GRIST AND SAW-MILLS. 355 



velocities in filling the fecond branch will be no ntiorc than half 

 the fum of the velocities on which we have been accuftomcd to 

 count ; from whence it follows that the branch FG will require 

 twice the time to be filled as was formerly imagined. It follows 

 alfo, that becaufe the complement MIKB, is but one-third of 

 the parallelogram AIMB ; therefore the branch BF will be three 

 times as long in filling as it would be with the uniform velocity 

 exprefTed by MB. And laftly it follows, that the fum of the 

 velocities of water afcending from Q^to q, inftead of being ex- 

 prefTed by the area of the mixed quadrilateral PO op, ought to 

 be exprefTed by the area of the quadrilateral KL Ik, which may 

 be found in the following manner. 



Let AB= (2, »B=^, NB=r and ri^—c. Now the uniform 

 velocities being as the ordinates, wc fliall have AI=V'^, nk = 



\/b, NK=A/r, and let 3— r= <r; but -Vb— -Vr=the feg- 



3 3 



ment ;; NK^, and c»/a — the parallelogram LNn/j confcquently 



c-^ a '^ b .s/r= the fpace LK/t/, or the fum of all the 



o . . 3 

 retarded velocities during the afcent from Q^to q. 



To give an example in numbers, wc will fuppofe a= 30, b = 24, 

 r— 20 and ^=4, then 8v'a=43.82j 8v/^=39.i9, and S-Zr^ 



35,78; hence 4X43-8i — ^^^Xsg.ip— ^^1^2x35.78= 175. 



3 3 



28. — 627.04 — 477-07 = *5-3i > but by the laws of accelerated 

 motion, the fpaces defcribed are as the fquares of the times of 

 defcription ; wherefore 32 : i"« : : 25.31 : 0.79 and ^^0.79 =: 

 0.89" = the tinie required for the water to afcend from C^to 5' 

 = 4 feet. 



DESCRIPTION OF the STEAM-ENGINE. Fig. 3. 



A. The receiver, which maybe made either of wood or Iron. 

 BBBBB. Wooden or caft-iron pipes for conveying the water 

 to the receiver and from thence to the penftock. 



C. The penflock or ciftern. 



D. The water-wheel. 



T A 2 E. The 



