GRIST AND SAW-MILLS. 259 



bottom ; but we have fuppofed the increafed daflicity of the 

 fleam to be equal to a column of water 8.5 feet high, which 

 being added to 4 feet, the dilTerence between the two columns, 

 makes «B in this cafe = 12.5 feet. An = 8.5 feet, «N=z 4 feet, 

 and NB = 4.5 feet. By thefe meafurements the parallelogram 

 N«/L will be found = 1 13.1368, the parabola BtikB — 132.1648, 

 and the parabola BNKB=5o.9i 18 ; hence B«/(-B— BNKB = 

 N«;&K = 81.253 5 but 113.1368 — 81. 25J =31.8838 =0/L, 



and -J — — ~ = o'.99 or i°= the time required to empty the 



receiver, when filled with 4 feet of water ; and as it appears 

 that it may be filled in ©".89 or ©".9 of a fecond, it is therefore 

 evident that this machine may make 30 ftrokes in a minute, fup- 

 pofing the pipes and receiver were all of the fame diameter ; but 

 it is not neceffary that it flaould exceed 1 o ftrokes per minute, 

 and confequently the pipes which convey the water to and from 

 the receiver, need not be more than one-third part of its area, 

 and on no occafion to exceed one half. 



It has been fuppofed, in what we have faid concerning the 

 fleam-engine, that the upper part of the penflock is on the fame 

 level with the bottom of the receiver, or 20 feet above the 

 level of the water in the refervoir, and admitting the penflock to 

 be 4 feet in depth, (inflead of 22 inches, fee page 350) there will 

 be a fpace equal to 16 feet left for the diameter of the wheel j 

 but that its motion may not be interrupted by wading through 

 the water in the refervoir, we have here fuppofed the diameter 

 to be no more than 15 feet. Now, if each revolution of the 

 wheel be performed in the time this machine makes one flroke, 

 the circumference mufl move with a velocity equal to 7.854 feet 

 in each fecond of time, admitting the fleam-engine works at the 

 rate of 10 flrokes in a minute. 



Previous to determining the capacity of the receiver, it will 

 not be improper to bring into one point of view, what has al- 

 ready been fiiid on the fubjecft of Beydler's grifl-mill and Key- 

 ger's faw-mill. 



Beydler's grifl-mill with one pair of flones, where Z>= 1.77 

 and (3=0.3125. 



8<75'-v//j = 20.38 in one fecond, and Sijj/V/^ =122.28 gallons, 



/ beinof 



