WATER. 



tbe compound of both. We can only meafure tlie weight 

 of any body or mafs of matter by its relation to feme other 

 weight with which we are acquainted ; hence we fay, the 

 weight is equal to fo many pounds, or fo many cubic feet of 

 water. In like manner, we meafure the velocity or intenfity 

 of the motion, by ftating the height or perpendicular dif- 

 tance from the earth, (meafured by relation to fome known 

 diftance, as a foot or a yard,) through which height the 

 weight is raifed m fome known fpace of time, as a fecond or 

 a minute. 



For inftance, 528 cubic feet of water is a known weight 

 or mafs of water : let a machine operate upon this, and raife 

 it upwards, through the fpace of one foot in the time of 

 one minute ; then 528 X I X i = 528 is the number 

 which reprefents the power which the machine exerts. Sup- 

 pofe another machine to operate on 132 cubic feet of water, 

 and raife it four feet in one minute, then ufing the fame 

 meafures to determine the quantities of weight, height, and 

 time, we fay 132 X4X 1 = 528 ; hence thefe two ma- 

 chines are equal in the power which they exert ; for in all 

 cafes the weight raifed is to be multiplied by the height to 

 which it can be raifed in a given time, and the produdl is the 

 meafure of the power expended in raifing it ; confequently, 

 all tliofe powers are equal whofe produfts made, by fuch 

 multiplication, are equal ; for example, take two powers, 

 it one can in any given time raife twice the weight to the 

 fame height, or the fame weight to twice the height, in the 

 fame time that the other power can, the firft power is 

 double the fecond ; or, if one power can raife half the 

 weight to double the height, or double the weight to half 

 the height, in the fame time that another can, thofe two 

 powers are equal : but note, all this is to be underftood 

 only in cafes of flow or equable motion of the body raifed, 

 for in quick, accelerated, or retarded motions, the vis iiier- 

 t'lii of the matter moved will make a variation. 



The machines actuated by the impulfe of flowing water 

 are, the underfhot water-wheel, horizontal wheels, and Dr. 

 Barker's m.U. It is a common exprcffion to call all wheels 

 in which tlie water runs or fhoots under the wheel, under- 

 fhot ; but in this place we (hall only fpeak of 



Underjljot IVater-IVheeh, ad'ing by the Impulfe of Jlowing 

 Water — Thefe are the moft ancient and original forms 

 of water-machines, although if they had been invented from 

 the refuk of reafoning, fuch as we have given, they would 

 have been the laft, becaufe their manner of aftioii is lefs 

 obvious ; but this was not the cafe. The lirll machines 

 were wheels placed in a river or running ftream, and pro- 

 vided with vanes or wings on the circumference, called 

 floats; the floats at the lower part of the wheel, dipped into 

 the Itream to intercept the water. When the plane of the 

 floats became perpendicular to the direftion of the current, 

 or nearly fo, they would refill or oppofe the motion of the 

 water, and the wheel would obtain motion from it in pro- 

 portion to the quantity of motion, its floats abftrafted from 

 the water of the ftream. Tlie power thus obtained would be 

 found to be only a fmall proportion of the power of the 

 ftream, becaufe the water would eaflly efoape fideways from 

 the floats, particularly if it were attempted to take away any 

 confiderable fliare of the velocity of the water, by refifting 

 or loading the wheel, fo as to make it move Howly. Hence 

 it became an obvious improvement to contract the river to 

 the exaft lize of the float-boards of the wheel, or to make 

 a clofe channel in which the wheel exattly fits. The next im- 

 provement would be to intercept the river or ftream of 

 water by a dam, orobftacle, in order to make it pen up, or 

 accumulate, till it had rifeij to the greateft height which 

 could be obtained, and to let the water out of the dam or 



refervoir into the channel or wheel-courfe, through a verti- 

 cal aperture or door, level with the bottom of the wheel- 

 courfe ; in this way, the water would be urged by the pref- 

 fure of the water in the dam, and would rufh out from the 

 aperture in a ftream or fpout, with a velocity proportioned 

 to the perpendicular preflTure, and would (Irike the float- 

 boards of the wheel fo as to urge them forwards. Such is 

 the form of the underrtiot wheels ftiU generally employed in 

 France and on the continent ; but in England they have 

 been long fuperfeded by more effeftual applications of the 

 power of the water, and it is very rarely we meet with 

 an underfhot wheel afting by the impulfe of the water. 

 They are called ground-fhot wheels, becaufe the water runs 

 or fhoots along the ground or floor of the channels in which 

 the wheels work. 



It was firft proved by Mr. Smeaton, in 1754, that 

 only a portion of the power of any fall of water could be 

 obtained by means of an underfhot wheel ; for M. Beli- 

 dor had not long before ftated the underfhot wheel as the 

 beft mode of applying a fall of water. It was one of the 

 continual occupations of Mr. Smeaton, during forty years, 

 to improve the old water-mills, by fubftituting breaft-wheels 

 for underfhot ; and the advantages were uniformly fo great, 

 that thefe mills were copied by others, until fcarcely any of 

 the original conftruftion remained. We do not mean that 

 Mr. Smeaton invented the breaft-wheel, for it is defcribed by 

 Leopold ; but he firft inveftigated its comparative ad- 

 vantages. 



It is from this cireumftance that we find, in all the mecha- 

 nical writings of foreign authors, much more mathematical 

 inveftigation relative to the underfliot water-wheels than the 

 importance of the fubjeft deferves, and we fhall difmifs it 

 more briefly. 



The excellent paper by Mr. Smeaton, in the Philofophi- 

 cal Tranfaftions for 1759, contains a numerous lift of expe- 

 riments moft judicioufly contrived by him, and executed 

 with the accuracy and attention to the moft important cir- 

 cumftances which are to be obferved in all that gentleman's 

 performances. 



Mr. Smeaton's rules were originally deduced from expe- 

 riments made on working models, which are the beft means 

 of obtaining the outlines in mechanical enquiries ; but in 

 every cafe it is neceffary to diftinguifli the circumftances in 

 which a model differs from a machine at large, otherwife a 

 model is more apt to lead from truth than towards it ; and 

 we muft not, without great caution, transfer the refults of 

 fuch experiments to large works. But we may fafely tranf- 

 fer the laws of variation, which refult from a variation of 

 circumftances, although we muft not adopt the abfolute 

 quantities of the variations themfelves. Mr. Smeaton was 

 fully aware of the limitations to which coiiclufions drawn 

 from experiments on models are fubjeft, and has made the 

 applications with his ufual fagacity. The beft ftrufture of 

 machines cannot be fully afcertaiiied but by making trials 

 witli them, when made of their proper fize. 



Mr. Smeaton's Principles for Underfoot Wheels. — In com- 

 paring the effeft produced by water-wheels with the powers 

 producing them ; or, in other words, to know what part of 

 the original power is neccffarily loft in the application, we muft 

 previoufly know how much of the power is Ipent in overcom- 

 ing the friftion of the machinery, and the refiftanco ot the 

 air ; alfo, what is the real velocity of the water at the in- 

 ftant it ftrikes the wheel ; and the real quantity of water 

 expended in a given time. 



The velocity Mr. Smeaton meafured in a moft fatisfaftory 

 manner in every experiment, by applying a cord and weight 

 to the asle of the wheel, not to wind up the weight by the 



motiou 



