352 CALCULATIONS for 



lieight of the column of water which propels this wheel. Now 

 by art. 7. we have Saq^bzr: the quantity of water which 

 Hows through the gateway in one fecond, z= 8X6.128X 1.5X 

 1.658 n 121.92 gallons. Again, haw zz 2. 75X 1.5X62.5 n 

 257.8 pounds, which is equal to the weight of the column 

 prefling againil the aperture ; alfo SVh = 13.264 feet, the 

 uniform velocity of the water every fecond as it iffues through 

 the gateway. 



In order to find the force of impacft on the wheel, we muft, 

 in the firft place determine (what may be called) the initial weight 

 of the water, or that with which it may be fuppofed to begin 

 to prefs at its furface in the penftock, viz. by dividing the mo- 

 mentum by the uniform velocity; but haw = 257.8 is the mo- 

 mentum at the aperture or gateway, and 13.264= the uniform 



velocity: therefore — ^ — = 19.406 lbs. = W, the initial 

 13.264 



wei?ht required = -r^= ~ s/l' ; confequently SW-ZA will 



exprcfs the force of imparl: fought, b being now = 13.75 and 

 v'Z> = 3.708; hence 8Wv'/j = 8x 19.406x3.708 = 575.66pounds 

 for the conftant impelling force on the ladle-board ; but S7S'^^ 



= haze, and a= ^^ — = — ■^^■^' ^ = o.67partsofafquare 



bio 13-75X62.5 



foot. To prove the truth of the above method for finding the 

 force of imparl, we need only try whether %aqVh (where /j = 

 1 2.75 and a = 0.67) will produce the fame number of gallons as 

 that before found, viz, 121.9 in one fecond. In the prefent 

 cafe 8rtyv//-' = 8Xo.67X6. 128X3. 708 = 121.8 being nearly the 

 fame as found above, and is a fufficient proof that the force of 

 impaft where the water impinges on the wheel is rightly dettr- 

 mined. 



KEYGER's SAW-MILL. 



This faw-mill is over-fliot, the wheel 12 feet diameter, the 

 penflock is 6 feet in depth by 2 feet wide, and when I foAv it at 

 work, there were only 4 feet and i-4th inch of water in the 

 ciftern, although the faw moved at the rate of 120 llrokes in a 

 i5ninute, whilft it paffed through a piece of oak at lead 12 inches 



<Jeep, 



