Viewing page 62 of 140
This transcription has been completed. Contact us with corrections.
58. inches wch is near ye square of G H of 8 inches 7 lines is to 30, wch is near ye square of g h of 5 inches 6 lines, as 47 to 19 near; and as 74 to 47 ye mean proportionall between 74 and 30, so is 19 to 12; whence we see that 47 is to 12 in a proportion composed of that of ye base G H to that of ye base g h, and of ye subduple proportion of ye same base G H to ye same base g h. RULE V Spouts of water of ye same swiftness and of different holes sustain weights by their shock wch are one to ye other in a double proportion of their holes: [[image: Diagram of two cylinders on backboards, left backboard labeled A B, and G E H where cylinder touches backboard, and N at the opening; the right backboard labeled C D, and K F L where cylinder touches backboard, and M at the opening]] Let y.e two surfaces A B, C D be perced at ye holes E and F and that ye two spouts of water pass thrô these holes; it is evident that ye surface of ye hole E is to ye surface of ye hole F in a duple proportion of ye diameter K L, and ye swiftness being supposed equall, if ye diameter G H is double to ye diameter K L there will be 4 times as many small corpuscles of water to shoc in ye base G H as in ye base K L. They therefore make a quadruple effect, and if ye surfaces of ye spouts are reciprocall to ye heights of ye reservations, they make an equilibrium with equall weights. To know ye force of runing waters when they strike ye wheels of mills or some other engines, we must know their swiftness and compare it to that of water, wch spout at ye bottom of a reservatory. It is therefore necessary to know ye specific weight of ye water in regard of other bodys, here are ye observations wch I have made. There was made a vessel of copper square at half a foot height, wch by consequence, would contain ye 8th part of a cubic foot; it was put into ye scale of a ballance and on ye other side a weight equall to it, it was filled afterwards with water with very great care by a small hole made towards ye angle of ye uppermost side: We found by experiments that ye water would weigh 8 pound 3/4, and by consequence that ye cubic foot of water ought to weigh 70 pounds, ye Maid of Paris contains 8 cubic feet, in each cubic foot 36 pints when they are measured just and that ye water doth not pass ye edges but when it passeth ye edges ye most it can without mounting over, it contains but 35 pints; each of ye last pints weigh 2 pound and ye other 2 pound less by 7 gross ye Maid of Paris of water whose base is a foot diameter and a foot heigh weighs but 55 pounds since ye proportion of ye circle to ye square of wch is circumscribed, is near is near at 11 to 14: Now as 14 to 11 so 70 pounds are to 55#, whence may be known that a cylinder of a foot heigh and of an inch base weighs ounces one gross near; for ye 14 4th part of 55 pounds is 6 1/7 ounces and a gross is 1/8; upon wch ye following experiments are made. Having tyed a small stick to another great one wch was immoveable in ye midle of ye course of ye river where it was very swift, we measured along from ye small stick a distance of 15 foot in length, we cast afterwards a small peice of wood or some peice of an herbe at two or 3 feet from ye stick, over against ye place where ye first mark of 15 feet was, and we counted by a pendulum that beat half seconds in what time it passed to ye other mark, if it was in 10 demiseconds we concluded that in that place ye water of ye river went 3 feet in a second. Afterwards we made us of ye turnpike where there was two rules wch crossed ye axis, so that ye plains where they were cut one ye other at right angles. There was elevated towards ye end of one of these rules a small square board of 6 inches large very fine, wch was dipped perpendicularly into ye running water till it passed 4 or 5 inches above it, and at ye same time there was put at ye extremity of ye other rule wch was in an horizontal situation, a weight equally distant from ye axis as ye middle of ye board [[?]] it was augmented or diminished till it made an equilibrium with ye shoc of ye water against ye small board or shovel. Many of these experiments were
Transcription Notes:
mandc: Reviewed. Added to description per following diagram:
http://echo.mpiwg-berlin.mpg.de/ECHOdocuView?url=%2Fpermanent%2Flibrary%2FQERNH1MN%2Fpageimg&start=11&mode=imagepath&pn=174&ww=0.1315&wh=0.1957&wx=0.4793&wy=0.7462
