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81. Experiment V The reservatory being at 24 feet 3 inches and at ye middle mark there was given thrô ye 3 lines 14 pints in 44 1/2 seconds and thrô ye 6 lines in 12 1/2 near, and permitting ye 13 1/2 pints to run from upper mark it employed 42 seconds thrô ye 3 lines and 10 1/2 thrô ye 6 lines: This last experiment renders ye proportions equall as well as ye second. We found near ye same in a reservatory of 35 feet. By these different experiments is seen that we may follow ye second rule without any considerable error, and that ye contrary causes, make always a compensation just enough when ye experiments are made. In respect of ye subduple proportion of ye heights of ye reservatorys there are two causes wch diminish it and two wch augment it; Those wch diminish it are that ye resists more in proportion a great swiftness than to a small, and that ye rubbing is greater against ye sides of ye ajutage [[space]] those wch augment it are ye same wch cause ye great holes sometimes to give more water in proportion than ye small viz that we must pour ye water with greater force to maintain ye reservatorys fall in a great height than in a small, and that ye water descends swifter when we permit it to run: These causes do near enough compensate one ye other: but it happens ordinarily that there is less than a little less than a subduple proportion in ye great heights: but when ye experiments are made in ye same bottom of ye reservatory in ye same time, ye great holes always give less in proportion than ye small ones: [[image: draqwing of a square A B C D with a circle at E the midpoint of line C D. There is a horizontal line across the square about 1/5 of the way down from the top. There is a swooping curved line descending from A to C.]] Toricellus hath demonstrated in a small tract wch he made of ye motion of ye water, that if there is a reservatory A B C D pearced at ye bottom in E with a small hole as of 4 or 5 lines, and that ye water being to ye line A B, it may run out in 10 minutes without adding anything to it, it will pass unequal spaces in descending in equal times, so that if we divide ye line B C into 100 equal parts it will descend in ye first minute 19 of these parts in ye second 17 in ye 3d 15 &c according to odd numbers unto a unity, so that ye half part shall be voided in ye last of ye 10 minutes. The reason of this effect is found upon ye first rule explained above that ye swiftness of running waters are in a subduple proportion of ye heights, and by consequence are one to ye other heights, [[strikethrough]] and [[/strikethrough]] as ye ordinates of a parabola A B C begining at ye greatest A B and ending at ye point C, wch causes ye spaces passed into ye same time by ye surface of ye water AB to be as the odd numbers following one ye other beginning at ye greatest. From thence is drawn a consequence that if we measure ye quantity of ye water wch is contained in ye reservatory to ye line A B, and that it is run out in 10 minutes, there will go out twice as much in ye same time, if we allways maintain ye reservatory full to ye height A B, wch proceeds from thence that if its swiftness acquired at ye poynt C without augmenting or diminishing it would pass in ye same time a space double to B C: Now ye water wch goeth in the beginning thrô ye hole E hath a swiftness equal to that ye falling drop would have acquired at ye point C, and all ye water wch goeth out hath always ye same swiftness if ye reservatory continueth full therefore there will go out twice as much in ye 10 minutes as there doth permitting it to run without adding anything to it, and in 5 minutes as much as it contains.
Transcription Notes:
Evangelista Torricelli - https://en.wikipedia.org/wiki/Evangelista_Torricelli
mandc: Revised image description.
