1100

THEORY AND PRACTICE OF ENGINEERING.

Book II,

Although the branches of a siphon were ofunequal thickness, the water in the lesser one,QQ, as wc have observed, was not the less inequilibrio with that of the larger one, M K,while their surfaces were level, because thelesser one is in equilibrio with all those ofwhich the larger is composed. If water ispoured into the small tube R O, to the heightN, the column N O will make an effort toraise all those of the branch M K to the levelE Q, which will push the piston IK frombelow upwards, with as much force as thecolumn G F would ; consequently, in order tomaintain the piston at the height I K, it mustbe loaded with a weight equal to that of thecolumn. As the size of the branch N O is in-different, we find that if it were reduced tocontain only a thread of water, this threadwould sustain in equilibrio the weight withwhich the piston is loaded.

Suppose that the superficies of the circle of

Fig.1670.

the thread N Q is

TO 53

of that of the diameter

Fig.167:

G II or 1 K, the weight of this thread ofthat of the column G F, or of the weight withwhich the piston is loaded. If we also sup-pose that the piston descends the height of oneline, this could not happen without 1000 smallcolumns, each a line in height, and of a dia-meter equal N Q, passing into the tube Q It,and without this column mounting in thetube 1000 times as high as the piston de-scended ; whence it follows that the weight ofthe fillet and that of the piston, being in the reciprocal ratio of their velocity, these twoweights are in equilibrio. It follows that if the thread N Q were 10 feet in height, and thepiston I K 1 foot in diameter, the weight loading the piston must be 550 pounds to bein equilibrio with this fillet, although it would only contain 1 ounce weight of water.

When a mass of fluid in a state of equilibrium is subjected to the action of any forces,every particle is pressed equally in every direction, and vice versa, if every particle of thefluid mass be pressed equally in every direction the whole mass will be in equilibrio : forsince the parts of a fluid yield to the smallest pressure, any particle more pressed in onedirection than another would move to the side where the pressure was least, and conse-quently the equilibrium would be destroyed ; if the particles are equally pressed in everydirection, it is evident that the mass of which they are composed must be in equilibrio. aprinciple adopted by Euler, D'Alembert ,

Bossut, and Prony: and the pressure exertedby a fluid upon any given portion of the vesselwhich contains it is equal to the column ofthe fluid whose base is the area of the givenportion, and wlio.se altitude is the depth of thecentre of gravity of the portion below the fluidsurface.

A single column of water may be in equili-brio with an infinity of others , together orseparately. — If we have a tube FM largerbelow than above, to receive a number ofsmall tubes A B, ending in a cylinder D Eclosed by a piston, if we pour water throughthe orifice E, to fill all these tubes and theircylinders, the single column G M being 10 feethigh, and each cylinder 1 foot in diameter; thiscolumn alone would sustain as many times 550pounds as this machine, which resembles alustre, had branches. Although the lengthand thickness of the tube of communicationO M only contributes indirectly to the effectwhich we have described in fig. 1671., we

Fig.1672.

may suppress this tube, and show the same things with a machine yet simpler than the siphon.