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59.

made at ye place were ye water was most swift, and in other places where it went less swift, and [[strikethrough]] in these [[/strikethrough]] there was found always very near ye same proportions correspondent to that force of ye water wch goeth out at ye base of a pipe of 12 feet heigh:  Here is ye manner of calculation.

  Having found that ye water in ye swiftest place made 3 1/4 feet in a second and that is sustained then by ye shoc of ye shovel 3 [[?3/4]] pound ye spout at ye base of a reservatory wch is 42 foot height as ye swiftness at its going out to make 24 feet in a second according to ye doctrine of Galileus, and wch hath been explained above; that swiftness is therefore about 7 1/2 is 56 1/4 and by consequent if ye spout is of ye same largeness as ye shovel it ought to sustain a weight about 55 times as great:  Now 12 cubic feet of water weighs 840 pound, where of ye 4th part is 210 pound wch we take because that ye shovel is but half a foot, and that a column of water of half a foot square at ye base and 12 feet heigh, weighs 210 pounds;  and if we divide 210 by 55 ye quotient shall be about 3 3/4 pounds wch is ye weight wch hath been found in ye experiment.

I have found likewise ye force of ye running water in many other places of ye rivers, and also in ye [[strikethrough]] any other pl [[/strikethrough]] Aqueduct of Arcüeil.  I made an experiment at ye side of ye river where ye running water made 1 1/4 foot in a second and it made an equilibrium with 9 ounces of weight, to compare it to ye swiftness of 3 1/4 feet we must take ye sq: of ye 1 1/4 wch is 25/16 contained about 6 3/4 times in ye square of 3 1/4 [[,,?]] wch is 10 9/16 for ye product of 6 3/4 by 25/16 [[strikethrough]] and 5 [[/strikethrough]] is 9 and 64 wch is a little more in value than 60 ounces wch make 3 3/4 pounds.

  The wheels of ye mills wch are [[strikethrough]] upon [[/strikethrough]] upon ye Seine at Paris between ye Pont-Neuf and ye Pont-auchange, have not at their extremity but half ye running water wch shocs then wch amounts to ye same thing as when a weight in motion incounters another of ye same weight, wch is immoveable and that it is found there, for being joyned together, they have immediately after ye shoc but if half of ye swiftness of that wch hath shoced, and so we may suppose that if resistance of ye rubbing of ye axis of ye wheel, of that of ye millstone and of ye corn wch is ground, joyned to ye weight [[strikethrough]] equall to ? of weight [[/strikethrough]] of ye weel and of its shovels, amounts near to as much of ye resistance of a weight equall to that of ye water wch shocks and by consequence they ought to retard near half of ye swiftness of ye water wch shocs them;  ye same proportion is observed in ye wheels of ye pump:

  It is necessary here to consider that ye water of a river doth not go equally swift at is surface, and in ye other parts;  for ye water near ye bottom is much hindered by the incounter of stones herbs and other inequalitys.

     Here are ye experiments I have made of ye different swiftnesses.

  I put into a small river runing uniformly balls of wax tyed to a thread of a foot long, one was charged with small stones in ye middle to render its specific gravity somewhat greater than that of water, so that when ye 2 bouls were in ye water ye heavier bended ye thread an sunck ye lighter farther than it would have sunck alone, and by that means its upper part was almost even with ye water that ye wind may not blow upon it.  I allways observed that if lower bowl would remain behind principally at ye places where there was some herbs at ye bottom of ye water near to wch ye lower bowl should pass;  for that river was but about 3 foot deep:  But when these bowls were put in a place where ye water incountering some obstacle was elevated a little, and afterwards took a more rapid [[strikethrough]] motion [[strikethrough]] course, as is observed under bridges, ye lower bowl would out go ye upper whence we see that ye water in ye midle goeth then further than ye surface;  and this proceeds from thence that ye water being elevated a little heigher by ye obstacle, acquires a greater swiftness in runing, thrô a steeper place, and that violent motion makes it plunge itself and pass below that of ye surface;  as A B C D is ye course of ye superior water, and that by an obstacle towards B it is elevated to ye pricked line E F, it will run swifter thrô ye steep place E F C and by ye swiftness it hath acquired

[[image:  Diagram of a straight horizontal line annotated A B C I D, with a perpendicular dotted line intersecting it at an anlgle annotated E F G H and showing C as the midpoint]]

Transcription Notes:
mandc: Reviewed. Image: http://echo.mpiwg-berlin.mpg.de/ECHOdocuView?url=%2Fpermanent%2Flibrary%2FQERNH1MN%2Fpageimg&start=11&mode=imagepath&pn=174&ww=0.1518&wh=0.1429&wx=0.6172&wy=0.7827 Note: in the second line of para 2 I changed the transcriber's "33" to [[?3 3/4]], however I did not change the ms authors "42", which may be a mistake based on the Desaguliers translation which Desaquliers transcribes as "12" on this page: http://echo.mpiwg-berlin.mpg.de/ECHOdocuView?url=/permanent/library/QERNH1MN/pageimg&start=11&mode=imagepath&pn=169&ww=0.7793&wh=0.4044&wx=0.0635&wy=0.2495 Another mistake: ms: "therefore about 7 1/2 is 56 1/4" is translated: "The square of 7 1/2 is 56 1/4,...." [7.5 x 7.5 = 56.25]