Brlggs.] oi4: [Nov. 3, 



form pressure); that the orifice is a circular hole in a thin plate — the flat 

 bottom plate of the vessel— and that the efTect of gravil}- on the stream 

 after emergence be neglected, as well as tlie atmospheric resistance and the 

 accelei'ation due to the column of discharge, in the production of a vacuum 

 upon the sectional area ; and the following sketch (Fig. 4) gives a general 

 ideal view of the vena contracta under these suppositions. 



„ "Weisbach* has observed that the ac- 



A^. _.D J, 



T'lmwiHMii ''.. y i/MM:,„m,!m , tual diamctcr = d of the vein of emer- 



\ / p gencefroma thin plate, is about 0.8 D; 



S W - *' ^'^"^ at the point B, which will be found 



from one-fourth to one-half the diameter (= D) from the plate ; and 

 this is accompanied with an efflux, as measured by the quantity of water 

 discharged, of = 0.97v, where v= the velocity of flow = i/2^hT K^ow it 

 is an obvious conclusion that at any point on the surface of the tend con- 

 tracta between A, the edges of the plate, and B, the point of mininmm 

 section, a particle of water must be in such equilibrium of pressure as to 

 establish its direction of flow, or in other words its curved path; when it 

 becomes apparent that some momentum must have been imparted to such 

 a particle, to induce it to follow in its line of trajectory, instead of follow- 

 ing the direction due to gravity, or to the application of the pressure nor- 

 mal to the head, or column of water above it. An attachment to the orifice 

 can be constructed which will exhibit this phenomenon, or rather provide 

 for its occurrence as a matter of necessity, as follows : Let there be an 

 opening in a thin plate as before (Fig. 5), and let this opening be guarded 

 or protected by a disc (Z) of the same diameter, = D, let this disc be placed 

 so that its edges (C C) shall be one-eighth the diameter = ^ D (C A) re- 

 moved from the hole. On these suppositious, if the diameter of the section 

 of least area, = d, be taken at 0.707 D, then the area of the peripheral 

 opening (at C A) will be equal to the area on the plane of (B). The line 

 of eftluent stream (A B) may be imagined to be a quadrant of a circle, 

 which will then have of coui-se, a radius, = 0.147 D. Now let the face of 



g. ^ D__ the disc Z be 



"e Tg" made a conoid, 



■ I SO that the areas 



""" I^ic 5 of the surfaces 



^ _p ^ of the conical 



^ X, — ^ frustra a b c d e 



shall be equal, or in other words, so that all the sections normal to the 

 curve A B shall be equal. 



[The co-ordinates for this curve of the face of the conoid Z, in terms of 

 X and y, where x is supposed to have its origin at point of the prolongation 

 of the line CA on the line B ; are given by the equation : 



-^/[r2 4- n2 ± /(r« + n^)^ — 4 n^x (2r — x)] — 4(r— x)*{r -f x) = 

 y= 2(2r — X) 



•Welsbach's Mechanics, 



