On the Velocity of Water Wheels. aj$ 



THERE are many cafes in which it is of importance to 

 I> n ( > w the proportion of power neceflary to give different degrees 

 of velocity to a mill *. But as the conduction of mills, and 

 thepurpofes they ferve, are various, it is perhaps impofiible to. 

 find any law of univerfal application. Mr. Banks, in his Trea- 

 tise on Mills f, has drawn a conclufion, which he appears 

 to confider as invariable, namely, that " when a wheel a&s 

 by gravity, its velocity will be as the cube root of the quan- 

 tity of water it receive!*;" 



But if we fuppofe a wheel railing water, by means of cranks 

 and pumps, on Mr. Banks's principle, it might eafily, I 

 think,, be demonftrated, that, by reducing the velocity of -the 

 wheel to a certain degree, the wheel would raife more water 

 than would be neceflary to move it at that velocity; a thing 

 evidently impofiible. 



Tn this view, it would feem there is no actual cafe in which 

 Mr. Banks's conclufions will hold true. But, however they 

 may apply to other mills, the experiments which I am going 

 to mention feem to me to prove, at leaft, that they do not 

 apply to cotton mills. On the ground of thefe experiments, 

 made at different times, and with all the attention in my 

 power, {and not from any abftra6t conflderation,) have I 

 prefumed to call in queftion an authority for which I enter- 

 tain the higheft refpect. 



In January 1796 I meafurcd the quantity of water the old 

 Rothefay cotton mill required, ift, when going at its common 

 velocity; and, adlv, when going at half that velocity. The 

 refult was, that the laft required jufi: half the quantity of 

 water which the firft did. It is to be obferved, that in thefe 

 experiments the quantities of water were calculated from the 

 heads of wafer and apertures of the lluices. 



From thefe experiments I inferred, " that the quantity of 

 water neceflary to be employed in giving different degrees 

 of velocity to a cotton mill, muft'be nearly as that ve- 

 locity." 



I was fatisfied with this experiment, and the inference I 

 <lrew from it, till fome gentlemen, well acquainted with the 

 theory and practice of mechanics, exprefled their doubts on 

 the fubject. I had then recourfe to another experiment, 

 which I confidered as lefs liable to error than the former. 



The water which drives the old cotton-mill falls, a little 

 below it, into a perpendicular-fided pond, which ferves as a 

 dam for a corn-mill. To afcertain, therefore, the propor*. 



» It was a fc*rcity of wattr for the Rothefay mills which directed my 

 attention particularly tq this iubju't. 



t tiej Buiks on Mills, p-i7, iS. 144, 145, 146. 



S 4 tionaj 



