VOL. LI.] PHILOSOPHICAL TRANSACTIONS. 345 



minute, viz. 264.7 lb. produces 481 for the power remaining in the water after 

 it has passed the wheel : this being therefore deducted from the original power 

 3970, leaves 3489, which is that part of the power which is spent in producing 

 the effect 1266 ; and consequently the part of the power spent in producing the 

 effect, is to the greatest effect producible by it, as 3489 • 1266 : : 10 : 3.62, or 

 as 1 1 to 4. 



The velocity of the water striking the wheel has been determined to be equal 

 to 86 circumferences of the wheel per minute, and the velocity of the wheel at 

 the maximum to be 30 ; the velocity of the water will therefore be to that of the 

 wheel, as 86 to 30, or as 10 to 3.5, or as 20 to 7. 



The load at the maximum has been shown to be equal to 9 lb. 6 oz. and that 

 the wheel ceased moving with 12 lb. in the scale: to which if the weight of the 

 scale be added, viz. 10 ounces,* the proportion will be nearly as 3 to 4 between 

 the load at the maximum and that by which the wheel is stopped. 



It is somewhat remarkable, that though the velocity of the wheel, in rela- 

 tion to the water, turns out greater than 4- of the velocity of the water, yet the 

 impulse of the water in the case of a maximum is more than double of what is 

 assigned by theory ; that is, instead of f of the column, it is nearly equal to 

 the whole column. 



It must be remembered therefore, that in the present case, the wheel was 

 not placed in an open river, where the natural current, after it has communi- 

 cated its impulse to the float, has room on all sides to escape, as the theory 

 supposes ; but in a conduit or race to which the float being adapted, the water 

 cannot otherwise escape than by moving along with the wheel. It is observable, 

 that a wheel working in this manner, as soon as the water meets the float, re- 

 ceiving a sudden check, it rises up against the float, like a wave against a fixed 

 object ; insomuch that when the sheet of water is not a quarter of an inch thick 

 before it meets the float, yet this sheet will act on the whole surface of a float, 

 whose height is 3 inches ; and consequently were the float no higher than the 

 thickness of the sheet of water, as the theory also supposes, a great part of 

 the force would have been lost, by the water's dashing over the float.-}- 



* The resistance of the air in this case ceases, and the friction is not added, as 12 lb. in the scale 

 was sufficient to stop the wheel after it had been in full motion ; and therefore somewhat more than 

 a counterbalance to the impulse of the water. — Oiig. 



f Since the above was written, I find that Professor Euler, in the Berlin Acts for the year 1748, 

 in araemoire intitled, Maximes pour arranger le plus avantageusement les machines destinees aelever 

 de I'eau par le moyen de pompes, page 192. § 9. has the following passage; which seems to be the 

 more remarkable, as I don't find he has given any demonstration of the principle therein contained 



either from theory or experiment ; or has made any use of it in his calculations on this subject. 



" Cependant dans ce cas puisque I'eau est reflechie, & qu'elle dtcoule sur les aubes vers les cotes, 

 elle y exerce encore une force particuliere, dont I'etFet de I'impulsioii sera augmente j & experience 

 VOL. XI. Y Y 



