Viewing page 106 of 140

This transcription has been completed. Contact us with corrections.

102.

      Probleme

  The mean height of a reservatory being given, and ye spout being oblique to find where it will touch ye horizontal plane.

[[image:  diagram of reverse J shape spout labeled A B C, with graph emanating from C with vertical axis annotated D M H Q C and horizontal axis annotated C R G and arcs labeled D L E O C (a semi-circle); and parabolas C N R; C F G; AND C P R.]]

 Let A B be ye pipe of ye reservatory, C ye passage, C D a line paralel to A B, D E C a semicircle, of wch H is ye center;  Galileus and Torricellius have shewn that if ye direction of ye spout at ye going out of ye passage is ye line C E wch makes an angle D C E with ye perpendicular D C of 45 degrees having continued H E perpendicular to D C unto F, so that E F be equall to ye semidiameter of ye circle H E, ye point F shall be ye top of the parabola C F G described by ye spout as is seen in ye figure C E shall be ye tangent of that parabola to ye point C;  and C G ye amplitude of ye parabola double to H F or C D.

  But if we give another direction to ye spout as C L, we must fall ye perpendicular L M upon C D and M L N being double to M L ye pain N shall be ye top of ye parabola wch that spout shall describe, whereof C R shall be ye amplitude equal to 2 times M N;  and ye same in respect of all other directions.  Whence it follows that if ye angle L C E is equall to ye angle E C O, ye spout at ye direction C O shall go as far as that whose direction C O shall go as far as that whose direction is C L;  and Q O P being equal and paralel to M L N, P shall be ye top of ye parabola of that spout;  and they both shall meet at ye point R in ye horizontall line C G, since their amplitude C R ye quadruple of M L or double of M N, shall be common to both.

  The spouts of bombs full of powder observe ye same rules:  Whence it follows that if we find by experience that a bomb whose direction is 45 degrees, goeth to 500 toises in length it will go perpendicularly 150 toises.  For if C G is 500 toises and that ye bomb hath described ye parabola C F G, it will be elevated but to ye height C D wch is ye diameter of the semicircle, wch by consequence shall be 250 toises half of ye amplitude C G of ye parabola CFG:  But we must consider that ye resistance of ye air changeth a little these measures, for there being more air to pass thrô C F O than in C D, ye bomb will go a little nearer ye point D in proportion than ye point G.  And for ye same reason it ye direction of ye bomb was C L and that it should fall at ye point R it would go a little further by ye direction C O, since there is more air to pass thrô 

Transcription Notes:
mandc: Reviewed, amended image description; changed E D to C D; Image: http://echo.mpiwg-berlin.mpg.de/ECHOdocuView?url=/permanent/library/QERNH1MN/pageimg&viewMode=images&mode=imagepath&pn=283&ww=0.2181&wh=0.203&wx=0.609&wy=0.2514