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then on elevating Q, the atmospheric pressure forces the water in E through ED into the space previously occupied by Q; on depressing Q, the valve D closes, and a portion of the water in CD is forced through the valve B, which prevents the return of the water, into AB, and causes M to ascend. This process is repeated till the substance between F and I is sufficiently compressed. The pressure may at any time be removed by unscrewing a plug at N, which permits the water in AB to escape.

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Let r, s be the radii of the cylinders M, Q; W the whole pressure on the platform F; P the force applied at L; p pressure of the water in the cylinders.

Then W = pressure on the lower end of M =

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When this machine is employed to produce tension, as, for instance, in extracting piles, or in proving cables, &c. a cylindrical bar of iron passing through a water-tight collar in the bottom of the hollow cylinder AB, has one end fastened into the cylinder M, while a ring at the other end serves to connect it with the pile or cable.

THE DIVING BELL. (Fig. 36).

81. The diving bell is a chest, the weight of which is greater than that of the water it would contain, suspended by a rope with its mouth downwards. If the bell be lowered out of air into water in this position, the air contained in it will prevent the water from rising in the upper part of the bell, and thus enable persons to breathe at considerable depths below the surface of the water.

82. To find the space occupied by the air in the bell at any depth below the surface.

Let BE be the bell, draw AM vertical meeting the surface of the water on the outside of the bell in A, and the surface of the water within the bell in M; and let h be the altitude of a column of water whose pressure is equal to that of the atmosphere (about 34 feet). When the bell was at the surface the air in it occupied the space DECB, under a pressure equal to that of a column of water the height of which is h; and the pressure at M is that of a column of water whose height is h+ AM;

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The water may be almost wholly expelled from the interior of the bell by a supply of air from above, forced by an air-pump through a flexible tube terminating under the mouth of the bell. In this manner also the air is changed as often as it becomes unfit for respiration.

sure.

THE SYPHON. (Fig. 37.)

83. The syphon is a bent tube ABC open at both ends. Let the ends be closed, after filling it with fluid, and place it with one end in a bowl of the fluid with which it was filled, so that the other end may be below the surface of the fluid in the bowl. Let the plane of the surface of the fluid in the bowl meet the legs of the syphon in A, K; and let ПI be the atmospheric presThen if the end A be opened, the pressure within the tube at H will be II; and if the end C be opened the pressure at C will be II, and therefore the initial pressure within the tube at K will be less than II. And since the pressure at K is less than the pressure at H, the column of fluid HBK will move in the direction HBK, and run out at C, while the fluid in the bowl is forced up AB by the pressure of the atmosphere. And this will continue till the surface descends to the level of the highest end of the syphon.

The syphon will not act when the altitude of the highest part of it above the surface of the fluid in the bowl, is greater than the height of a column of the fluid, whose pressure is equal to that of the atmosphere. For on opening 4, the fluid in BA

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 4.

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 = gpПIr2 (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 A, 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.

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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.

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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

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