WATER. 



AH kinds of machines, where the water cannot defceiid 

 thro\igh a given fpace, unlefs the wlieel moves therewith, 

 are to be confidered as of the fame nature with overfliot- 

 wheels, and equal in power and effeft to an overlhot -wheel, 

 in which the perpendicular height that the water defcends 

 from is the fame. All thofe machines that receive the im- 

 pulfe or fliock of the water, whether in an horizontal, per- 

 pendicular, or oblique direftion, are to be confidered of the 

 fame nature as underfhot-wheels. Therefore, in a wheel 

 which the water Itrikes at a certain point below the fur- 

 face of the water in the mill-dam, and after that de- 

 fcends in the arc of a circl?, preffing by its gravity upon the 

 floats of the wheel, the power will be equal to the effedt of 

 an underfliot-wheel, whofe fall is equal to the difference of 

 level, between the furfece of the refervoir and the point where 

 it ftrikes the wheel, added to that of an over/hot, whofe 

 height is equal to the difference of level between the point 

 where it ftrikes the wheel and the level of the tail-water. 



It is here fuppofed that the wheel receives the fhock of the 

 water at right angles to its radii, and that the velocity of its 

 circumference is properly adapted to receive the utmoft ad- 

 vantage of both thefe powers ; otherwife a redudlion muft 

 be made on tliat account. 



Mr. Oftel, an experienced engineer, informs us, that the 

 velocity of the water-wheel's circumference fhould always be 

 between three and four fcet^frfecoud ; but he has not been 

 able to determine which of thefe two velocities is the beft, 

 except in cafes where a wheel is fubjeft to be flooded by 

 tail-water; and in that cafe four feet per fecond is beft. 

 Mr. Smeaton advifed 3^ feet. 



On overfljot Water-lVheels — An overfhot-wheel is fimply 

 a circular ring of open buckets, fo difpofed round the cir- 

 cumference of a vertical wheel, as to receive the water from 

 a fpout placed over the wheel in fuch a manner, that the 

 buckets on one fide of the wheel (hall be always loaded with 

 water, whilft the other fide is empty : in confequence, the 

 loaded fide will caufe it to defcend ; and by this motion the 

 water runs out of the lower buckets, while the empty 

 buckets of the rifing fide of the wheel, in their turn come 

 under the fpout, and are filled with water. 



A machine fo fimple does not appear to prefent any diffi- 

 culties in its execution, which fliould require any application 

 of theoretic reafoning to remove them ; but in reality it is 

 a matter of fome delicacy to conftrudt a wheel in fuch a man- 

 ner as to obtain the greateft effeft from a given fall of water. 



It is probable, that the earlieft overfliot water-wheels con- 

 fifted of a number of wooden boxes or bowls, faftened on 

 the circumference of tlie wheel ; but thefe would foon give 

 place to a better mode cf conftruftion, in which the cir- 

 cumference of the wheel being furrounded by a circular 

 ring at each fide, the fpace between them was divided into 

 feparate buckets by partition-boards. Thefe partitions 

 did not point to the centre of the wheel in the direc- 

 tion of radii, but were inclined thereto nearly in an angle 

 of forty-five degrees. By this means, the water which 

 iffued from the fpout of the trough above, nearly in an 

 horizontal direftion, as a tangent to the wheel, would run 

 into the buckets, and fill them as they arrived in fucceftion 

 at the top or higheft point of the wheel ; but as the 

 buckets changed their pofition by the dcfcending-motion 

 of one fide of the wheel, they would become inclined, and 

 the water contained in the buckets would begin to run 

 over the edges of the partitions between th« buckets, and 

 by the time the bucket arrived at the bottom point of the 

 wheel, the whole of the water would be run o\it and leave 

 the bucket empty, and they would remain empty whilft 

 they afcendcd on the oppofite fide of the wheel. By this 



means, a conftant preponderance of one fide of the wheel 

 would be kept up by the water faUing into the buckets at 

 the top of the wheel, and flowing from it at the bottom. 



The points chiefly to be confidered in conftruding an 

 overfhot-wheel are, firft, that the water ftiall be applied 

 on the circumference of the wheel, fo as to be incapable 

 of defcending without communicating motion to the wheel 

 until the water has defcended to its loweft pofition, and 

 that it fhall then quit the wheel entirely ; fecondly, that 

 the utmoft height of fall fliall be attained and ufefully em- 

 ployed ; and thirdly, that the load or refiftance to the 

 motion of the wheel fhall be fo adapted and proportioned 

 to the weight of water which is applied in the defcending- 

 buckets of the wheels, that the wheel will move flowly ; 

 becaufe we have before ftiewn, that whatever velocity the 

 wheel moves with, fo much velocity the water muft retain 

 when it quits the wheel, and will thus carry away fome 

 power with it. 



We (hall now proceed to confider all the particulars 

 which contribute to the attainment of thefe objefts, taking 

 Mr. Smeaton for our guide, afid only adding fuch obftr- 

 vations as appear neceffary to render his maxims more 

 clear. 



I. On the maximum EfftS which can be obtained from a 

 Fall of Water by Means of an uverJIiot-Wheel. — The effeftive 

 power of the fall of water muft be reckoned upon the 

 whole defccnt, becaufe it muft be raifed that height, in 

 order to be in a condition to produce the fame effeft a 

 fecond time. The ratio between the powers of the falling 

 water fo eftimated, and the mechanical effefts produced 

 by the wheel at the maximum, deduced from the mean 

 of feveral of Mr. Smeaton's experiments, is as 3 to 2 

 nearly. We have before, in our obfervations upon the 

 effefts of underftiot-wheels, (hewn that the general ratio of 

 the power to the effeft, when greateft, was 3:1. The 

 effeft, therefore, produced by an overfhot-wheel, under the 

 fame circumftances of quantity and fall of water, is at a 

 medium, double that produced by an underfliot. From 

 this, it appears that non-elaftic bodies, when afting by their 

 impulfe or coUifion, communicate only a part of their ori- 

 ginal power ; the other part being fpent in changing their 

 figure in confequence of the ftroke. 



The ratio of the power to the effeft, computed upon the 

 height of the wheel only, was, at a maximum, as 10 : 8, 

 or as 5 : 4 nearly, becaufe Mr. Smeaton made the wheel of 

 a lefs height than the fall of water, in order to allow fome 

 run or defcent of the water through the fpout or trough, 

 which conducted it into the buckets of the wheel. We 

 find the ratio, between the power and effeft, to continue 

 the fame, in cafes where the conftruAions are fimilar; hence 

 we muft infer, that the effefts, as well as the powers, are as 

 the quantities of water and perpendicular heights multiplied 

 together refpedlively. 



II. On the mofl proper Height of the Wheel, in Proportion 

 to the ivhole Defcent. — The preceding obfervation (hews, that 

 the effeft which can be obtained from the fame quantity of 

 water, defcending through the fame perpendicular fpace, is 

 double when it is made to aft by its gravity upon an over- 

 fhot-wheel, to what could be obtained from it when made 

 to aft by its impulfe upon an underfhot-wheel. 



Hence it follows, that the higher the wheel is, in propor- 

 tion to the whole defcent, the greater will be the effeft ; 

 becaufe an overfhot-wheel depends lefs upon the impulfe of 

 the water when it firft ftrikes the wheel, and more upon the 

 gravity of the water in the buckets. The water which is con- 

 veyed into the buckets can produce very little effeft by its 

 impulfe, even if its velocity be great j both on account of 

 M 2 the 



