HYDROMECHANICS 117 top with a smaller metallic cylinder which ad- mits the compressing screw c, and also a funnel, d, for introducing the liquid. The vessel a with its capillary stem, having been filled with the liquid, is placed in position, together with the manometer; the outer cylinder is filled with water, the stopcock of the funnel closed, and pressure produced by turning the screw with a lever. Mercury will be seen to rise in the capillary tube connected with the vessel a, showing that its contents are diminished in volume. The air contained within the ma- nometer, being reduced in bulk in proportion to the force exerted, according to the law of Boyle and Mariotte, will therefore be a measure of that force. Oersted at first assumed that the external and internal pressure on the vessel was precisely the same ; but the external pres- sure is slightly the greater, because the exter- nal surface is greater than the internal, so that the capacity of the vessel is diminished, instead of being increased as in all preceding experi- ments. Colladon and Sturm with the use of this apparatus made very exact experiments, in which they calculated the change of capa- city of the vessel a, and estimated that an additional atmospheric pressure would reduce the volume of water -00005, mercury -000005, and sulphuric ether -000133. For water and mercury it was found that within certain limits the decrease in volume is proportional to the pressure. I. HYDROSTATICS. In consequence of the mobility of the particles of a liquid over each other, they yield to the force of gravity, and consequently when at rest present a level surface ; and for the same reason each particle, and therefore each portion of the liquid, must exert and receive equal pressures in all direc- tions. If this were not true, the particles of a liquid could not come to a state of rest. From this principle it follows that equal surfaces of the sides of a vessel containing a liquid re- ceive equal pressures at equal depths below the surface ; and also that if a close vessel is filled with a liquid which we will suppose to have no weight, and if an aperture of the size of one square inch be made in one side of it and fitted with a piston upon which there is exert- ed a pressure of 10 Ibs., there will also be ex- erted the same pressure of 10 Ibs. upon every square inch of the internal surface of the ves- sel. Consequently, if another aperture of 100 square inches area is made in the side of the vessel, and a cylinder of the same size is fitted to it, a piston fitted to this will receive a pres- sure of 1,000 Ibs. Upon this principle (which has been ascribed to Pascal, but which, as w have seen, was before his time explained by Stevinus) the hydraulic press is constructed, as represented in fig. 2. A suction and force pump, a, supplied from the cistern B, forces water through the tube C into the strong cylin- der V, which communicates pressure to the piston A. The power gained is the proportion which the cross section of the large piston or plunger bears to the small one. It will be ob- served that the pistons do not fit the cylinders in the usual manner, but only fit tightly at the collar. This mode of construction greatly in- creases the efficiency of the machine, which, though described by Stevinus and by Pascal, remained practically useless in consequence of Fio. 2 Hydraulic Press. the escape of water between the cylinder and the piston, until Bramah invented the cupped leather collar, which makes the apparatus equally water-tight under all pressures. This engine is a good illustration of the law in mechanics that " what is lost in velocity is gained in power." If the cross section of the large piston is equal to 100 square inches, and that of the small piston to 1 square inch, the latter must be moved through a space of 100 inches to cause the large piston to move through one inch, but it will move with 100 times as much power as the small one. The hydrostatic bellows, shown in fig. 8, acts upon the same principle as the hydrostatic press, the cover of the bellows, upon which the weight is placed, performing the office of the large piston, while the column of water in the tall vertical pipe acts the part of the small pis- ton of the press. The hydro- static bellows also illustrates the principle of the hydrostatic par- adox, for the vertical pipe and the bellows are virtually one vessel, whose base is the bottom of the bellows. Now the pres- sure exerted by the liquid in the pipe upon the upper plate of the bellows is received by the lower plate, which also has an additional pressure equal to its distance below the upper plate ; and if the water in the pipe is ten times as high as that in the bellows, it follows that the pressure on the bottom plate will be ten times as great as that which would be produced by the liquid contained within the bellows itself, for that only is equal to its own weight. If a barrel of water there- fore have a tall tube inserted in one head FIG. 8. Hydrostatic Bellows.
