell is a large vessel closed at the sides and at the top, but open at the bottom. It should be perfectly impenetrable to air and water. When such a machine, with its mouth downwards, is pressed into the water by sufficient weights suspended from it, the air contained in it at the surface will be enclosed by the sides, the top, and the surface of the water which enters the mouth of the machine. As it descends in the 268 A TREATISE ON PNEUMATICS. CHAP. VII. liquia, tne air enclosed in it is subject to the pressure, which increases in proportion to the depth, and by virtue of its elas- ticity will become condensed in proportion to this pressure. Thus at the depth of about 34 feet, the hydrostatic pressure will be equal to that of the atmosphere ; and since the air at the surface of the water is under the atmospheric pressure, it will be affected by double, the pressure at the depth of 34 feet. It will, therefore, conformably to what was explained in (132.), be condensed so much as to be reduced to half its original dimensions. Half the capacity of the machine will, therefore, be filled with water, and the other half will contain all the air which filled the machine at the moment of its immersion. As the depth is increased, the space occupied by the air in the bell will be proportionably diminished. It is well known that if an animal continue to respire in a space from which a fresh supply of atmospheric air is excluded, the air confined in the space will at length become unfit for the support of life. This is owing to an effect produced upon the air drawn into the lungs, by which when breathed it contains carbonic acid, an ingredient not present in the natural atmos- phere, and which is highly destructive to animal life.* When the air in which the animal is confined has been breathed for a length of time, this effect being repeated, the air enclosed becomes highly impregnated with this gas ; and if its escape be not allowed, and a fresh supply of atmospheric air admitted, the animal cannot live. If, therefore, a diving bell be used to ena- ble persons to descend in water, it will be necessary either to raise them to the surface after that interval in which the air confined in the bell becomes unfit for respiration, or means must be adopted to send down a supply of fresh air, and to allow the impure air to escape. But besides this, there is another reason why means of sending down a supply of air are necessary. It has been already proved, that the hydrostatic pressure causes the water to fill a large part of the capacity of the machine, the air contained in it being condensed. It is necessary, therefore, in order to maintain sufficient room for the diver free from water, to supply such a quantity of air, as that in its condensed state it will keep the surface of the water near the mouth of the machine. Thus, at the depth of 34 feet, it will be necessary to supply as much air as would fill the bell in its natural state. At double that depth, as much more will be necessary, and so on. * There is always present, however, in every part of the atmosphere, a very small and variable proportion of carbonic acid. Animal respiration greatly in- creases the quantity of this deleterious gas in a confined portion of air, and also diminishes the quantity of oxygen gas, that constituent of atmospheric air OB which its power of iustaining life depends. AM. ED. CHAP. VII. DIVING BELL. 269 The air necessary for these purposes is supplied by one or more large condensing syringes, constructed on the principle explained in (162.). These syringes, or pumps, are placed above the surface of the water into which the bell is let down, and they communicate with the interior of the bell by a flexible tube carried through the water and under the mouth of the bell. Through this tube any quantity of fresh air, which may be requisite for either of the purposes already mentioned, may be supplied. A tube furnished with a stopcock is placed in the top of the bell, by which the diver can let any quantity of impure air escape, to make room for the fresh air which is admitted. The impure air will rise by its levity in bubbles to the surface. i The diving bell received its name from the shape originally given to it. It was constructed with a round top, increasing in magnitude towards the mouth, thus resembling the shape of a bell. It is now, however, usually constructed square at the top and bottom, the bottom being a little larger than the top, and the sides slightly diverging from above. The material is some- times cast iron, the whole machine being' cast in one piece, and made very thick, so that there is no danger either from leakage or fracture. In this case the weight of the machine itself is sufficient to sink it. Diving bells, however, are also sometimes constructed of close-grained wood, two planks being connected together with sheet lead between them. In the top of the machine are placed several strong glass lenses for the admission of light, such as are used in the decks of vessels to illuminate the apartments below. The shape of the machine is generally oblong, with seats for the diver at the end ; shelves for tools, writing materials, or any other articles necessary to be carried down, are placed at the sides ; and below the seats there are boards placed across the machine to support the feet. Messages are communicated frona below to above either in writing or by signals. A board is car- ried in the bell on which a written message may be chalked. This board communicates by a cord with the arm of the super- intendent above, who, on a signal given, draws it up, and who, in a similar way, is able to return an answer. When the bell is of cast iron, a system of signals may be made by very simple means ; a blow struck by a hammer on the bell produces a peculiar sound distinctly audible at the surface of the water, arid which cannot be mistaken for any other noise. The number of strokes made on the bell indicate the nature of the message, the smaller number of strokes signifying those messages most frequently necessary. Thus, a single stroke calls for a supply of fresh air ; two strokes command the bell to stand still ; three express a desire to be drawn up ^ four to b 23* 270 A TREATISE ON PNEUMATICS. CHAP. VII. lowered, and higher numbers express motion in different direc- tions. Of course this system of signals is arbitrary, and liable to be varied in different places. The bell is usually suspended from a crane, which is placed above the surface of the water ; and in order to move it, this crane is placed on a railway, by which it is enabled to traverse a certain space in one direction. The carriage which traverses this railway supports another railway in directions at right angles to it, on which the crane is supported. By these means two motions may be given to the crane, the extent of which may be determined by the length of the railway, and the bell may be brought to any part of the bottom which is perpendicu- larly below the parallelogram formed by the length of the railway. INDEX. A. Adulteration of milk ; of spirits, page 126. Air, its color, 175 ; has weight, 176 ; the effects of its inertia, 177 ; proofs of its materiality ; impenetrable, 178 ; its elasticity ; its elasticity explained, 181. Air-pump, 223 ; experiments with, 229, Air-vessel of forcing-pumps, 248. Air-balloon, 257. Air-gun, 257. Alloys, 123. Amazon, river, its disappearance, 48. Animals, birds, and fishes, their shape explained, 147. Archimedes, his experiment on Hiero's crown, 126 ; his screw, 157. Aristotle, his knowledge of the weight of air, 190. Arlandes, Marquis de, his ascent in a balloon, 262. Atmosphere, its probable limits, 182. Atmospheric air, its properties, 174 ; its elasticity equal to its weight, 187 ; its height, 205; its pressure, 205; pressure bursts a bladder, 229 ; effects in the higher strata observed in bal- loons, 266. B. Balance, hydrostatic, 116. Ballast, its effect in ships, 99. Ballcock ej:plaincd, 77. Balloons, air, 257 ; formed of air rare- fied by heat, 260'; Montgolfier's, 261 ; Pilatro de Rozier's ascent ; Marquis do Arlandes's ascent; first inflated with hydrogen, 262 ; Blanchard's as- cent, 263 ; ascents of Gay-Lussac, Biot, and Garnerin, 265; their military use, 266. Barker's mill, 156. Barometer discovered by Torricelli, 190. applied to the measurement of heights by Pascal, 191 ; construction of, 192 ; diagonal, 197 ; wheel, 198 ; its uses ; a weather glass, 201 ; measuring heights by, 203. Bellows, hydrostatic, 12; domestic forge, 208. Birdcage fountain, 211. Birds ; their flight depends on air, 178. Blanchard, his ascent in a balloon, 263. Boiling water, the process of, 85. Bramah, his press, 10. Breathing accounted for, 207. Buoyancy explained, 74. C. Camel for lifting vessels over shoals, 78. Campbell, his experiment on a bottle sunk in the sea, 34. Canals, construction of, 49 ; locks of, 49 ; their defect as means oftransport, 148. Cataracts, their heights, 47. Chain pump, 165. Cities, method of supplying them with water, 37. 51. Clocks, ornamental fountain, 46. Color of air, 174. Compressibility, 172. Condenser, 237. Condensing syringe, 234. Contrivance to prevent foundering, 76. Cream floats on milk, 84. Cupping, 233. D. Dectot, his hydreoles, 90. Density, 109. De Parcieux's hydrometer, 122. Diagonal barometer, 197. Discovery of atmospheric pressure, its history, 188. Diver, effect upon, at great depths, 35. Diving bell, 267. Double forcing pump, 250. Elasticity of air, 170 ; proportional to its density, 182; of atmosphere equal to its weight, 187 ; of air bursts a bladder, 229. Engine, fire, 251. Exhausting syringe, 215. Fire engine, 251. Fish, their power of rising and sinking, ' 81 Flies, their power of walking on ceil- ing?, 207. 272 INDEX. Floating bodies, their position ; equilib- rium of, 91 ; on water explained, 79 ; bodies explained, 71. Forcing pump, 246 ; double, 250. Fountains, natural ones explained, 47 ; for birdcages, 211. Fruit dried or shrivelled, experiments on with air-pump, 228. G. Galileo rejects the ancient doctrine of a vacuum, 190. Garnerin, his ascent in a balloon, 265. Gas-holders, 212, Gasometers, 213. Gauge of air-pump, 224. Gay Lussac, his ascent in a balloon, 265. Governor sluice, 162. Guinea and feather experiment, 232. Gun, air, 257. H. Heat, its effects, 171. Heating houses, method of, 87. Hydraulics, 130. Hydrogen first used for balloons, 262. Hydrometer, Sikes's, 120 ; Nicholson's, 121 ; De Parcieux's, 122. Hydrostatic press, 10 j bellows, 12. Ice lighter than water, 82. Jets d'eau, 249. Immersion of solids in liquids, 58. Impenetrability of air proved experi- mentally, 179. Inertia of air, its effects, 177. Ink bottles to prevent ink evaporating, 210. K. Kettle, form -of its spout, 41 ; effect in boiling, 209. Lana, Francis, his balloon, 259. Level, its exact meaning, 52. Leveling, instruments for, 54. Life preservers, 79. Lifting parnp, 238. Limits, probable ones of atmosph-ore, 182. Liquids machines, 8; experiment to prove their compression, 35 ; main- tain their level, 37; their surface level, 42 ; resistance of, J.43. Liquors, effervescing, 214. Locks of canals, 49. M. Machines, hydraulic, 150 ; for raising water, 238. Magdeburg hemispheres, 231. Matter, its mechanical forms, 1. Mercury, why used in barometer, 197 ; method of purifying it, 195. Mill, Barker's, 156. Montgolfier, his balloon, 261. N. Nature abhors a vacuum, 189. Nicholson's hydrometer, 121. O. Oil floats on water, 83. Oronoko, river, its disappearance, 48. P. Parachute, 263. Paradox, hydrostatic. 8. Pascal, his verification of Torricelli'g discovery of the effects of atmospheric pressure, 191. Penetration of dimensions, 127. Pilatre de Rozier ascends in a balloon, 262. Pneumatics, 169. Pneumatic trough, 212. Pressure of liquids, 3 ; hydrostatic, ex- amples of, in animal economy, 16 ; proportional to the depth, 17 ; equal in all directions, 21 ; on the sides of a vessel, 23 ; on embankments, 26 ; greater than the weight which pro- duces it, 27 ; independent of the shape of the vessel, 29. Proof, spirit, 84. Pumps, their theory discovered by Tor- ricelli, 191 ; water cannot rise in, without atmospheric pressure, 230 ; lifting, 238; without friction, 240; suction, 241 ; forcing, 246 ; double forcing, 250. R. Railroads, their advantages, 149. Rarefaction of air, 214. Regulation of mill-work by governor, 162. Resistance of air, its effects, 177. Respiration rightly accounted for by an ancient writer, 190. Rivers, their origin and course explain- ed, 46 ; their disappearance explained, 48 ; eddies of, 149 ; flowing through a lake, 138. Rocks split by the pressure of liquids, 36. -s. Scale of barometer, 194. Screw of Archimedes, 157. Ships, their form explained, 76 ; why they lean sidewards, 101. Sikes's Hydrometer, 120. Siphon gauge, 225; Wurtemberg, 256. Sky, its color accounted for, 174 Fluice, governor, 162 INDEX. 273 Solids measured by immersion, 59. Sound can only be produced in air, 234. Specific gravity, 102 ; methods of find- ing it, 115; of a mixture, 128. Spirit level, 56. Spouting fluids, velocity of, 131. Springs explained ; submarine ones ex- plained, 47. Steam-boats, use of movable weights on deck, 101. Suction, ancient theory of, wrong, 189. Suction pump, 241. Syringe, exhausting, 215 ; condensing, 234. T. Tea-pot, form ol its spout, 41 ; why a hole in the lid of, 209. Tequendama, cataract of, 47. Torricelli accounts for the elevation ot water in pumps ; discovers the ba- rometer, 190. Toys, philosophical ones, 82. V. Vacuum, ancient doctrine respecting, Vapor. 173. Vaporization, 173. Vena contracta, 136. Vent-peg, 209. Vernier applied to barometer, 200. Walking on water, 99. Water apparently converted into wine, 85; how obtained pure, 105; wheel, overshot, 151 , undershot, 154; breast, 155. Waves, optical deception of, 43 ; causes of this appearance, 44. Weather-glass, common rules absurd 202 ; correct rules of it, 203. Weight lost by immersion, 63 ; of air, 176 ; of atmosphere equal to its elas- ticity, 187. Wells of water explained, 47. Wheel barometer, 198. Wind arises from the inertia of air, 178 ; its effects, 179. Wine, guggling noise in decanting, 213 j error in the common method of cool- ing, 88. Wurtemberg siphon, 256. THE END. m UNIVERSITY OF CALIFORNIA LIBRARY