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86.

      Part The Fourth
       of the Height
        of Spouts
[[line]]

       DISCOURS I
   of the height of perpendicular spouts.

  It is seen above that ye spouts ought to mount to ye height of ye reservatorys but that ye rubbing at ye sides of ye holes and ye resistance that ye air makes causes that in spouts heighly elevated ye height of ye spout doth not arrive to that of ye reservatory.

  To explain well ye rules wch we ought to observe in calculation ye heights of ye spouts according to ye heights of ye reservatorys, we must concider ye following rules

      Rule the First.

  When ye pipes wch furnish ye water are sufficiently large, ye larger ye hole ye further it pusheth its spout.  An experiment is easily made, if we have a muid full of water and perced at ye side towards ye lower end with 5 or 6 different holes of ye same horizontal height as of 1, 2, 4, 6, 10, 12 lines &c for, we shall always see ye largest hole push ye water furthest provided ye holes be at ye same distance from ye surface of ye water:  Ye same thing will happen in 2 pipes of 3 or 4 inches large provided that ye hole exceeds not in a diameter.

  The cause of this effect is easily to be explained to bouls of wood of different bigness:  For since they are one to another in triple proportion of their diameters, their weights will be also in that proportion;  as also their force to surmount ye resistance of ye air:  and by consequence if we cast with ye same swiftness a boul of 2 lines diameter and another of 4 that last will go furthest.  We see an experiment when we put into ye same gun lead in powder shots and bullets;  for althô they go out with ye same swiftness ye that goeth further than ye powdered lead, and ye bullets get much further than ye shot.  And for ye same reason will go further than a small ball of ye same metall pushed with ye same force.  It is true that if ye reservatory is but 2 or 3 feet a spout of 8 lines will not be sensibly different from a spout of 10 or 12 lines, and one of 4 lines will go sensibly as far as one of 6 but ye difference will be very considerable to spouts of 30, 50 and 60 foot heigh, and beyond.

      Rule II

  The spouts diminish of ye height of ye reservatory in a double proportion of ye height where they are elevated:

[[image:  drawing of a "J" shaped pipe A (top) B C, the upright part of larger diameter than the lower part opening at D. Markers spaced down from the top: A L M N G.  Dotted line across the larger diameter, with markers E and H below E. Spout of smallest diameter at the tip of the bottom of pipe D.]] 
  Let A B C be a reservatory or pipe spouting thrô ye hole D, and let ye height of ye water in pipe successively be A and E:  I say that if ye line E H is ye default of ye small spout to E and G A ye default of ye great spout to A, A G shall be to E H in a double proportion of D H to D G.

  For let us suppose that ye weight of ye air is to ye weight of ye water as 1 to 600 or for the sake of calculation as 1 to 50 and that one sole drop or parcel of air is incountered by ye going out from ye hole by ye first drop of water and that it afterwards it mounts freely as in a vacun̄.  It is evident by what hath been demonstrated in ye rules of ye motions of bodys wch shoc one the other that ye drop of water will loose 1/61 of its swiftness, if its swiftness is expressed by 61.  Therefore let D E be 61, and D H 60, and that ye drop is retarded 1/61 viz E H.  Furthermore let ye height be D A, ye swiftness of ye drop shall be to ye first swiftness in a subduple proportion of D E to D A and that drop by incountering a small parcell of air 

Transcription Notes:
mandc: Reviewed. For "bouls" read "balls." Regarding "vacun? "n" topped with a macron was used to represent "mn."