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87.

will loose yet a part proportionall to H E according to ye proportion of D E to D A.  Let AL be that deminution, D E shall be to D H as D A to DL:  But as we suppose one parcel of air for ye space D E there will be many parcells of air for ye space D A in proportion as D A or D G is greater than D E or D H, and each parcell diminisheth sensibly ye height of ye drop of water in ye same proportion, that shall be a second proportion equall to ye first, and by consequence A L being to A G as D E to D A or H E to AL;  AG shall be ye defect of ye height of ye elevation of ye drop of water but because there is many parcells of air between D and E each of wch retards ye motion of ye drop in ye same proportion ye motion of ye drop in ye [[strikethrough]] same [[/strikethrough]] space D E shall be much more retarded than by ye incounter of one sole parcell, as is supposed.  But we may consider all ye spaces of air as one sole parcel, and ye space of air D A is in ye same proportion as D A to D E and by consequence we must add a second proportion equal to ye first:  Whence it follows that if A L is to A G in a double proportion of D E to D A: G A shall be ye defect of ye spout below ye height of ye water of ye reservatory D A if E H is that of ye height DE wch it ought to be:

Exampla

Let D A be ye quadruple of D E, ye swiftness of ye spout of water pressed by D A shall be double to that of ye spout of water pressed by D E.  If we take therefore as above ye height D E for 61, ye height D H shall be 60, and as ye swiftness of ye great spout is double and that it ought to be elevated to a quadruple height it will loose by ye incounter with as much air in D G, 4 times as much of its height as H E that is that instead of ye spouts being elevated to D A 244 it will be elevated but to D E 240, but ye [[strikethrough]] spouts [[/strikethrough]] space E A being divided into 3 equal each shall be equall to D E, and if ye first looseth ye height A L, ye second shall loose as much in ye same proportion as ye different parts of D E loose to ye first spout:  For in each part of ye spout wch goeth out ye swiftness of ye great one is always double to that of ye small, for it hath always a quadruple space to pass thrô.  It will loose besides ye first part 3 other equal ones L M, M N, N G and A L being supposed A AG shall be 16;  and by consequence ye default A G shall be to the default E H in a double proportion of D E to D A, and if E H is I such G A shall be 16.

The rubbing changeth a little these measures and ye complication of ye spaces of ye air wch resists:  For in ye great spouts it will be very convenient that ye space of ye air passed may be in proportion at ye heights of ye reservatory wch ought a little to diminish ye default and it is ye height of ye spounts must be considered, and so if H D is 60, D G shall be 240, ye small reservatory being at 61 foot and ye great one at 256 foot:

  Upon that supposition it will be easy to calculate ye heights of ye spouts to all heights of ye reservatorys one being known as that of a reservatory of 5 foot wch as is found by many experiments to want an inch.  If we suppose therefore that a spout of 5 foot whereof ye water wch furnisheth it is not straight and runs easily in ye pipes, ought to have ye upper surface of ye water of its reservatory at 5 foot 1 inch, a spout of 10 foot shall have its reservatory at 10 foot 4 inches;  that of 15 foot at 15 foot 9 inches:  that of 20 at 20 16 inches and so in order according to ye squares: we must not calculate by diminishing ye heights of ye reservatorys:  For if we take a reservatory of 100 foot it will diminish 400 inches, that is 33 foot 1/3 one of 200 foot should have its diminution about 133 foot, and one of 400 foot ye quadruple of 133 foot viz 532 and by consequence will not spout at all wch is impossible:  for ye spouts to that height ought allways to increase:  but we must take for a spout of 200 foot a reservatory of 333 foot and for a spout of 400 feet 932 foot

Far all the different heights we may make use of ye following Tabla.

Transcription Notes:
mandc: Reviewed changed DEA44 to D E 244 (i.e., 4 x 61 = 244), and DEE40 to D E 240 for the same logic. The "2's" do look like E's. Translator's error "A AG" should have been "4 A G," Changed "dA to BA." to "D A to D A."." Translators "r's" look almost exactly like his "n's" and "u's." Changed "chargeth" to changeth," Fall to For.