WATER. 



In thefe experiments, the motion of the water-wheel 



■ , being exaftly proportioned to the quantity of water ex- 



' pended, the load upon the wheel muft have been equal when 



' it moved quick or flow, that is to fay, the buckets mull 



have been equally filled when the wheel moved at its ordi- 



'nary motion, or at half that motion. 



' The efFedl, therefore, of letting more water on a wheel 

 Iwhen the reiiilance continues the fame, is not to lodge a 

 , greater quantity in each of the buckets, but to fupply the 

 I fame quantity to each bucket when the wheel is in a 

 greater motion. 



The greateft velocity that the circumference of an over- 

 ifliot wheel can acquire, depends jointly upon the diameter 

 lor height of the wheel, and the velocity of falling bodies ; 

 I for it is plain, that the velocity of the circumference can 

 I never be greater, than to defcribe a femicircumference, in 

 ithe time that a body let fall from the top of the wheel 

 would defcend through its diameter, nor indeed quite fo 

 ■great ; as a body defcending through the fame perpendicular 

 ifpace cannot perform its courfe in fo fmall a time, when 

 'palling through a femicircle, as would be done in a pcr- 

 ipendicular line. Thus, if a wheel is fixteen feet one 

 inch diameter, a body will fall through the line of its dia- 

 |meter in one fecond : this wheel, therefore, can never arrive 

 ;at a velocity equal to the making one turn in two feconds. 

 An overlhot wheel can never come near this velocity, for 

 when it acquires a certain fpeed the greateft part of the 

 iwater is prevented from entering the buckets ; and the reft, 

 iat a certain point of its defcent, is thrown out again by the 

 Icentrifugal force. The velocity, when this aftion will be- 

 Igin to take place, depends in a great degree upon tlie form 

 ■of the buckets as well as other circumilances ; fo that the 

 ytmoit velocity that an overftiot wheel may be capable of is 

 not to be determined generally ; and indeed the knowledge 

 of it is not at all neceftary in practice, becaufe a w heel, in 

 fuch cafe, would be incapable of producing any mechanical 

 leffeft. 



V. On the proper Load for an overjhot Wheel, in ordir that It 



\may produce a maximum Effell The maximum load or re- 



fiftance for an overftiot wlieel, is that which will reduce the 

 circumference of the wheel to its proper velocity, of three or 

 three and a half feet per fecond ; and this will be known, by 

 dividing the effeft it ouglit to produce in a given time, by 

 the fpace intended to be defcribed by the circumference of 

 Ithe wheel in the fame lime ; the quotient v/ill be the refiftance 

 to be overcome at the circumference of the wheel, and is 

 equal to the load required, the friftion and refiftance of the 

 jmachinery included. 



I VI. On the grealejl Load that an overjhot Wheel can overcome. 

 \ — The greateft load an overftiot wheel can overcome depends 

 :',ipon the magnitude of the buckets; and the refiftance 

 > which will ftop the wheel, muft be equal to the cifort of 

 lUU the buckets in one femicircumference, when quite filled 

 jwith water. 



; The ftrufture of the buckets being given, the quantity 

 |of this effort may be affigned, but is not of much import- 

 itance in praftice, as in this cafe alfo, the wheel lofes its 

 I power ; for though the water makes the utmoft exertion of 

 gravity upon the wheel, yet, being prevented by a counter- 

 balance from moving at all, it is not capable of producing 

 any mechanical eff^eft, according to our definition. An 

 overftiot wheel, generally ceafes to be ufeful before it is 

 loaded to that pitch, for when it meets with fuch a refift- 

 ance as to diminifti its velocity to a certain degree, its mo- 

 tion becomes irregular ; yet this never happens until the ve- 

 locity of the circumference is reduced to lefs than two feet 

 per fecond, where the refiftance is equable, as appears not 



only from the preceding fpecimen, but from experiments 

 on larger wheels. 



VII. Conjlrultion of the Pentrough for fupplying the Water to 

 ovcrjljot Wheels. — We have hitlitrto Ipoken of the ftream of 

 water, as if it iftued from a fpout nearly in an horizontal direc- 

 tion, or with only fo much inclination as will make the line of 

 the ftream correfpond with the direftion of the oblique part of 

 the bucket -board. This is the ancient, and ftiU the common 

 way ; Mr. Smeaton's, which is a much better, is ftiewn in 

 Jig. 2. Plate I. Water-wheels. G reprefents the pentrough 

 through which the water flows, and F F ftrong crofs-beams on 

 which it is fupported ; the wheel is fituated very clofe beneath 

 the bottom of the trough, as the figure fliews. E E are two 

 arms of the wheel, which are put together, as ftiewn in_fg. 7. 

 D B is the wooden rim of the wheel ; the narrow circle beyond 

 this is the feflion of the fole planking, and on the outfide of 

 this the bucket-boards are fixed as the figure ftiews ; one of 

 the bottom boards, i, of the trough at the end is inclined, and 

 an opening is left between that end and the other boards of 

 the bottom, to let the water pafs through ; this opening is 

 clofed by a fliding ftiuttle, e, which is fitted to the bottom 

 of the trough, and can be moved backwards and forwards 

 by a rod, d, and lever, e, which is fixed into a ftrong axisy"; 

 this axis has a long lever on the end, which, being moved 

 by the miller, draws the ftiuttle along the bottom of the 

 trough, and increafes or diminiflies the aperture through 

 which the water iffues. The extreme edge of the ftiuttle is 

 cut inchned, to make it correfpond with the inclined part l>, 

 and by this means it opens a parallel paflage for the water 

 to run through, and this caufes the water to be delivered in 

 a regular and even ftieet ; and to contribute to this the edges 

 of the aperture where the water quits it, are rendered fliarp 

 by iron plates ; the ftiuttle is made tight where it lies upon 

 the bottom of the trough by leather, fo as to avoid any 

 leakage when the fliuttle is clofed. When the wheel is of 

 confiderable breadth, the weight of the water might bend 

 down the middle of the trough until it touched the wheel ; 

 to prevent this, a ftrong beam, O, is placed acrofs the trough, 

 and the trough is fufpended from this by iron bolts winch 

 pafs through grooves in the fliuttle, fo that they do not in- 

 terfere with the motion of the ftiuttle. 



Fig. 3. of the fame plate is an overfliot wheel, for which 

 Mr. Nouaille took a patent in 1813 ; he recommends that 

 the water-wheel be made the full heiglit of the fall of water, 

 and tdat the water be applied upon the wheel at 53 degrees 

 from, the vertex. The pentrough is made nearly on the 

 fame plan as Mr. Smeaton's. O R is the trough, hg the 

 end inclined in the direction in which the vi'ater is intended 

 to be direfled, f the fliuttle, fliding horizontally on the 

 bottom of the trough, cde the lever for drawing the fliut- 

 tle, to which motion is given by a regulating fcrew a and 

 nut h. 



Fig. 9. Plate II. Water-ivheels, is the method of laying on 

 water, which has for feveral years been in common ufe in York- 

 fliire and the north of England. In this the water is not ap- 

 plied quite at the top of the wheel, but nearly in the fame 

 pofition as the laft defcribed ; but the advantages of this wheel 

 over all others is, that the water can be delivered at a greater 

 or lefs height, according to the height at which the water 

 ftands in the trough ; but in all the preceding methods if the 

 water is fubjeft to variations of height, as all rivers are, then 

 the wheel muft be diminillicd, fo that in the loweft ftate of the 

 water it will ftand a fufficient depth above the orifice in the 

 bottom of the trough to ifl"ue with a velocity rather greater 

 than the motion of the wheel. In this cafe, when the water 

 tii'cs to its ufual height, or above it, the increafe of fall thua 

 obtained is very Ikile advantage to the wheel ; the improved 



wheel 



