TRACT 38.

PROBLEMS.

355

rounding parts of the fluid, which is in commotion quitearound ; and the particles thus entering the hole in all direc-tions, strike against each other, and impede one another’smotion : from which it happens, that it is the particles in thecentre of the hole onlv that issue out with the whole velo-city due to the entire height of the fluid, while the otherparticles towards the sides of the orifice pass out with de-creased velocities; and hence the medium velocity throughthe orifice, is somewhat less than that of a single body only,urged with the same pressure of the superincumbent columnof the fluid. And experiments, on the quantity of waterdischarged through apertures, show that the quantity mustbe diminished, by those causes, rather more than the fourthpart, when the orifice is small, or such as to make the meanvelocity nearly equal to that in a body falling through halfthe height of the fluid above the orifice.

Experiments have also been made on the extent to whichthe spout of water ranges on a horizontal plane, and com-pared with the theory, by calculating it as a projectile dis-charged with the velocity acquired by descending throughthe height of the fluid. For, when the aperture is in theside of the vessel, the fluid spouts out horizontally with auniform velocity, which, combined with the perpendicularvelocity from the action of gravity, causes the jet to formthe curve of a parabola. Then thedistances to which the jet spouts onthe horizontal plane bg, are as theroots of the rectangles of the seg-ments AC . CB, AD . DB, AE . EB. Forthe ranges bp, bg, are as the timesand horizontal velocities ; but the ve-locity is as \/AC; and the time of thefall, which is the same as the time of moving, is as y'cE ;therefore the distance ef is as ^/(ac . cb) ; and the distanceBG as -/(ad . db). And hence, if two holes be made equi-distant from the top and bottom, they will project the waterto the same distance; for if ac = eb, then the rectangle