5

B

7

H

1

which is above it, because the valve in the piston remains shut by its own weight. In the mean time, the pressure of the surrounding water forces it into the working barrel, through the fixed valve; and the barrel is now filled with water. Now, let the piston be pushed down again; the fixed valve immediately shuts by its own weight, and in opposition to the endeavours which the water in the barrel makes to escape this way. This attempt to compress the water in the barrel causes it to open the valve in the piston: or rather, this valve yields to our en deavour to push the piston down through the water in the working barrel. By this means we get the piston to the bottom of the barrel; and it has now above it the whole pillar of water reaching in the pump. Drawing up the piston to the surface a second time, must lift this double column along with it, and its surface now will be higher. By this means the water brought up by the successive strokes of the piston rises to such a height in this cistern, as to produce an efflux by the spout nearly equable.

has a valve at some convenient place, as near as possible to its junction with the cylinder. This valve also opens upwards. This pipe, usually called the rising pipe or main, terminates at the place where the water must be delivered. Now suppose this apparatus set into the water, so that the upper end of the cylinder may be under or even with the surface of the water; the water will open the valve, and after filling the barrel and lateral pipe, will also open the valve in the lateral pipe, and at last stand at an equal height within and without. Now let the piston be put in at the top of the working barrel, and thrust down. It will push. the water before it. This will shut the valve at the bottom, and the water will make its way through the other valve, and fill a part of the rising pipe, equal to the internal capacity of the working barrel. When this downward motion of the piston ceases, the side valve will fall down by its own weight and shut this passage. Now let the piston be drawn up again: the side valve hinders the water in the rising pipe from returning into the working barrel. But now Sucking PUMP. This does not the bottom valve is opened by the differ essentially from the lifting pressure of the external water, and pump above described, except that the water enters and fills the cy-in the former the piston is suplinder as the piston rises. When the piston has got to the top, let it be thrust down again: the bottom valve will again be shut, and the water will be forced through the passage at the side valve, and rise along the main, pushing before it the water already there. Repeating this operation, the water must at last arrive at the top, however

posed to work in the water of the reservoir, which is in many cases very inconvenient on account of the length of the rod necessary for such a construction. In the sucking pump therefore the piston is situated considerably above the surface, and in most cases in the very body of the pump, if this is not more than 32 or 33 feet above the surface of the water in the well.

In this construction, suppose the piston to be forced down; then the elasticity of air will shot the fixed valve and open tliat of the piston, and a certain quantity of air will escape. Now, let the piston be drawn up, and the valve in it will be shut, and the air in the barrel will expand itself so as to occupy the whole space; but its elasticity being thus diminished, the pres sure of the external atmosphere on the surface of the water in the well will open the fixed valve,

and force into the barrel a quantity of water sufficient to establish an equilibrium, between the internal and external air. Let us suppose the water thus admitted rises to any height, then repeating the stroke of the piston, another por tion of air will be excluded, and on raising it again, another portion of water will be admitted into the barrel; and thus, by repeated strokes, it will finally arrive at the piston, if this do not exceed 32 or 33 feet, after which the operation will be precisely the same as in the former case. As to the limit of 33 feet, it follows necessarily, from what has been observed under the articles of AIR and ATMOSPHERE, where it is shown that a column of water of 33 feet is about equal to a column of at mosphere of equal base; and hence it follows, that this construction can only be made use of when the distance between the surface of the water and the sucker is within the above limit.

PUNCHEON, a measure for liquors containing 84 gallons.

PURSUIT, Curve of, is one generated by the motion of a point which is always directed towards another point, also in motion along a right line, the velocity of the two points bearing any determinate

ratio to each other.

Thus let A and B be two bodies, the one A moving along the line with any given velocity ; and the other B, moving with a velocity V, and in such a manner as to be always directed towards the body A, then is the curve thus described by B, the curve of chase or the curve of pursuit, the equations and proper ties of which are as follow;

Let the velocity of B be to the velocity of A as n: 1. Call also the perpendicular BA=a, AD z, B'D=y, then the equation of the curve is

21=

an yl—n

1-76

+

+

a―nyn +1

1 + n 2 na 1-24

The line B A, or B/A/, joining any two contemporaneous positions of A and B, is a tangent to the curve at that point,

PYRAMID, in Geometry, is a solid having any plane figure for its base, and triangles for its sides, all terminating in one common point or vortex. If the base of the pyramid is a regular figure, the solid is called a regular pyramid, which then takes particular names cording to the number of its sides, as triangular, square, pentagonal, &c. the same as the prism.

ac

If the perpendicular demitted from its vertex falls on the centre of the base, the solid is called a right pyramid; but if not, it is oblique.

The principal properties of the pyramid may be stated as follows: 1. Every pyramid is one-third of a prism of equal base and altitude.

2. Pyramids of equal bases and altitudes are equal to each other, whether the figure of their bases be similar or dissimilar.

3. Any section of a pyramid parallel to its base will be similar to the base, and these areas will be to each other as the squares of their distances from the vertex.

4. Pyramids, when their bases are equal, are to each other as their altitudes, and when their altitudes are equal they are to each other as their bases; and when neither are equal, they are to each other in the compound ratio of their bases and altitudes.

To find the Solidity of a Pyramid. Multiply the area of the base by its perpendicular altitude, and one third of the product will be the solidity.

To find the Surface of a Pyramid,

Multiply the perimeter of the base by the slant altitude of one of its faces, and half the product will be the surface. Or, find the area of one of its triangular faces, and multiply by the number of them, which is the same thing.

Frustrum of a Pyramid. Is tne solid formed by cutting off the upper part of a pyramid by a section parallel to its base.

To find the Solidity and Surface of a Frustrum of a Pyramid. Let A represent the area of the greater end, a that of the less, and hits height or altitude; also let S and s represent the corresponding sides of the two ends, and p the tabular