will sink till its altitude is such that the pressure it exerts at H, becomes equal to the pressure of the atmosphere, leaving a vacuum at B. THE COMMON PUMP. (Fig. 38.) 84. AB, BC are two hollow cylinders having a common axis; C the surface of the water into which the extremity of BC descends; M a piston capable of being moved up and down by a rod MA, and containing a valve opening upwards; AB the range of the piston; B a valve opening upwards; D a spout placed a little above A. Suppose M to be at A, and the pump to be filled with air, the pressure of which is equal to that of the atmosphere; and let M be elevated to A. Then, the air in BC will open the valve B and fill AB, and the pressure of the air in the pump being less when it occupies the space ABC, than when it occupied the space BC, the pressure of the atmosphere will force the water up BC till the pressure at C is the same as before, or equal to the pressure of the atmosphere. As soon as M begins to descend, the valve B closes, and the air between M and B escapes through the valve M. The water will ascend in the pump each time this process is repeated, and will finally pass through the valves B and M; and then, when M ascends to A, it will flow through D. If h be the altitude of a column of water whose pressure is equal to that of the atmosphere, BC must always be less than h, otherwise the water would never reach B. COR. If P be the surface of the water in BC, r the radius of the cylinder AB, p the density of water, and if we suppose M to ascend very slowly; the pressure of the air in MP =gp(h- PC), therefore the pressure upwards on M = gpIIr2 (a - PC), and the pressure of the atmosphere downwards on M = gpπr2h, therefore the tension of the rod AM = gpπr2.PC. 85. To find the height through which the water rises each time the piston ascends. Let P be the surface of the water in BC when M is at B; Q the surface of the water when M is at A.. Then, the pressure of the air in BP = gp (h – PC), and the pressure of the air in AQ=gp (h – QC); but (pressure of the air in BP): (pressure of the air in AQ) = (vol. AQ): (vol. BP), .. h-PC h- QC = (vol. AQ): (vol. BP). 86. When AE is the range of the piston, the pressure of the air between B and M, when M is at E, must be greater than the pressure of the atmosphere, otherwise the air will not escape through the valve in M, and M will reascend without increasing the elevation of the water in BC. Let P be the surface of the water in BC when M is at A, then, the pressure of the air in AP = gp (h - PC), and when M comes to E the pressure of the air in BE=gp(h-PC) AB÷EB, and this must be greater than gph, the atmospheric pressure, therefore AE.h must be greater than AB. PC, and BC is the greatest value of PC, therefore AE.h must be greater than AB.BC. 87. Suppose the whole pump to be part of the same cylinder, and the valve to be at, or near the surface of the water. Let AE (fig. 39.) be the range of the piston, P the surface of the water within the pump, C the surface of the water on the outside. When the piston is at 4, the pressure of the air in AP gp (h - PC); when the piston descends to E, the pressure of the air in EP = gp (h – PC) AP÷EP, and this must be greater than gph, the atmospheric pressure, in order that the valve in the piston may open, therefore h.AE must be greater than AP. PC, and the greatest value of AP. PC is AC, therefore 4h. AE must be greater that AC2. = THE FORCING PUMP. (Fig. 40.) · 88. M is a solid piston working in a hollow cylinder ABC, the lower end of which is immersed in water; DF a tube ascending from AB; B, D valves opening upwards; AE the range of the piston. Let M be at E, and the pressure of the air in the pump equal to the atmospheric pressure. Let M be elevated to A, then the pressure of the air below M is diminished, and the pressure of the atmosphere will force the water up the tube BC. When M descends the valve B closes, D opens, and a portion of the air between M and B escapes through DE. When M ascends, the water rises in BC as before, and at last rises above B, and is forced up the tube DE when M descends. On elevating M, D closes, and a fresh portion of water enters AE through B, and is forced up DE by the next descent of M. A solid cylinder working in a water-tight collar at A, is frequently used instead of the piston M. The stream of water may be rendered continuous by means of a close vessel DF (fig. 41.) filled with air; HF is the lower extremity of the ascending tube. When the surface of the water in DF rises above H, the pressure of the air, which is condensed in the upper part of DF forces the water up HF in a continued stream. THE FIRE ENGINE. (Fig. 42.) 89. AB, A'B', are two forcing pumps, having a common air vessel DF, and suction tube C. The pistons are worked by a lever LGL', so that one descends while the other ascends. The jet of water may be pointed in any direction by means of the flexible tube F. The action of the engine is in all respects the same as that of the forcing pump. 90. AB is a hollow cylinder, of which the end B is screwed into the neck of a strong vessel C; M a piston containing a valve opening downwards; B a valve also opening downwards. Suppose M to be at A, and the barrel AB and the receiver C to be filled with air of the same density as the atmospheric air. When M begins to descend the pressure of the air in MB, which is increased in consequence of the diminution of its volume, closes the valve M, and opens the valve B; and when M is thrust down to B, a quantity of air, which, under the pressure of the atmosphere, occupied the space AB, is forced into C; when M begins to ascend, the pressure of the air in C closes the H valve B, and the pressure of the atmosphere opens M, and when M comes to A, AB is filled with air under the pressure of the atmosphere, and this is forced into C by the next descent of M. 91. To find the density of the air in the receiver after n descents of the piston. Let A, B, be the capacities of the receiver and barrel re spectively; p the density of atmospheric air. Then P A will be the mass of the air contained in the receiver at first, and P В the mass of the air forced into the receiver at each descent of the piston, therefore pA+npB will be the mass of the air in the receiver after n descents of the piston; and its volume is A, therefore its density will be p (1+n). 92. The gauge of a condenser is a glass tube AB (fig. 44.) sealed at A and communicating with the receiver of the condenser at B, the part AP of the tube is filled with air which is separated from the air in PB by a drop of mercury P. When the air in the receiver is condensed, P is forced towards A, till the pressures, and, therefore, the densities of the air in AP, PB are equal. Let p be the density of atmospheric air; then, when the drop of mercury is at M, the density of the air in AM or MB HAWKSBEE'S AIR PUMP. (Fig. 45.) 93. AB, A'B' are two hollow cylinders communicating at B, B', with a strong vessel by means of a pipe C; M, M' pistons containing valves opening upwards, and worked by a toothed wheel E; B, B', valves opening upwards. Suppose M to be at A, and M' at B', and the density of the air in the receiver C, and in AB, to be equal to the density of atmospheric air. Then if E be turned so that M may descend and M' ascend, the valve B' opens, B and M' close, and a quantity of air, which at first occupied the space AB, is forced through the valve M, by the time M reaches B; when the wheel is turned in the opposite direction, the valve B opens, M and B close, and a quantity of air, which after the first turn of the wheel occupied the space A'B', is forced through M' by the descent of M' from A' to B'. The exhaustion may be carried on to any required extent, by a repetition of this process. 94. To find the density of the air in the receiver after any number of turns of the wheel E. Let A, B, be the capacities of the receiver and barrel respectively; p, the density of the air in the machine, pr, P... Pr the densities of the air after 1, 2,......n turns. Then, the air, which occupied the space A when M was at B, will occupy the space A + B when M comes to A, therefore ρι (A + B) = PA, similarly p2 (A + B) = p1 A, and so on, COR. Hence if h be the altitude of the mercury in a barometer, σ the density of mercury, and therefore goh the pressure of the atmosphere, the pressure of the air in the receiver The employment of two pistons worked by the same wheel diminishes considerably the labour of working the pump. For the pressures of the atmosphere on the upper surfaces of M, M' being equal, the pump may be worked by a force sufficient to overcome the friction together with the difference of the pressures on the under surfaces of M, M'; while the ascent of a single piston is opposed by the friction together with the difference between the pressures on its upper and under surfaces. SMEATON'S AIR PUMP. (Fig. 46.). 95. AB is a hollow cylinder communicating with the receiver by means of the pipe BC; M a piston worked by a rod AM passing through an air tight collar in a plate which closes the upper end of the cylinder; at A, M, B, are placed valves opening upwards. Let A, B be the capacities of the receiver and barrel respectively; the density of the air in the machine; and suppose M to be at A. Then, as soon as M begins to |