WATER. 



and the readinefs of its dhTpofal, muft be a fource of great 

 wealth to the country. It fliould, of courfe, be encouraged 

 as much as pofTible, wherever it can be done with conve- 

 nience and fuccefs, in all parts of the kingdom. See FisH- 

 Pond, FoSD-Fi/heries, and SALMO'S-FiJJjeries. 



Water, Aj'ccni of, in Hydraulics. See Ascent and 

 Capillary Tubes. 



Water, High and Zow. See Flux, High, and Tide. 

 ' Water, Motion of. The theory of the motion of run- 

 ning water is one of tlie principal objefts of hydraulics, and 

 mapy eminent mathematicians have applied themfelves to 

 this fubjeft. But it were to be wifhed that their theories 

 were more confiftent with each other, and with experience. 

 The curious may confult fir Ifaac Newton's Principles, 

 lib. ii. prop. 36. with the comment. Dan. Bernouilli's 

 Hydrodynamica. Jo. Bernouilli, Hydraulica, Oper. torn. iv. 

 p. 389, feq. Dr. Jurin, in the Phil. Tranf. N°452, and in 

 Dr. Martyn's Abridg. vol. viii. p. 282, feq. S'Gravefande, 

 Phyfic. Elem. Mathemat. lib. iii. par. ii. Polenus, de Caf- 

 tellis, and others. 



Mr. Maclaurin, in his Fluxions, art. 537. feq., has illuf- 

 trated fir Ifaac Newton's doftrine on this intricate fubjeft, 

 which flill, notwithilanding the labours of all thefe eminent 

 authors, remains in a great meafure obfcure and uncertain. 

 Even the fimple cafe of the motion of running water, which 

 is when it iifues from a hole in the bottom of a vefiel kept 

 conftantly full, has never yet been determined, fo as to give 

 univerfal fatisfaftion to the learned. We fhall here mention 

 fome of the phenomena of this motion, as ftated by Dr. 

 Jurin from Poleni ; referring for other obfervations on this 

 fubjeft to Fluids, and Hydraulic Laius of Fluids. 



1. The depth of the water in the veflel, and the time of 

 flowing out being given, the meafure of the effluent water is 

 nearly in proportion to the hole. 



2. The depth of the water, and the hole being given, the 

 meafure of the effluent water is in proportion to the time. 



3. The time of flowing out, and the hole being given, 

 the meafure of the effluent water is nearly in a fubdupli- 

 cate proportion to the height of the water. 



4. The meafure of the effluent water is nearly in a ratio 

 compounded of the proportion of the hole, the proportion 

 of the time, and a fubduplicate proportion of the depth of 

 the water. 



5. The meafure of the water flowing out in a given time, 

 IS much lefs than that which is commonly afligned by ma- 

 thematical theorems. For the velocity of effluent water is 

 commonly fuppofed to be that which a heavy body would 

 acquire in -vacuo in falling from the whole height of the 

 water above the hole ; and this being fuppofed, if we call 

 the area of the hole F, the height of the water above the 

 hole A, the velocity which a heavy body acquires in faUing 

 In vacuo from that height V, and the time of falling T ; and 

 if the water flows out with this conftant velocity V, in the 

 time T, then the length of the column of water, which 

 flows out in that time, will be 2 A, and the meafure of it 

 will be 2 A F. But if we calculate from Poleni's accurate 

 experiments, we (hall find the quantity of water which flows 

 out in that time to be no more than about 4^4^ of this mea- 

 fure 2 A F. Polen. de Caftellis, art. 35. 38, 39. 42, 43. 



Poleni alfo found, that the quantity of water flowing out 

 of a veflel through a cylindrical tube far exceeded that 

 which flowed through a circular hole made in a thin lamina, 

 the tubs and hole being of equal diameter, and the height 

 of the water above both being alfo equal ; and he found it 

 to be fo when the tube was inferted, not into the bottom, 

 which others had obferved before, but into the fide of the 

 yeffel. 1 2 



6. Since the meafure of the water running out in the 

 time T, is 2 A F x \i^, the length of the column of water, 

 which runs out in that time, is 2 A x Mi-n. Therefore 

 if each of the particles of water, which are in the hole in the 

 fame fpace of time, paiTes with equal velocity, it is plain that 

 the common velocity of them all is that with which the fpaee 

 2 A X -J^i5 0- would be gone over in the time T, or the ve- 

 locity V X 4Jire* But this is the velocity with which water 

 could fpring in vacuo to near 'd of the height of the water 

 above the hole. 



7. But when tlie motion of water is turned upwards, as 

 in fountains, thefe are fecn to rife almod to the entire height 

 of the water in the ciftern. Therefore the water, or at leaft 

 fome portion of the water, fpouts from the liole with almoft 

 the whole velocity V, and certainly with a much greater ve- 

 locity than V X fj-^Tr- 



8. Hence it is evident, that the particles of water, which 

 are in the hole in the fame point of time, do not all burfl 

 out with the fame velocity, or have no common velocity ; 

 though fome mathematicians have hitherto taken the con- 

 trary to be certain. 



9. At a fmall difl;ance from the hole, the diameter of the 

 vein of water is much lefs than that of the hole. For in- 

 fl:ance, if the diameter of the hole be i, the diameter of 

 the vein of water will be -J^, or 0.84, according to fir Ifaac 

 Newton's meafure, who firll obferved this phenomenon ; 



20 20^ 

 and according to Poleni's meafure — , or --^, that is, taking 



the mean diameter O.78, nearly. 



As to the manner of accounting for thefe phenomena, we 

 have already obferved that authors are not agreed ; and 

 it would be far beyond our defign to (late their different 

 theories, we mull therefore refer to the originals above 

 quoted. 



Neither are authors agreed as to the force with which a 

 vein of water, fpouting from a round hole in the fide of a 

 veflel, prelfes upon a plane direftly oppofed to the motion 

 of the vein. Moft authors agree that the prefigure of this 

 vein, flowing uniformly, is equal to the weight of a cylin- 

 der of water, the bafis of which is the hole through which 

 the water flows, and the height of which is equal to the 

 height of the water in the veflel above the hole. The ex- 

 periments made by Mariotte, and others, feem to counte- 

 nance this opinion. But Mr. Daniel BernouilH rejefts it, 

 and ellimates this prefigure by the weight of a cylinder, the 

 diameter of which is equal to the contradled vein (accord- 

 ing to fir Ifaac Newton's obfervation above-mentioned), 

 and the height of which is equal to twice the height of the 

 water above the hole, or, more accurately, to twice the al- 

 titude correfponding to the real velocity of the fpouting 

 water ; and this prefiure is alfo equal to the force of repul- 

 fion, arifing from the rcadion of the fpouting water upon 

 the veflel. For he fays that he can demonllrate, that this 

 force of repulfion is equal to a prelTure exerted by a vein of 

 fpouting water upon a plane direftly oppofed to its motion, 

 if the whole vein of water fl;rikes perpendicularly againft the 

 plane. From whence it would follow, that the preffure or 

 force of the vein will be greater m proportion, as its con- 

 tradlion is lefs ; and this contraftion vanifliing, as it does 

 when the water fpouts through a fliort tube, and the vein 

 being at the fame time fuppofed to have the whole velocity 

 it can acquire by theory, the fpouting water will then exert 

 a preflure double to what is commonly fuppofed. But the 

 aftual velocity of the water being always fomething lefs 

 than it ought to be by theory, and the vein of water 

 being not uncommonly contrafted to almoll one half, expe- 

 riments 



