63 
The figure (4) shows approximately the arrangement of 
such stream. But for the mathematical difficulty of in- 
tegrating the equations of motion the exact form of these 
streams might be drawn. We should then be able to 
determine exactly the necks of each of these streams. 
Without complete integration, however, the integration may 
be carried far enough to show the lines bounding the 
streams are continuous curves which have for asymptotes 
on discharging vessel side lines radiating from the middle 
of the orifice at equal angles, and further that these lines all 
curve round the nearest edge of the orifice, and that the 
curvature of the streams diminishes as the distance of the 
stream from the edge increases. 
These conclusions would be definitely deducible from the 
theory of fiuid motion could the integrations be effected, but 
they are also obvious from the figure and easily verified 
experimentally by drawing smoky air through a small orifice. 
From the foregoing conclusions it follows, that if a curve 
be drawn from A to B, cutting all the streams at right 
angles, the streams will all be converging at the points 
where this line cuts them, hence the necks of the streams 
will be on the outflow side of this curve. The exact position 
of these necks is difficult to determine, but they must be 
nearly as shown in the figure by cross lines. The sum of 
the areas of these necks must be less than the areas of the 
orifice. Since, where they are not in the straight line A B, 
the breadth occupied on this line is greater than that of the 
neck. The sum of the areas of the necks may be taken as 
the effective area of the orifice, and since all the streams 
have the same velocity at the neck, and the ratio which this 
aggregate area bears to the area of the orifice put equal to 
K a coefiicient of contraction. 
If the pressure in the vessel on the out-flow side of the 
orifice is less than *527pi this is the lowest pressure possible 
at the necks, as has already been pointed out, and on 
