GRIST A^D SAW-MILLS, 353 



deep, and the gateway no more than half an inch high. Hence 

 h = 4, and ^/j = 2 feet. The aperture a = 24X0.5 = 12 = 

 0.0833 parts of a fquare foot ; wherefore 8aq'//}= 8X0.083:; 

 X 6. 128X2 = 8.2 gallons which falls on the wheel in the fpace 

 of one fecond, 8a'//j= 8X0.0833X2 = 1.32 cubic feet in the 

 fame time, and 8V/}= 16 feet, the uniform velocity per fecond, 

 as the water leaves the aperture; alfo /jaw =4X0.0833X62.5 

 = 20.8 pounds for the force of impact where the water firft en- 

 ters on the wheel. When this mill is fupplied with a 6 feet head, 

 and the gate drawn up one inch, the faw makes i8o flrokes in a 

 minute through an oak log 1 8 inches deep. We have now /j = 

 6, -//?= 2.45 feet, and a = 24 inches = 0.167 parts of a fquare 

 foot. Here 8^5' Wj = 8X0.167x6.128x2.45 = 20 gallons per 

 fecond, Sa\//j:iz 8X0.167X2.45 = 3.273 cubic feet in the fame 

 time, and S'//j= the uniform velocity acquired by a fall of 6 

 feet ; alfo /jazu = 6X0.167x62.5 = 62.6 for the weight of the 

 column or force of impacft on the wheel. 



I have been the more particular in making thefe calculations 

 in order to afcertain the dimenfions of the fteam-enginc for vari- 

 ous purpofes ; on which account we muft again have recourfc 

 to the parabola, and alfo to the inverted fyphon. 



To find the retarded velocity and time of afcent of ivater into an 

 exhausted receiver, through a vertical pipe or tube, by the af- 

 fistance of the parabola. Fig. 2. 



Let CBFG be an inverted fyphon, the diameter being every 

 ■where equal, accompanied with a cock T, and the firft branch 

 AE always kept full of water : it is certain that if all the reft 

 of the fyphon be empty, and the cock be fuddenly opened, the 

 water will immediately rufh into the tube of communication VX 

 with a uniibrm velocity equal to that which a heavy body would 

 acquire by falling from A to B, and vyill be continually diminifli- 

 ed in proportion as the fecond branch is filled. 



To fliew in what order this retardation of the water dimi- 

 niflies its velocity at any point Q^of the tube GS, where it is 

 fuppofed to be afcending towards qr, we mull defcribe on the 

 hnes AB, CD as an axis with the fame parameter, two equal 

 parabolas CPH and BKI, lituated in oppoiite direftions. Com- 

 jilcte the parallelogram APvI, and draw as many lines LR as 



^ A vou 



