SYLLABUS OF A COURSE OF EXPERIMENTAL LECTURES €fftots of iBquiXihvium, TO BE DELIVERED AT THE KING'S COLLEGE, LONDON, OCTOBER TERM OF THE YEAR 183L THE REV. H. J^OSELEY, PKOl'ESSOn OF NATURAL AND EXPERIMENTAL PHILOSOPHY LONDON: B. FELLOWES, BOOKSELLER & PUBLISHER TO THE COLLEGE, 39, LUDGATE-STREET. 1881. LOAN STACK TJiese Lectures require no introductory course of mathematical reading; the method of demonstration being exclusively experimental. LONDON : R. CLAY, PRINTER, BREAD-STREF.T-HILL, CHEAPSIDE. '?339J) SYLLABUS, &c. &c. Time Space, — Matter Force, On the nature of a Property or Quality. The Properties of Matter, — Impenetrability — uselessness of the term, as simply implying the distinction of matter and space. — Divisibility. Molecules, — Quantity, — Motion, — Force. — Quantity of motion, — Velocity, — Direction Resist- ance, — Pressure, — Equilibrium, All the mutual relations of Time — Space — Matter — and Force, belong properly to the science of Mechanics. a2 " 090 According to the usual acceptation of the term. Mechanics, that science is, however, confined to the investigation of the conditioms of the equilibrium and the rnotiori of masses, or aggregates of matter, acted upon hy known and appreciable forces. To the theory of Equilibriwn belong — the science of Statics, or the Equilibriwn of Solids — and the science of Hydrostatics, or the Equilibrium of Fluids, To the tJieory of Motion belong — the science of Dynamics, or the Motion of Solids — and of Hy- dronamics, or the Motion of Fluids, On the Abstract or Mathematical Method in Physics. On the Experimental Method — Nature and limits of the proof by experiment. ON STATICS, OR THE EQUILIBRIUM OF SOLIDS. Substitution of the term pressure for force in Statics, as implying force held in equilibrium. The equality of pressures. The unit of pressure. The quantity of pressure- The direction of pressure. The representation of pressures, in quantity and direction, by lines. Forces, to sustain one another upon a flexible line, must be equal ; act from one another, and in the direction of the line, at the points where they are applied to it. These conditions being satisfied, the form of the line is immaterial, and the pressures may be any where appHed in it. Application of pressure by means of the cord and pulley. If any number of pressures, acting upon the parts of a rigid system, are in equilibrium among themselves, and if to the same system there be applied other pressures, such as do not disturb the equilibrium thus existing ; these last are in equili- brium amongst themselves. Difficulty of ascertaining the conditions of the equilibrium of given pressures applied to a rigid system, arising from the impossibility of obtaining any such system not already acted upon by the pressure of gravity, or weight. This difficulty obviated by placing the system in equilibrium with respect to that pressure. On the equilibrium of two j^i'^'s^^^fc's acting upon 6 a rigid system, — They must be equal — they must act in opposite directions, but in the same straight line. These conditions being satisfied, the form of the system and the points of application of the pressures may be any whatever, and they may act either to or from one another. Pressure is propagated through rigid bodies in right lines. On the equilibrium of three pressures in the same plane acting upon a point. The parallelogram of forces. The equilibrium of a weight suspended by two cords. ' The resistance of a surface is in a direction per- pendicular to that surface. The equilibrium of three pressures, one of which is supplied by the resistance of an inclined plane, or a curved surface. The equilibrium of a weight upon an inclined plane — when the power acts (1st) parallel to the surface of the plane — (2d) parallel to its base — (3d) at any angle above the plane — (4th) at any angle below it. The force required to retain the plane at rest, when acted on by given forces. The wedge when it is in equilibrium. — The screw. The equilibrium of weights sustaining one another on two inclined planes, by means of a string passing over a pulley. The equilibrium of weights sustaining one another, as above, on two curved surfaces. On curves of equilibration. The equilibrium of any number of pressures acting, in the same plane, upon a point. The polygon of forces. The equilibrium of three pressures in different planes, acting upon a point. The equilibrium of any number of pressures in different planes, acting upon a point. The equilibrium of three pressures acting uj)on a rigid system in the same plane. Case in which the three pressures are parallel. Case in which one of the pressures is supplied by the resistance of a fixed axis, about which the sys- tem is moveable. Pressure upon the axis. Conditions of equilibrium in the case in which the forces are parallel — deduced from the above — proved independently. 8 The straight lever (1st) when the forces are ob- lique, — (2d) when they are parallel. The balance. — The false balance — means of weighing correctly with it. — The steelyard. — The handspike. — The crooked lever. — The crooked balance. — The hammer lever. — The crank. — Combinations of levers. — The weighing machine. — The Russel press lever. — The Stanhope press lever. — The genou. The wheel and axle. — The capstan. — The fusee. The cog-wheel.— Pinion. — Trundle. The forms of the cogs, leaves, and staves of these, necessary to an uniform action of the machinery. Precautions as to form, &c. may be in a great measure neglected, where the cogs are small. — System of toothed wheels. — The crane. The screw— the relation of the power and weight independent of the diameter of the screw. — The endless screw. — Hunter's screw. — Combinations of the screw and lever. — The camb. The pulley. — The single moveable pulley. — Smeaton's pulley. — White's pulley. — The Spanish burton. — The system of pulleys in which the last supports the weight. — The system of pulleys in which each string is attached to the weight. — The American burton. 9 Different mechanical contrivances for varying the quantity and direction of pressure and motion. — The crank. — Crown, spur and bevelled wheels. — Hook's joint. — Parallel motions. — The sun and planet wheels^ &c. — The eccentric. The equilibrium of any number of forces in tJie same plane applied to a rigid system. Lemma, — I-f there be a parallelogram in a given plane, and a point be anywhere taken in the same plane ; the difference of the areas of the triangles formed by drawing lines from the given point to the extremities of two adjacent sides of the parallelo- gram, shall be equal to the area of the triangle formed by lines drawn from the given point to the extremities of the diagonal. Theory of areas. Theory of moments. Case in which the system revolves upon an axis perpendicular to the plane of the forces. Pressure upon the axis. Equilibrium of any number of parallel forces acting upon a rigid system in the same plane. Equilibrium of any number of parallel forces acting any where upon a rigid system. The centre of gravity. 10 Examples, — the centre of gravity of a parallelo- gram — of a triangle — of a pyramid — of a prism — of a circle — of a semicircle — of a parabola — of a cycloid. Conditions of the equilibrium of a heavy body sustained on a horizontal plane — on an inclined plane — and on a curved surface. — (1) When the base of the body is a plane. — (2) When the base is a curved surface. The hanging tov/ers of Pisa and Bologna. Comparative stability of structures of different forms. Theory of the carriage v^^heel. — The drawbridge. Stability of loaded vehicles. Guldinus's properties. The centre of gravity of a body or system of bodies, in equilibrium, is at its highest or lowest possible point. This proposition proved generally. — Exemplified in the case of the inclined plane. — The crooked lever, &c. The equilibrium of a beam supported upon a roller and a vertical plane^ — of a rectangle upon two rollers — of a beam upon two surfaces. The equilibrium of a beam supported by a string fastened at its extremities — supported by two strings passing over pulleys, and carrying weights. it The position of the centre of gravity in animals. The attitudes of animals dependent upon the position of the centre of gravity. TJie conditions of stable — unstable — aud mixed equilibrium. Examples. — A hemisphere and a parabolid upon a plane surface. — The same upon a spherical surface. The common balance— its sensibility — the rapi- dity of its vibrations — its adjustments. These require to be different for every different loading, in order that the sensibility may be greatest of which the balance is capable. The equilibrium of a body, or system of bodies, stable or unstable, according as the centre of gravity is at its low^est or highest point. Conditions of the equilibrium of any number of forces acting, in any given number of directions, upon a system of invariable form. Case in which any number of forces act in dif- ferent directions perpendicular to a rigid line. Case in which a system acted upon by any number of forces is moveable about a fixed axis. Pressure upon the axis. Conditions of the equilibrium of any number of forces acting upon a system of variable form. 12 The jointed polygon of r^ocls. The equilibrium of a frame-work of two or more jointed polygons of rods connected together. The conditions of the equilibrium of a jointed frame-work loaded with weights, and placed in an upright position, is the same as though the frame were suspended and the same loading applied. Stability of its equilibrium when suspended. Instability in the opposite position. Easy practical method of determining the proper form of a roof, bridge, or other jointed frame under a given loading ; and the pressure, on its different parts and its abutments. Equilibrium of the arch with polished voussoirs. Instability of its equilibrium. On tlie equilibrium of the funicidar polygon. — Case in which the pressures are applied to rings, moving freely on the thread. — The elastic polygon. The equilibrium of the funicular curve. — The common catenary. — The tension on the catenary at the lowest point varies as the radius of curvature at that point. — Easy method of ascertaining the tension at any other point. On the position of equilibrium of a string of a given length, suspended over two given points. 13 On the relation between the length of the string and the tension on its parts when suspended. On the positions of equilibrium of a string whose extremities hang freely over two pulleys, in the same horizontal line. Of all the curves, of given length, which can be drawn so as to terminate in two given points, in the same horizontal line, the catenary is that whose centre of gravity is most distant from that line. On the catenary loaded with weights.— A catenary may be so loaded as to assume any required form. Variation in the tension of the catenary, produced by an irregularity in its loading, and consequent variation in its form. The catenary approximates at its vertex very nearly to a parabola. ON FRICTION. The statical laws of friction, Rennie's apparatus and experiments. The friction of hard metals under pressures of less than 32lbs. 8oz. the square inch, nearly one- sixth of the pressure. With higher pressures this ratio increases. The friction of woods. 14 The friction of stones. The diminution of friction by unguents, varies as the insistant weights and the nature of the un- guents; the lighter the weight, the finer and more fluent should be the unguent, and vice versa. On the modifications introduced hy friction in the conditions of the equilibrium of tJie different mechanical 'powers. On the two states bordering upon motion in the inclined plane. The wheel and axle. Methods of diminishing friction by means of fric- tion wheels. — Friction of the carriage wheel. — The screw. — The system of toothed wheels. ON THE RIGIDITY OF CORDS. Coulomb's experiments. States bordering on motion in the different sys- tems of pulleys. — The proper ratios of the wheels, axles, and cords of the different pulleys of each system. ON THE STRENGTH OF MATERIALS. Absolute resistance. — Rennie's experiments.— The resistance of different masses of metal, wood, and 15 stone to the compression of their parts in given directions. — The resistance of different masses of metal and wood to the separation of their parts in given directions. — Anomalous results. On the strain w^hich produces permanent altera- tion of structure.— There is reason to believe that all bodies are perfectly elastic, as to any pressure less than that which produces permanent alteration of structure. Galileo's hypothesis of the rigidity of fibres. — Leibnitz's hypothesis of the extensibility of fibres. — Theory which admits the compressibility as well as the extensibility of fibres. Relative resistance. — The neutral line — its pro- perties. On the strength of a horizontal bar fixed im- moveably at one end, and carrying a weight at the other. On the strength of a bar fixed immoveably at both ends, and carrying a weight between. On the strength of a bar supported in the middle^ and carrying weights at the ends. On the strength of a bar carrying weights variously distributed over its surface. On the strongest forms of beams. 16 On the construction of open beams. On the deflexion of beams by their own weight, when supported horizontally at their extremities — when inclined to the horizon. On the deflexion of columns sustaining weights. On the proper forms of columns sustaining weights. The elasticity of flexure. On the deflexion of elastic laminae. The equilibrium of springs. The elasticity of torsion. On the proper forms , and tlie strength of solid arches of wood and iron. On the loading of solid arches. On the strength of open arches. THEORY OF ROOFS. The Shed Roof The angle of its elevation dependent on the height and the strength of the walls or pillars on which it abuts. — The strength of its timbers. — Ingenious method of getting rid of the horizontal thrust, by supporting the timbers beneath their centres of gravity. TJie commonTruss Roof — The theory of this roof. 17 — The horizontal thrust on its abutments. — The different pressures upon its parts, and the consequent variation in the strength of its timbers. The deflexions in the tie beam and principal rafters. The variations in the lengths of the timbers. The strength of the joints. On the different forms of the trussed roof Examples, — The roof of the Bazilica of St. Paul's at Rome. — The roof of the Theatre Argentina at Rome. — The roof of the Birmingham Theatre. Methods of giving support to roofs — by means of additional frame-work abutting in the wall beneath the tie beam — by means of buttresses, &c. On truncated roofs. The roof of Drury Lane Theatre. On the loading of roofs, hy the suspension of ceilings, S^c, The roof and ceiling of the Teatro Alia Scala. On various methods of dispensing with the tie beam at the foot of the rafters. The collar beam — great objections to its use unless supported by pillars, or otherwise, at its extremities. Roof of the Church St. Genevieve at Paris. B 18 Roof of the Theatre Odeon. The roof of a church in Wiltshire. On g'othic roofs. The roof of Westminster School. The roof of the Middle Temple Hall. The roof of Westminster Hall. On the polygonal roof. Roofs formed with four principal rafters. Conditions of he equilibrium of four such raf- ters. The roof of the Theatre at Bordeaux. Roofs of sheds in the Arsenal at Cherbourg. Roofs of sheds in the Dockyard at Plymouth. The roof of the shed for containing Mahogany in the West India Docks. Method of supporting roofs hymeans of polygonal frames or arches of short rafters. Great advantages of this method of support. The proper form and strength of the polygon. The roof of the Riding House at Moscow^ On the arch of curved timber. On the use of iron in the framing of roofs. The roof of the Brunswick Theatre Roof at Mr. Maudeslay's manufactory. On trussed floors. 19 Example.— The trussed floor in the Teatro Alla- scala at Milan. ON THE THEORY OF WOODEN BRIDGES. The wooden bridge in which the timbers are straight, and rest immediately upon the piers. The bridge of Caesar over the Rhine. The bridge of Cayuga in America. Method of constructing a wooden bridge over a rapid torrent. The bridge across the rapids of Niagara. On the straight wooden bridge where the timbers of the roadway are trussed from above, and there is no horizontal pressure upon the abutments. The bridge of Palladio over the Cismone. The great bridge formerly at SchafFhausen. Wooden bridge near Baltimore, N. America. The wooden bridge, in which the roadway is principally supported yrow? beneath by timbers, which rest obliquely upon the abutments. The bridge over the Kendal near Berne. On wooden bridges supported by polygonal ribs. The wooden bridge at Lyons. On wooden bridges with curved ribs. B 2 20 The bridge of Trajan over the Danube. The bridge of Freysingen in Bavaria. The bridge of Bamburgh on the Regnitz in Germany. The great wooden arch at Scuykill, in N. America. The proper variation in the strength of the parts of the curve of a wooden arch. ON THE THEORY OF IRON ARCHES. Strength requisite in the different portions of the arch. — Colebrook-Dale bridge. — Buildwas bridge. — Sunderland bridge. — Bonar bridge. — The bridge of the Louvre. — Vauxhall bridge. — Southwark bridge. — Telford's proposed bridge over the Thames, ON SUSPENSION BRIDGES. Application of the theory of the loaded cate- nary. — The method of constructing the chain. — Easy practical method of determining the tension. — It is less at the vertex as the curvature is greater. On the method of suspending the roadway. — On the piers of the bridge, and the attachment of the chain. — The wire bridge over the Tees near Durham. — The wire bridge over the Tweed near 21 Peebles. — The Kelso suspension bridge. — The sus- pension pier at Leith. — Brunell's suspension bridge erected in the Island of Bourbon. — The suspension bridges over the Cataracts of Sckuylkill, and at Merimac, in North America. — The Hammersmith suspension bridge. — The Menai suspension bridge. Any jointed polygon, or arch, placed in an upright position so as to be sustained by the pressure of its parts upon one another and upon its abutments, is in a position of unstable equilibrium, the centre of gravity being at its highest possible point. To the stability of such a polygon, or arch, it is therefore necessary that its joints should be rendered rigid, in the directions in v^^hich their position is liable to disturbance, — by additional framing or otherwise. In the suspended polygon, or curve, the equili- brium is stable, the centre of gravity being at its lowest possible point. There is therefore no neces- sity for rendering the joints rigid ; and the material, requisite in the other case for producing this rigi- dity, may be here dispensed with. The advantage of the upright over the suspended arch of the same materials, lies in this, that in the former case the arch is sustained by the resis- tance of its parts to compression, and in the latter 22 by their resistance to separation, and that mate- rials are torn asunder more readily than they are crushed. ON THE THEORY OF THE STONE ARCH. True theory of the arch, allowing for the friction of the voussoirs. General conditions of the stability of the arch. The two states bordering upon motion. Method of describing the line of the least loading necessary to the equilibrium of an arch whose key- stone is given. Line of the greatest loading which such an arch will bear. On the comparative strength of different por- tions of the arch. Generally the strength of an arch is greater as its curvature is less. The curvature being given, the stability of an arch properly constructed increases with the loading. On the line of pressure. When the voussoirs are exceedingly narrow, and the loading considerable, the curve of equilibrium is the catenary. Different steps in the fall of an arch. Example, — Pont y Prydd. 23 The circular arch. Easy method of describing the lines of greatest and least practicable loading. The great strength of the circular arch, and variety of loading under which conditions of its equilibrium obtain. The segment of a semi-circular arch. Its advantages over the whole semicircular arch. No semicircular arch can be safely constructed with equal voussoirs — A segment may. A straight wall of any height may be built over a segment of a circular arch. Exarnjdes of circular arches. The bridge of Rimini. The aqueduct bridge at Nismes. The bridge of Avignon. The bridge of Briande. The bridge of Ulm, &c. &c. The elliptical arch. Method of describing the lines of loading in the two states bordering upon motion, and for given dimensions of the key-stone. Weights which an elliptical arch of given dimen- sions is capable of sustaining on its crown. 24 Comparative weakness of the semi - elliptical arch. Cases of semi-elliptical arches, in which, under the irregular pressures to which they are subjected, their stability must be dependent upon other causes than the friction of their parts. Examples of elliptical arches. Bridge of the Rialto at Venice. Bridge over the Arno at Florence. Bridge of Neuilly. Waterloo bridge. London bridge. On segments of elliptical arches. Advantages in the use of segments raised upon high vertical piers, where a clear water way is required. A segment of an elliptical arch may be built with equal voussoirs. The loading on certain points about the haunches of a semi-elliptical arch may be any whatever. Examples of flat arches. Bridge over the Oise. Pont de la Concorde. 25 The arch between the western towers of Lincoln Cathedral. On the pointed gothic arch. Equilibrium of the pointed arch. Method of determining the states bordering upon motion. The loading of the key-stone. Comparative strength of the varieties of the pointed arch. Conditions of the equilibrium of an arch, taking into account the tenacity of the cement. On the piers of arches. On the centering of arches. On the equilihrium of the dome. The weight on the haunches may be increased without limit, and their convexity diminished, but not the contrary. A dome may be built w^ithout centering. — Ex- ample, — The dome of the cathedral of Florence. On the equilibrium of a dome loaded on the crown — The domes of the cathedral at Florence, St. Peter's of Rome, and St. Paul's in London. — On ^he equilibrium of a dome in which the crown is wanting. 26 On the theory of the groin. On the conoidal groin, ON THE PRINCIPLE OF VIRTUAL VELOCITIES. Lagrange's proof. The principle of virtual velocities shewn to obtain in the following cases of equilibrium. The equilibrium of any number of forces acting upon a point. — Of weights on the straight lever. — Of forces acting obliquely on the crooked lever. — In the case of the single pulley where the strings are inclined. — Of a system of compound levers. — Of the inclined plane. — Of equilibrium on a curve — on two curves — of the screw — of the wheel and axle — of toothed wheels, &c. &c. — In the case of motion about the centre of gravity of any system of bodies. The centre of gravity of any system of weights is at its highest or lowest points, when those weights are in equilibrium— proof deduced from the prin- ciple of virtual velocities. On the quantity of motion. The quantity of motion, a measure of the moving force. Demonstration of the principle of virtual velocities founded on this consideration. 27 ON THE USEFUL EFFECT OF MACHINES. If any system of forces be in equilibrium upon a machine, and certain quantities of motion be com- municated to one or more of those forces, these quan- tities of motion shall together be equal to the sum of the initial quantities of motion 'produced by them in the remaining forces ; the motions being in both cases estimated in the directions in which the forces act. If a machine, on which certain forces are in equili- brium be put in motion, and the equilibrium of those forces remain throughout the motion ; the whole quantity of motion communicated to one part of the system will be equal to that produced in the other ; the motions being estimated in the proper direc- tions of the forces. Where the forces remain the same, the whole quantity of motion, in each force, is proportional to the product of that force, by the space it is made to describe in its proper direction. Where the forces vary, the whole quantity of motion is measured by the sum of the spaces described in given times multiplied each by the force employed in describing it. 28 The effect produced in a given system of forces, by the communication of a given quantity of motion to the parts of a machine, is the same, whatever that machine may be, and however the motion may be communicated to it. If a number of forces be in equilibrium as above, and additional force be communicated to one of them, that additional force will be wholly effective in producing motion — friction, &:c. being neglected. Where any part of the quantity of motion com- municated to a machine, is destroyed by forces already acting upon it, and not in equilibrium, there, the same quantity of motion might have been produced by a less real expense of power, had that power been immediately applied without the inter- vention of machinery. Distinction between the case in which machinery is applied only to the sustaining of certain pressures in equilibrium, and the case in which a certain quantity of motion is to be communicated. In the former case, the difference between the power and weight is in fact sustained by the resis- tance presented by different parts of the system. In the latter case, the quantity of motion pro- duced in the weight cannot, under the most favour- 29 able circumstances, exceed that applied in the power. A weight raised by the intervention of machinery requires at least the same expense of force (measured by the quantity of motion) as though the power used to raise it were applied immediately to lift different portions of the weight. Taking into account the retardation of friction, the expense of force in the latter case is essentially less than in the former. Application of the principle of virtual velocities, to determine the whole amount of animal force required to lift a weight through a given height, by means of machinery, where the power through- out the motion is just that necessary to overcome the weight. — The overturning of a heavy body. — The lifting of a body by means of the lever. — The dragging of a carriage-wheel over an obstacle. The drawing of a wheel up a curved surface, &c. Application of the principle of virtual velocities, to shew that when any system of weights is in equili- brium, in every position which it is made to assume, the centre of gravity neither ascends nor descends. 30 ON THE FORCE OF ANIMAL AGENTS. On the absolute force of man. — Regnier's Dyna- mometer. — On the permanent force of man. — Coulomb's experiments. — On the force of beasts. — The force of horses. — The work of mules. — On the advantageous employment of animal strength. — On the performance of extraordinary feats of strength. — On the relation of the force and the velocity of the agent. — On the difference between the force of animals, applied in the production of pressure and motion. In machines put in motion, or kept in equili- brium, by the force of animal agents, there is re- quired a continual production of power. In drawing, the immediate cause of the force is the weight of the animal, but the power which keeps the force in continued action, is the animal's strength. ON THE MOST ADVANTAGEOUS DISPOSITION OF ROADS FOR TRAVELLING AND THE TRANSFER OF MATERIALS, WITH THE LEAST POSSIBLE EXPENSE OF ANIMAL FORCE, Where the inclination is inconsiderable, the shortest practicable road is the best. 31 There is a limiting angle of inclination, beyond which, the shortest practicable road ceases to be the best. This angle is the same whatever be the incli- nation or curvature of the surface. It determines the depth a road should be cut through a hill, and the direction of a road round it. On oblique roads of constant inclination, and spiral and zigzag roads. Loss of force in the latter description of roads, where loads are drawn by teams. The limiting angles different for the ascent and descent. Where the passing and repassing are equal, the least of these to be taken for the limiting eleva- tion. — On the case in which the transport is wholly in one direction. — Determination of the culmi- nating point of a road intended to pass over a hill, so that the expenditure of force in the ascent and descent may be the least possible. On the case in which different articles are to be taken up at different points, and conveyed to other points, not upon the same road. 32 ON HYDROSTATICS, OR THE EQUILIBRIUM OF FLUIDS. Definition of a fluid. Property/ of the equal distribution of fluid pres- sure — proved experimentally — shewn to be a con- sequence of the principle of virtual velocities. Bramah's press. On tlie pressure transmitted to the sides of vessels containing fluid, any portion of which is subjected to pressure. On the best forms of vessels containing fluid subjected to pressure. On the resolution of fluid pressure. Pressure applied to a fluid at rest, has no ten- dency to communicate motion to a body wholly contained in that fluid. If the pressure be by any means removed from any portion of the body immersed, (as by making an aperture in it) motion will ensue. On the force tending to communicate a motion of translation in any given direction to the sides of a vessel containing a fluid subjected to pressure. 33 On density and specific gravity. On the specific gravity of a compound body. On the equilibrium of fljUids acted upon hy gravity. The pressure on a horizontal plane, any where taken in a heavy fluid, is equal to the weight of a vertical column of fluid, of which that plane is the base, and which is continued to the surface. The hydrostatic bellows. The free surface of a heavy fluid is a hori%ontal plane. — Any surface of equal pressure in a fluid, is a horizontal plane. The common surface of two fluids which do not mix, is a horizontal plane. The common surface of the atmosphere, and any fluid at the earth's surface, is a horizontal plane. Fluid of uniform density contained in a system of communicating vessels, stands at the same height in all. The screw of Archimedes. If the pressure of the atmosphere be taken from the surface of the fluid in any one of a system of communicating vessels, the fluid will ascend in that vessel. The syphon. — The Danish syphon. 34 The reciprocating spring. On the position of equilibrium of fluids oi differ- ent densities in a system of communicating vessels. Method of determining the specific gravities of liquids. On the barometer. On the pressure sustained by the surfaces of vessels containing fluid, or immersed in it. Lateral pressure and motion produced by re- moving of a portion of the sides of a vessel con- taining fluid. BernouilUs locomotive machine. Barker's mill. On the thickness and strength of vessels. On the form of embankments. On the centre of pressure. Relative positions of the centre of gravity and centre of pressure. Cecil's lamp. On the flood-gate. On the position and strength of the hoops of vessels formed with staves. The centre of pressure of a hemisphere. On the surfaces of flexible vessels containing fluid. 35 General conditions of the equilibrium of a float- ing body. Equilibrium of symmetrical bodies. — The sphere. — The elypsoid. The hydrometer. The hydrostatic balance. The equilibrium of a triangular prism. The equilibrium of an irregular prism, of which the part immersed is triangular. Case of the sector of a circular prism. Equilibrium of an irregular prism, of which the part subject to immersion is a portion of a rectan- gular parallelopipedon. Equilibrium of the above figures in inverted positions. On the force which will hold prisms taken as above, in given inclined positions. Application to the case of a loaded barge. Determination of the force necessary to overturn it. On the stability of floating bodies. The positions of stable and unstable equilibrium occur alternately. Position of mixed equilibrium. Error in the received theory. The metacenter. General conditions of stability. 36 Examples. — A cone — A parabolid, or parallelo- pipedon. On the loading of ships. On the oscillations of floating bodies. Small vertical oscillations. Finite vertical oscillations. Oscillations about the centre of gravity. ^ On the equilihrium and stability of vessels con- taining fluid. Conditions of equilihrium of a floating body partially sustained hy a surface, or retained by a string. Example, — The conical buoy. General conditions of the equilibrium of a fluid, acted upon by any forces. Surfaces of equal pressure. These are spherical, when the force tends to a centre. They are homogeneous. The pressure and density of each. Equilibrium of Elastic Fluids, The atmosphere is an elastic fluid. The barometer. The air pump. Smeaton's air pump. \ Hawksbee's air pump. 37 The valves of the air pump. The barometric giiage. Various pneumatic experiments. The condenser. The density of the contained air. The diving bell. Meikle's hydrometer. Say's hydrometer. The force of gravity tending to the centre of the * earth ; the atmosphere is disposed in a series of consentric spherical shells — throughout each of v^^hich its density, if at rest, would be the same. Principle on which the mensuration of heights by the barometer is founded. The common pump. The height through which the water will rise at every stroke of the piston before it begins to flow. Limits to the length of the suction-pipe depen- dent upon the length of the barrel and play of the piston. Height to which the piston must ascend that the discharge at each stroke may be the greatest possible. Pressure upon the piston. Fergusson's table to determine the bores of pipes for wells of different depths, so that the labour of working may be the same. 38 On the pump without friction. Taylor's double piston suction pump. Todd's double valve pump. The forcing pump. — The lifting pump. — Ctesibus' pump. Franklyn's double piston forcing and suction pump. Brunton's pump. — Smeaton's three-barrell pump. — The chain pump. Martin's double-barrelled suction pump, with bag valves. Jekyl's pump and fire engine. Newsham and Rowntree's fire engines. The air pump. The density of the air after a given number of strokes. The tympanum — De la Faye's construction. The noria. The Persian wheel. The chain pump. The Hungarian machine. The conical spiral pump. Desaguilier's machine for raising water. The hydrostatic pressure engine. Subjects for the Term commencing in January: Dynamics. Hydrodynamics. Subject for the Easter Term, The Application of Mechanical Science in the Arts and Manufactures. The first Course will commence on the 8th of November, and will be delivered on each succeeding Tuesday, Thurs- day, and Saturday, at Three o'Clock, p. m. Terms — For each Course 3 3 Or for the Three Courses .... 7 7 An Evening Course will shortly be commenced on the Theory of Heat and the Steam Engine. BY THE SAME AUTHOR. A TREATISE ON HYDROSTATICS & HYDRODYNAMICS. 8vo. price I2s. LONDON: — R.CLAY, PRINTER, BKEAU-STREET-IIILL.