122. =Sluice-Gates, Dams, etc.=--The application of the above principles in the construction of sluice-gates, dams, etc., is a matter of great practical importance. Let us look at this. As pressure in a fluid is always in proportion to the height of the fluid above the point of pressure, the pressure upon any portion of the side of a vessel containing a fluid must be in proportion to its distance from the surface; or, in other words, it is the weight of a column of water extending from this portion to the surface. Let A B C D (Fig. 75) represent a _section_ of a cubical vessel, that is, one in which each side is of the same size with the bottom. The pressure on the point _a_, in the line A B, is that of a column of particles, A _a_. But A _a_ is equal to _c b_, and _c b_ is equal to _b a_. Therefore _b a_ may represent the pressure on _a_. In the same way it can be shown that _e d_ represents the pressure on _d_, _n m_ the pressure on _m_, C B that on B. Therefore the pressure on all the points in A B will be represented by lines filling up all the triangular space A B C, and this is half of A B C D, which represents the pressure on the line C B. It is clear, then, that as the pressure on a vertical line in the side is half that on a line at right angles to it in the bottom, the pressure on the whole side is half that on the whole bottom. [Illustration: Fig. 76.] We see from the above demonstration why it is that a dam is built in the form represented in Fig. 76. We see, also, why in the monstrous vats in some of the English breweries (some of them holding many thousand barrels) the hoops and other securities at the lower part of them require to be made of very great strength. It is manifest, also, that if a sluice-gate is to be kept shut by a single support, this must be applied at one third of the distance from the bottom, there being as much pressure, as seen by Fig. 75, on the lower third as on the upper two thirds of the gate. 123. =Lateral Pressure in Fluids.=--The pressure of a liquid on the side of a vessel, of which I have spoken above, is a _lateral_ pressure, and it is caused by the downward pressure of gravitation in the liquid. But how? The particles of a fluid are freely movable among each other, and therefore are ready to escape from pressure in any direction. The particles at _a_, Fig. 75, pressed upon by the column of particles extending above them to the surface, are ready to escape laterally, and would do so if there were an opening made in the vessel at that point. But if the vessel contained a block of ice, fitting it as accurately as the body of water, there would be no escape at the opening, because the particles of the solid are so held together that the downward pressure of the earth's attraction occasions no lateral pressure. [Illustration: Fig. 77.] [Illustration: Fig. 78.]