Öf Hydraulk Engines,

inches: 6r rather with more eafe, because its velocity in a large pipcwill be less than in a small one; and therefore its friction against thesides of the pipc will be less also.

And the force required to raise water depends not upon the lengthof the pipe, but upon the perpendicular height to which it is raisedtherein above the level of the spring. So that the fame force, which F%.would raise water tö the height in the upright pipe AiklmnopqB ,will raise it to the fame height or level BIH in the oblique pipeAEFGH. For the pressure of the water at the end A of the latter,is no more than its pressure against the end A of the former.

The weight or pressure of water at the lower end of a pipe, is alwaysas the sine of the angle to which the pipe is elevated above the levelparallel to the horizon. For, although the water in the upright pipe ABwould require a force applied immediately to the lower end A equalto the weight of all the water in it, to fupport the water, and a littlemore to drive it up, and out of the pipe j yet, if that pipe be inclinedfrom its upright position to an angle of 80 degrees (as in A 80) theforce required to fupport or to raile the fame Cylinder of water willthen be as much less, as the sine 80 A is less than the radius AB-, oras the sine of 80 degrees is less than the sine of 90. And so, de-creasing as the sine of the angle of elevation lessens, until it arrives atits level AC or place of rest, where the force of the water is nothingat either end of the pipe. For, although the absolute weight of thewater is the fame in all positions, yet its pressure at the lower enddecreafes, as the sine of the angle of elevation decreafes; as will ap~pear plainly by a farther consideration of the figure.

Let two pipes, AB and BC, of equal lengths and bores, join eachother at A ; and let the pipe AB be divided into 100 equal parts, asthe fcale S is; whofe length is equal to the length of the pipe.—Upon this length, as a radius, describe the quadrant BCD, anddivide it into 90 equal parts or degrees.

Let the pipe AC be elevated to io degrees upon the quadrant, andthen filled with water ; then, part of the water that is in it willrise in the pip e AB, and if it be kept füll of water, it will raise thewater in the pipe AB from A to / j that is, to a level i 10 with themouth of the pipe at 10: and the upright line a 10, equal to Ai,will be the sine of 1 o degrees elevation; which being meafured uponthe fcale S, will be about 17.40s such parts as the pipe contains 100in length : and therefore, the force or pressure of the water at A, inthe pipe A 10, will be to the force or pressure at A in the pip cAB tas 17.3 to ico.