of the Motion of Fluids, Sfc. 413 



Also p'^ hyp. log. -r- = —-tt-^ . 



Hence the law of the variations of «. and p remains the same, 

 whatever be the size of the disc, if c and n be the same. Ac- 

 cording to these formulse m is less and p is greater as r is greater. 

 But it is to be observed, that the theory supposes every particle 

 of the air at the same distance from the centre of the disc, to 

 be moving with the same velocity. This will not be the case 

 if the disc be at any considerable distance from the orifice, 

 because the current, from the manner of its passage out of the 

 orifice, must, when entering upon the disc, suffer contraction in 

 the vertical sense, supposing the disc to be situated with its 

 plane horizontal : and the equation 



20= hyp. log. ^ =-a,^, 



shews that, as w will in consequence increase, the pressure di- 

 minishes. This diminution will continue up to a certain distance, 

 at which the velocity will be greatest and the pressure least, 

 and where the vena contracta of the stream may be said to be 

 situated. The distance of the vena contracta from the circum- 

 ference of the orifice, will be greater as the distance of the disc 

 from the orifice is greater. When this latter distance is .031 of an 

 inch, or any quantity less than this, and the radius of the orifice 

 is .188, experiment shews that the distance of the vena contracta 

 from the centre of the disc is .28 nearly (See Tables IV. and V, 

 in Mr. Willis's Paper, Camh. Phil. Trans. Vol. III. Part I.) 

 Past the vena contracta, the preceding tbrmulee give the law of 

 increase of density and diminution of velocity, up to the edge 

 of a di.sc the radius of which was 1.2, with accuracy, provided 

 the interval between the disc and orifice be not much less than 



