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83.

[[image:  drawing of a wooden staved barrel A B C D, left side G, right side F, and an opening in the center of the side of the barrel, with a small tube E extending down from the bottom of the barrel.]]

Whence we may judge in what time a muid will be void permitting it to run thrô a certain hole:  For let A B C D be a muid of Paris placed on one end having a hole of 4 lines in E, ye ordinary height of ye wine between ye heads wch is 30 inches, or 2 1/2 feet, by 13 feet makes 32 1/2 whereof ye root is 5 12/17 near, and as 13 to 5 12/17 so is 14 to 6 1/6 near:  Therefore if ye hole E is of 3 lines, there will go out of ye muid being kept full 6 1/6 pints in a minute but being of 4 lines the surface of ye holes are as 9 to 16:  Therefore as 9 to 16 so is 6 1/6 to 10 25/27 that is to say to almost 11, and if 11 pints give 1 minute, what time will 280 give, we shall find about 25 1/2 minutes keeping ye vessel always full of water therefore but what is said above, a double time is necessary, viz 51 to let it run out.

[[image:  diagram of parabolic-shaped (U-shaped) curve labeled A B C D, with a vertical midline D B, with mark points]]t E, F, P, H, N, L and I; a horizontal line G H K about 3/5ths of the way down, another horizontal line from I to R 9/10ths if the way down the midline; and two dotted lines N O and L M between G K and I R.]]

  It is convenient here to resolve a problem sufficiently curious wch Torricellius hath not 
attempted to solve althô he proposed it:  Ye problem is to find a vessel of such a figure that being pearced at ye bottom with a small hole ye upper water passes in descending from equall heights in equall time.  It in ye conoidal figure B L is to B N, as ye Sq Sq of L M is to ye Sq Sq of N O, and B N to B H as ye Sq Sq of N O to ye Sq Sq of H K and so on ye water will descend from A D C uniformly to ye hole wch is in B:  For let B P be a mean proportionall between B D and B H, since ye Sq Sq of K H and of D C are one to another as ye heights B H B D ye Sq of H K, D C will be in a subduple proportion of B H to B D, or as ye heights B P B D;  but ye swiftness of ye water wch goeth out in B by ye charg of ye height B D is to that wch goeth thrô ye charg of ye height B H in a subduple proportion of B D to B H  ie as B D to B P:  Therefore the swiftness of ye water descending from it is to ye swiftness of ye water descending from D, as ye Sq of H K to ye Sq: of D C:  but ye circular surface of the water in H is to ye circular surface of ye water in D as ye Sq: of H K to ye Sq: of D C therefore they will run and descend as swift one as ye other.

  And if ye surface A D C runs out in one second, ye surface G H K will run out also in one second since ye quantitys are as ye swiftnesses.  Ye same thing will happen to ye other surfaces in E and F &c but it is necessary that ye hole in B be very small that it may not make any considerable acceleration and that ye water may not go out of ye hole B sensibly, but in proportion of its weight.  Such a vessel may serve for a [[space]] or water hourglass.

Transcription Notes:
mandc: Revised image description. Muid is French for hogshead (eight French cubic feet, about 274 liters). The Desaguliers translation uses the Greek word: "clepsydra or water clock."