1877.] 125 
| Briggs. 
the edge of the aperture to the plane of least section is taken to be an arc 
of a circle—the internal surface of a segment of a ring. Let D be the 
diameter of the opening in the plate. Suppose d, the diameter of 
the least section of the vena contracta, to have the value given by 
observation, d = 0.8D. Then following the previous conditions of form 
of the conoid Z we have, the diameter of the Disc =-D, = 1.13137D, 
and the radius of the arc of contour = n — 0.16569D. It will now be 
observed that the line of the are of contour, if it is continued within the 
opening to supposed point of horizontal efflux—the circle of periphery of 
the disc, gives a strata of water f (shown more distinctly in Fig. 7), which 
is cut off from the effluent stream. This 
strata has its greatest thicknesss of f= 
0.01358D. These suppositions place the 
plane of least section = 0.152D below the 
opening. 
In Fig. 8 will be seen similar delineation of the contour of the vena con- 
tracta, and the lines of the cur- 
rent of maximum constant vel- 
ocity, as modified by placing the 
plane of least section at its ob- 
served position, or 9.25D, below 
the opening in the plate. The 
contour of the vena contrdacta is 
here depicted as an arc of an 
ellipsis which has 0.166D for its 
minor radius and 0.275D nearly 
for its major one, which will approximate closely to the true parabolic form 
as suggested in the first paper. The thickness of the film or strata f which 
represents the resistance arising from friction of water against the bottom 
and at the edge of the aperture now becomes {about 0.025D. The angle @ 
which the current makes with the edge of the aperture becomes about 35°. 
If these suppositions are correct, a re-entering mouth-piece, shaped to con- 
form to the upper part of the elliptical arc wouid give the same contour and 
sections to the vena contracta as that now found to proceed from free dis- 
charge at a plain aperture. It would seem also from the tenor of this dis- 
cussion that by substituting a re-entering curve at A fig. 7, making the bot- 
tom of the vessel to conform to a reversal of the curve A f, giving the re- 
versed elliptical arc a at the edge of the orifice, so that the tangent of the 
curvature upwards at the edge should be about 35°, we should then obtain 
the theoretic least section from a frictionless horizontal surface of — half 
the area of the opening. And that such a form would be equally effec- 
tive with the re-entering tube of Mr. Froude, in giving the current at the 
edge of the aperture its horizontal direction of least resistance accompanied 
by the greatest liquid pressure. 
