WATER. 



motion of the wheel, but that the weight by defcending 

 fliould turn the wheel. He applied fo much weight as would 

 make the wheel turn, and make its floats move with the ve- 

 locity which he defired or expefted the effluent water to 

 have ; and this weight he adjufted until he found, by re- 

 peated trials, that the wheel moved juft at the fame rate, 

 whether the water was fuffered to flow and fl:rike its floats, or 

 whether the water was fl;opped, which proved that the floats 

 of the wheel moved with precifely the fame velocity as the 

 effluent water ; then by meafuring the circumference of the 

 wheel, and counting the number of turns it made in a mi- 

 nute, he obtained the meafure of the velocity. 



From the velocity of the water at the inftant that it 

 ftrikes the wheel, the height of head produftive of fuch 

 velocity can be deduced from acknowledged and experi- 

 mented principles of hydroftatics ; fo that by multiplying 

 the quantity or weight of water really expended in a given 

 time by the height of a head fo obtained, which muft be 

 confidered as the effeftive height from which that weight of 

 water had defcended in that given time, we fhall have a pro- 

 duct equal to the original power of the water, and clear of 

 all uncertainty that would arife from the friftion of the water 

 in pafling fmall apertures, and from all doubts arifing from 

 the different meafure of fpouting waters, affigned by dif- 

 ferent authors. 



On the other hand, the fum of the weights raifed by the 

 aftion of this water, and of the weight required to over- 

 come the friftion and refiftance of the machine, multiplied 

 by the height to which the weight can be raifed in the time 

 given, the produft will be equal to the effeft of that 

 power ; and the proportion of the two produAs will be the 

 proportion of the power to the effeft : fo that by loading 

 the wheel with different weights fucceflively, we fhall be 

 able to determine at what particular load and velocity of the 

 wheel the effeft is a maximum. 



From experiments condufted in this manner, Mr. Smea- 

 ton fettled the following maxims : 



Maxim I . That the virtual or effeftive head of water, and 

 confequently its effluent velocity being the fame, the mechani- 

 cal effeft produced by a wheel aftuated by this water will 

 be nearly in proportion to the quantity of water expended. 



Note. The virtual or effeftive head of any water which is 

 moving with a certain velocity, is that height from which a 

 heavy body muft fall in order to acquire the fame velocity. 



The height of the virtual head, therefore, may be eafily 

 determined from the velocity of the water ; for the heights 

 are as the fquare of the velocities ; and the velocities, con- 

 fequently, as the fquare roots of the heights. Mr. Smea- 

 ton obferved the velocity of the effluent water in all his ex- 

 periments, and thence calculated the virtual head ; he ftates 

 that the virtual head bears no proportion to the real head or 

 depth of water ; but that when either the aperture is 

 greater, or when the velocity of the water iffuing therefrom 

 lefs, they approach nearer to a coincidence ; andconfequently, 

 in the large openings of mills and fluices, where great quan- 

 tities of water are difcharged from moderate heads, the 

 aftual head of water, and the virtual head, as determined by 

 theory from the velocity, will nearly agree. 



For example of the application of his firft maxim. Sup- 

 pofe a miU driven by a fall of water, whofe virtual head is 

 5 feet, and which difcharged 550 cubic feet of wzler per 

 minute ; and that it is capable of grinding four bufhels of 

 wheat in an hour. Now another mill, having the fame vir- 

 tual head, but which difcharges 1100 cubic feet of water 

 per minute, will grind eight bufliels of corn in an hour. 



Maxim 2. That the expence of water being the fame, the 

 effeft produced by an underihot wheel will be nearly in pro- 



portion to the height of the virtual or effeftive head. Thi» 

 is proved in the preceding example. 



Maxim 3. That the quantity of water expended being the 

 fame, the effeft will be nearly as the fquare of the velocity 

 of the V ater ; that is, if a mill driven by a certain quantity , 

 of water, moving with the velocity of j 8 feet per fecond, ! 

 is capable of grinding 4 bufhels of com in an hour, another 1 

 mill, driven by the fame quantity of water, but moving 

 with the velocity of 22^ ieet per fecond, will grind nearly \ 

 7 bufhels of corn in an hour ; becaufe the fquare of 18 is : 

 324, and the fquare of 22^ is 5065. Now fay, as 324 I 

 is to 4 bufhels, fo is 500:5 to 6^ bufhels ; that is, as 4 , 

 to 6^. 



Maxim 4. The aperture through which the water iflues 

 being the fame, the effett will be nearly as the cube of the 

 velocity of the water iffuing ; that is, if a mill driven by 

 water rufhing through a certain aperture with the velocity 

 of 18 feet per fecond will grind 4 bufhels of corn in an 

 hour, another mill, driven by water moving through the 

 fame aperture, but with the velocity of 22^ feet per fecond, 

 will grind 51 bufhels ; for the cube of 18 is 5832, and the 

 cube of 22^ is 11390J; then, as 5832 is to 4, fo is 

 ii39o|-to 7f.^ 



Maxim 5. The proportions between the power of the water 

 expended, and the effeft produced by the wheel, was 3 to I. 

 Upon comparing feveral experiments, Mr. Smeaton fixed the 

 proportions between them for large works ; that is, if 

 the weight of the water which is expended in any given 

 time be multiplied by the height of the fall, and if the 

 weight raifed be alfo multiplied by the height through 

 which it is raifed, the firfl of thefe two produfts will be 

 three times that of the fecond. 



Maxim 6. The beft general proportions of velocities 

 between the water and the floats of the wheels will be 

 that of 5 to 2 ; for inftance, if the water when it ftrikes 

 the wheel moves with a velocity of eighteen feet per 

 fecond, the wheel muft be fo loaded that its float-boards 

 will move with a velocity of 7.2 feet per fecond, and the 

 wheel will then derive the greateft power from the water, 

 becaufe as 5 to 18, fo is 2 to 7.2. 



Maxim 7. There is no certain ratio between the load 

 that the wheel will carry when producing its maximum of ef- 

 feft, and the load that will totally ftop it ; but it approaches 

 neareft to the ratio of 4 to 3, whenever the power exerted 

 by the wheel is greateft, whether it arifes from an in- 

 creafe of the velocity, or from an increafed quantity of 

 water ; and this proportion feems to be the raoft applicable 

 to large works. But when we know the effeft a wheel 

 ought to produce, and the velocity it ought to move with 

 whilft producing that effeft, the exaft knowledge of the 

 greateft load it will bear is of very httle confequence in 

 praftice. 



Maxim 8. The load that the wheel ought to have, in order 

 to work to the moft advantage, can be always affigned thus : 

 afcertain the power of the whole body of water, by multiply- 

 ing the weight of the water expended in a minute by the height 

 of the fall, take one-third of the produft, and it gives the 

 effeft of power which the wheel ought to produce : to find 

 the load, we muft divide this produft by the velocity which 

 the wheel fhould have, and that, as we have before fettled, 

 fhould be two-fifths of the velocity with which the water 

 moves when it ftrikes the wheel. 



The wheel muft not be placed in an open river to be ac- 

 tuated by the natural current, in wliich cafe, after it has 

 communicated its impulfe to the float, it has room on all 

 fides to efcape : this is the fuppofititious cafe on which moft 

 mathematicians have proceeded ; but in all thefe experi- 

 1 1 ments. 



