1102

THEORY AND PRACTICE OF ENGINEERING.

Book II.

effect, which only depends on its elevation in the tune, and the extent of the base over whichit is spread.

Supposing the surfaces C D and A Q, each 6 feet square, are so near each other that wecan still take something from the interval; if we give 24 feet to the height of the columnG N, each surface will be driven in the opposite direction by a force of 60-180 pounds, andproduced by a weight of 3 or 4 ounces.

Belidor took two plates, each 1 foot square and 30 lines thick: having placed themabove each other, about 3 inches apart, he nailed a leather band all round, and formed a kindof bellows, having the form of a parallelepiped. After having taken all proper precautionsto prevent the water with which it was filled from escaping, he attached the upper surfacesin a firm manner horizontally to a beam supported by two uprights, so as to make thebottom work upwards ; at the four corners of this were iron rings answering to cordsattached to the arm of a balance ; he then loaded the other arm as much as possible sothat the lower part of the machine was applied to the upper : this latter was pierced withtwo holes, to one of which a vertical plug was adapted to be opened, solely for the escapeof the air when water was poured in: at the other was a copper tube, whose interiordiameter was 3 lines and 10 feet high, attached to a beam firmly fixed at both ends.

The question he. wished to solve was, if by pouring water into the tube it would raise aweight of a column of water 1 foot square at the base and 10 feet high ; this happened whenabout 3 pints of water were poured into it; he then remarked that the velocity of theweight increased as it elevated, for, as by pouring the water in, he took care to keep a funnelsoldered to the summit of the tube full, the water with which the bellows was filled wouldincrease by its own weight the action of that of the tube.

As the gates of a canal often sustain 22 and 23 feet of water when the sea is low, ithappens that small threads pass under the sill, and insinuate themselves below the platformand foundations ; this water not finding means of escaping, pushes upwards everythingwhich could prevent it from mounting to the level of the canal, and causes the gates tobend, notwithstanding their weight and solidity.

Having a cylindrical tube, A 13 C D, inclinedon its base A D, supposed horizontal, and filledwith water to a height E F, it would load thebottom A D as much as if it were an uprightcylinder A G II D of the same base. Drawthrough any point P of the height FI thehorizontal line LM, and consider that the waterenclosed in the space AEG is sustained bythe side E A ; then all the threads K,L of whichit is composed have each a lean on the point Lof the inclined surface E A ; consequently thebase A D is not charged therewith.

It is not the same with that which comprisesthe opposite space I F 1), for as the thread F I

acts on the smaller M N, to elevate them to the height of the level E II, being prevented bythe surface F D, each of them will press all the points M of this surface from belowupwards, with a force equivalent to the weight of the thread F P, the difference of FI fromMX ; and as the height FP is equal to KL, the point M will be as much pressed frombelow upwards as the point L is from above downwards, which shows that the surfacesE A and F D are driven in opposite directions with a force equivalent to the weight ofwater enclosed in the space AEG, or what is equal to it, DFH. But as all the threadswhose action is sustained by the surface F D cannot press it from below upwards withoutpressing as much the point I D of the bottom, which serves as abase, from above downwards,we see that if we add to this latter pressure the weight of the threads which the spaceI F D contains, each point of the bottom A D will be loaded with a weight equivalentto that of the thread FI.

It follows that having a vessel BCDE similar to a reversedtruncated cone, to which the tube A B E F is fitted to receive apiston serving as a bottom ; filling this vessel with water, thepower applied to the piston will only sustain the weight of thecolumn BGHE; then all the remainder of the water will reston the sides CB and DE. This consequence shows the errorof making the pipes of descent larger above than below, withthe intention of giving more elevation to a fountain in which thepipe terminates, forgetting that the portion leaning on the sidesof the tube does not contribute to drive that which descends; thispractice, however, may be useful when the hole through which thejet issues is too large.

If a piston answered to the great circle of the precedingvessel, it would happen, on the contrary, that being filled with

f o H

k G

Fig. 1676.

Fig. 1C77.