192 Dre. BARKER’s MILL 
the gravity of the water in the tube, = 125ar, which ta- 
ken from the impelling force, leaves 62,5(ah-+r)—125ar= 
62,5a x h—r (taking r=+h)= 41 3 ah Ib. avoirdupois= 
the real moving force, at the diftance of the centres of the 
apertures from the centre of motion. And, by a like fub- 
ftitution, the velocity 4V¥h+r becomes 4 /ith=4,62Vhb 
feet per fecond, QE F. 
Area of the apertures. 
If A =the area'of a fection of the race, perpendicular 
to the direGtion of its motion; V= its velocity per fe- 
cond, both in feet; aand has before; then it will be, AV = 
6144 
8avh a -cubic feet = the quantity of water emitted 
i AV 
per fecond; hence, a= —-- the area proper for one 
8.924Vh 
of the apertures. 
Scholium. ° 
Were the apertures quiefeent, their area fhould be en- 
larged inthe proportion cf ¥ hto v1 +h, or of 1 toy 14 
to difcharge the fame quantity; but then the efluent velo- 
city would be diminifhed in the fame ratio; wherefore, 
awah — 41° ah, with the fame velocity, 4,62Vh as above, 
will be alfo very nearly the true moving force ofa wellcon- 
firucted underfhot wheel (J. Smeaton, &c.) Wherefore 
may be. confidered, in effect, nearly, if not exadlly tanta- 
mount, when they have the fame quantity and fall of wa- 
ter; the beft overfhot being nearly double to either. 
From the preceding calculus arededuced the following 
Eajy 
