358

MISCELLANEOUS

TRACT 38.

be t — for the time of exhausting the paraboloid at

the base, or the vertex upwards. Hence it may be observed,that this latter time is just double the former, when the ver-tex was downwards; also that this last, with the vertex down-wards, is but the y part of the time for the prism of equalbase and altitude first above found ; or that the three timesare in proportion respectively as the three numbers 3, 2, 1,having all the same base and altitude; also that all their timesare proportional to the base and root of the altitude directly,and as the orifice inversely’.

The times for many other figures may be seen in the firstarticle in my Mathematical Miscellany.

In the above investigation, the resistance made by the airto the issuing fluid, is neglected, the issue being supposed tobe made in a vacuum. But the difference of effect oughtnot to be neglected, when the density of the medium bearsany considerable proportion to that of the issuing fluid. Itwill make no difference in the account, in whatever part ofthe base the aperture is placed, the altitude of the surfaceabove it being the only consideration. Nor is it materialwhat the figure of it is; whether circular, square, triangular,&c, or regular or not; its area alone being the only neces-sary consideration.

PROBLEM XXV.

To determine the Issue of a Fluid through a Notch at the Topof a Vessel.

If a notch or slit eii in form of a parallelogram, be cut inthe side of a vessel, full of water, ad ; the quantity of waterflowing through it, will be -j- of the quantity flowing throughan equal orifice, placed at the whole depth eg, or at the basegh, in the same time; it being supposed that the vessel isalways kept full.