Chap. XVI.

HYDROSTATICS.

1099

Fig. 1607.

To compare the specific weights of different liquids an instrumentinvented by Homberg is used, called an areometer, composed of a smallphial E, having two necks A B, DC, very narrow, but the second stillnarrower than the first: through the opening A with a funnel I\ theliquid to be weighed is poured, which as it falls into E drives out theair through the tube C D, and the place exactly marked at G on the neckA B, to which the liquid reaches : having weighed the phial full of liquidin a good balance, and the weight of the empty areometer subtracted, theweight of the liquid poured in is obtained ; the areometer is then emptied,cleaned, and filled with another liquid to the same mark G, which isweighed as before, to obtain the ratio of the specific weights of these twoliquids. As liquids are subject to dilate with heat and contract with cold,

Homberg reports his experiments on their weights, and remarks on theirdifference in the greatest heat of summer and in the greatest cold ofwinter, so as to ascertain very nearly the difference between these two extremities at thetimes in which the areometer is used.

On the vertical Action of Water against the Sides of the Vessel containing it. — One of the pro-perties of liquids is the effort which they make in every direction against the sides of thevessel containing them, caused by the motions of their parts, which being detached from eachother only seek to escape.

Having a right tube, A B C D, open at both ends fixed against a verticalsurface, if we introduce into this tube at the lower end a piston G III toserve as a bottom, and pour water to any height E F, the power applied tothis piston will sustain a weight equal to that of the column of water con- F 'tained in the tube. If we pay attention to the fact that liquids have thisproperty in common, that the motion of their parts in every direction, andthe effort they make sideways to discharge the pressure of those withwhich they are loaded, diminshes nothing of the action of the weightwhich causes them to tend towards the earth’s centre like all other bodies,we shall find that the power P being in the direction of the line KLdrawn through the centre of gravity of the column GEFII cannotprevent this column from descending without sustaining the whole weight:another proof that this power is in equilibrio with the weight of thecolumn of water which it sustains, is, that if we push the piston from belowupwards, to make it ascend, this column of water will have the same velocity,and consequently the same quantity of motion.

To estimate the effort which the power makes, suppose that the diameterof the tube, or that of the piston, is 5 inches, and the height E G 18 inches;the superficies of circles being as the squares of their diameters, we can, by using the weightof the cylindrical foot of water, which was found to be 55 lbs., say, as the square of 12 is tothe square of 5, or as 144 is to 25, so is 55 to the fourth term, which we shall find is

9 pounds 8 ounces, for the weight of a cylinder of water whose base is a circle 5 inches

diameter and whose height is a foot: but as the column is 1 foot 6 inches in height, itsweight will be 14 pounds 5 ounces.

It will be remarked that if the circle GII of the piston were less thanthe bottom AD, the power P would only sustain the weight of a columnof water L I KM, which has for its base the circle of the piston, and forits height the level of the water above the same piston, since it can onlysustain the column of water to which it is a base, all the others, whichmake the difference of the columns A E F D and LI K M, resting on thebottom A D. We may add that if the power works the piston so as toelevate the column which it sustains, it would be easier than if thiscolumn were enclosed in a tube, in which we must surmount the re-sistance which causes the friction, or the friction of the water against itssides.

Having a siphon consisting of two branches A B, CD of the samediameter, place in the second a piston I LK at a determined height I K ;pour water into the first branch to the height E F; it cannot rise to thislevel in the second, on account of the obstacle which the piston presents.

If we draw the horizontal line G K, the columns A II and M K, havingtheir surfaces level, would be in equilibrio if they made an equal effort on theirbase to surmount each other; but as the first sustains all the weight of the column G F,A F, which is composed of the two, will push with the weight of the part G F the latterfrom below upwards, to make it rise to the level E Q. Thus subtracting the friction andweight of the piston, we must, to prevent it from yielding to the effort which the columnM K makes to lift it, load it with a weight equal to that of the column G F, which is toonatural to need any further explanation.

Fig. 1668.

Fis. 1669.