ClIAF. XVI.

HYDROSTATICS.

1 OS

Fig. 1078.

water, the power would sustain a weight equal to that of thecolumn A I K C: if we close the orifice E II, and hold a tube KBfilled with water to the height G, all the points of the base A Cbeing pressed with the same force as the fillet GX presses thepoint X, the power would sustain a weight equal to that of thewater which the column A L M C would comprise, provided, asalready observed, that this vessel is attached to a fixed plan.

As a power cannot act in any direction without a fulcrum, it isnecessary, in order that the piston may press upwards with thesame force that the water presses downwards, that the machineshould be fixed, otherwise the action of the water would raisethe vessel, and leave the piston unmoved by the power : if thewater were to freeze, then, being without action, the fulcrumwould become useless, and the machine would only be chargedwith the real weight of the water and the machine.

Fig . 1G79. Suppose we take another pipe A B C I), wherenone of the points of the level K K of the water answer to thebottom A D, and we suppose that the column A K F D isdivided into several others, G F, III, AK, by planes GII, IK,parallel to the horizon : the base GII will be loaded with a weightequal to that of the column G LAI II, in fig. 1676. If we sup-press the diaphragm GII the column X (.), havingno other base than the summit X of the column X I,these two together will only make one, O I, whichcommunicates with all those enclosed in the spaceIT K ; these latter will each press the base I K withas much force as the first O I : thus this base will beloaded with a weight equal to that of the water whichthe column IOPK comprises. In the same manner,since the point Q of the base I K is pressed with aforce equal to the weight of the columns OI or RQ,suppressing the diaphragm IK, the columns II Qand Q A only composing one, II A, which is in equi-librio with all those comprised by the space A VD,the bottom, AD, will be loaded with the water of theoblique column A E F D, which would be the case ifthe column were straight, A II S D.

Fig. 1680. If we have a tube whose parts, 13 D,

D F, l’Q, were disposed in zigzag, and this tube,which we suppose placed against one or more verticalsurfaces, were filled « ith water, the bottom 13 E wouldbe loaded with a weight equal to that of a column,of water 13 K. O E, having the same base, and the line13 K, which expresses the elevation of the level I1Qof the water above the base 13 E, for its height. Re-garding the line F G as the bottom of the tube F Q,the water of this tube will load the bottom as muchas that contained in the column FLI Q; suppressingthe diaphragm F G, the column L G, having no otherbase than the film F G, will increase with its wholeweight that of the column FD, and the bottom CDwill be loaded with a weight equal to that of thecolumn C M X D: we shall also find that the base13 E, being loaded with a weight of the right and in-clined columns M D and D 13, will be in the same case as if it served as the base of thecolumn B K O E. If the tube, instead of being zigzag, were serpentine, the same principlewould hold good, for, by dividing the water of the tube in horizontal sections, we divide itinto small right or inclined cylinders, which being contiguous may be regarded as the tractsof a tube like the preceding: whatever be the size of a tube, whether it be uniform or notthrough its whole extent, in whatever manner its parts are disposed, whether in a vertical orinclined plane, the power applied to a piston of an equal, greater, or less diameter than the bot-tom of the tube, it will always be loaded with the weight of a column having for its base thecircle of the piston, and for its height that of the level of the water above the same piston.

On the Action of Water against vertical and rectangular Surfaces _After having shown

the manner in which water acts to surmount the resistance of surfaces which prevent itfrom descending towards the earth's centre, or from rising to its level, we shall proceed toexplain according to what law it presses the sides of the vessels containing it apart; butfirst it must be observed that this pressure is always made in a horizontal direction: sup-

Fig. 1C79.

I H

Fig. 1G80.