itJ EffeSi on underjhot and over/hot Wheels, . *(,&■ 



per number of float-boards, each fix feet long and two deep : It is required to determine,. 

 ift,What quantity of water might be raifed by that power, during the day often hours, 

 to the height of thirty feet ? or, 2dly, VVhat number of bufiiels of wheat, or malt, might 

 be ground in the fame time ? or, 3dly, What number of men or horfes might this wheel 

 fupply the place of, in performing any other kind of work or manufadure ? 



In the firft place, to find the virtual f<tll,. multiply 9 feet by itfelf, which gives 8r, and 

 divide this by 64,2882: the quotient will be 1,26 feet. — Again, the furface of the float 

 being 6 feet by 2 feet, is 12 fquare feet; which, multiplied by the velocity 9, gives 108 = 

 the number of folid feet of water which has in cSqCl fallen from the virtual head in a fe- 

 cond. But this power will partly be confumed in producing eddies and lateral motions, 

 and partly remain uncommunicat^d in the tail watCi as it flows off. P'or which rea- 

 fons, as has already been remarked, the effe£t will only be one-third of the power. That 

 IS' to fay, one-third pare of 108, or 36 cubical feet of water will be raifed in a fecond 

 to the height of 1,26 feet. The queftion however is directed to the height of thirty feet, 

 and the quantities of water, or other weights, raifed by equal powers, are inverfely as 

 their heights : that is, 30 feet : 1,26 feet :: 36 cubical feet : 1,512 cubical feet raifed 

 30 feet in a fecond. But the hour confifts of 3600 fecondi, and the day of ten hours, 

 = 360CO, which multiplied bj 1,512 produces 54432 cubic feet, or 6437 hogflieads, 

 (reckoning the gallon at 231 folid inches) which are raifed 30 feet in the day *. 



With regard to the operation of grinding, it is allowed that about 34.20 cubic feet of 

 ■water with a fall of 10 feet will, by an overfliot wheel, grind one bufliel of wheat into 

 Iteur, and the fame force will cut five quarters of malt. But our underfhot wheel will-, 

 only do half the work. From the foregoing calculations our flream is equivalent to 13,6 

 folid feet per fecond with a fall of ten feet, or 8 1 6,5 folid feet per miimte. Therefore 

 as 3420 cubic feet : one bufliel of wheat : : 816,5 cubic feet : 0,239 of a bufhel which 

 would be ground per minute by an overfliot wheel ; or 0,1195 by our underfliot wheel.. 

 This lafl; number multiplied by 60 produces 71,7 bufliels per hour, or nearly 72 bulhels 

 or 9 quarters of wheat per day of ten hours. And by the proportion of malt to wheat 

 juft mentioned, it will follow that 360 quarters of the' former grain might be cut in the- 

 fame time. 



Animal ftrength is of fo flufluating a nature, that it is difficult to fubje£l: it to any 

 ^ftimate. Phyfical caufes muft affeft both the quantity and duration of the efforts 



• This is an outfide eftimate, and gives.no allowance for friftions and errors in tHe conftruftion of the liy- 

 draulic work. The reaft'on in Smeaton's Experiments was afforded merely by a weight and pulley, which 

 isgreailyin favour of the mill in deducing the effe£t. I find in the " Reports of the late Mr. John Smeaton 

 F. R. S.'' printed'in quarto, London 1797, the power of the water called " Hubbert's mill ftream'.' is deduced- 

 from the quantity and fall, < p. 24;.) by a rule which he does not mention, but is evidently this, for overfliot ov. 

 clofe brcaft wheels : Multiply the number of cubic feet of -water ciifc barged per minute by the fall in feet : this 

 number may be called the power. Dii/ide the ptnver byiwo, and t!je quotient may be called the effe^. AJfiimt ^ 

 any height ot pleafure in feet t divide the effeii b^ the height, and the quotient -will be the cubic, feet of'iuater 

 •vjhich a good hydraulic apparatus ivitl raife to that height per minute. 



The underfhot wheel will raife half that quantity : or in general lefs than one-fixth of the power; 



I have retained the proportion of tht Treatife on mills in the text, becaufc the ratio of the efteft to the power. 

 Kin be eafily altered at pleasure in computing, 



poffibJqi. • 



