Briggs. } 124 [Aug. 17, 
The Flow of Water Through an Opening in a Pierced Plate. 
By Rospert BriGces. 
(Read before the American Philosophical Society, August 17, 1877.) 
At the meeting of the Society on the 3d of November, 1876, I presented 
an hypothesis of the origin of the form of the vena contracta under cer- 
tain conditions stated in the paper then offered. It was shown that on the 
assumption that the efflux occurred from the layer or strata of water under 
greatest pressure of water column, at the maximum velocity due to that 
column, the least section of the vena contracta would have half the area of 
the opening of efflux, provided the effect of frictional adhesion of the 
water to the bottom of the vessel and the effect of the internal friction or 
viscosity of the water were not considered. And it was noticed that the 
effect from these causes tended to enlarge the least section of the vein and 
increase the quantity of effluent water. 
Referring to the words of the paper: ‘“‘If however there is admitted to 
exist a certain 
ee Des ee E adhesion to the 
bottom of the 
Fes vessel or to the 
_ surface or the 
edges A A, so 
that the velocity of a particle on A B is less than that fully due to the head; 
the surface (d) would then become larger than } D, the dimension C A 
would be properly increased to give a corresponding area of efflux, and the 
conoid Z would also have such contour as would permit the uniformity of 
flow of each and every particle of the liquid at unchanged velocity, in any 
section of the vena contracta transverse to the flow. This increase of 
dimension of the cross section d, and the effect of the descending pencil in 
accelerating the flow through it, can be taken as sufficient to account for 
Weisbach’s observed value of d=0.8D, and the position of the plane of 
least section will be found at about + D below the orifice as has been before 
quoted.” 
A further illustration of this subject can be instituted by accepting the 
observed value of the least section of vena contracta, which is found to be 
0.64D in place of the hypothetical one of $ D, and by deducing the form of 
the effluent vein backwards to the strata of water under greatest 
pressure. Thus, let it be supposed that Fig. 6 represents (as in Fig. 5) 
an opening in a thin plate, guarded or 
protected by a Disc Z, of such contour 
Se YP”. \ and sc placed that a current flowing 
— _Y z= towards the opening shall obtain the 
eas a maximum velocity due to the head, and 
Fig. 6 be diverted from its horizontal to the ver- 
tical direction without change of velocity 
of any particle of the current. The contour of the vena contracta from 
