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MISCELLANEOUS

TRACT 3-8.

Thus, for instance, for a wave of 18 inches breadth, as*/394 : 39| : : VlS : </(39j r X 18) = 1V313 •= 26‘53 11the velocity of the wave of 18 inches breadth.

PROBLEM XXIV.

To assign the Velocity with which Water , or other Fluids ,spouts out from the bottom of a Vessel.

The velocity with which water runs out by a hole in thebottom or side of a vessel, is equal to that which is generatedby gravity through the height of the fluid above the hole ;that is, the velocity of a heavy body acquired by fallingfreely through the height ab.

For, divide the altitude, ab into a greatnumber of very small parts, each being ],their number a, or a = the altitude ab.

Now, by prop. 6 1, vol. 2 of the Course,the pressure of the fluid against the hole e,by which the motion is generated, is equalto the weight of the column of fluid above it, that is the co-lumn whose height is ab or a, and base the area of the holeb. Therefore the pressure on the hole, or small part of thefluid 1, is to its weight, or the natural force of gravity, as ato 1. But the velocities generated in the same body in anytime, are as those forces; and because gravity generates thevelocity 2 in descending through the small space 1, therefore1 : a : : 2 : 2 a, the velocity generated by the pressure of thecolumn of fluid in the same time. But 2 a is also the velocitygenerated by gravity in descending through a or ab. Thatis, the velocity of the issuing water, is equal to that which isacquired by a body in falling through the height ab.

The same otherwise.

Because the momenta, or quantities of motion, generatedin two given bodies, by the same force, acting during rhe