WATER. 



which wfU be exerted upon each ftoiie of the mafonry to 

 thruft it outwards. 



Depib ben'-^ili I'rtffurc on ei,th St ne, 



the Surface or on every fqii^re Fool, 

 in Feet. in 1 • utuIs. 



1 62.5 



2 125 



3 187.5 



4 250 



5 3'2-S 



6 375- 



7 437-S 



8 500 



9 56^-5 

 10 625. 



The length and width of the tank does not influence the 

 prefTure upon each itone ; becaufe, following our firft pro- 

 pofition, we are only to regard the magnitude of the plane 

 againft which the water afts, and the depth at which it is 

 fituated beneath the furface. But in all cafes when the 

 plain is not horizontal, the depth of the water will be greater 

 upon fome parts of the plane than upon others. The 

 depths muft therefore be taken from the centre of prejfure of 

 the plane ; fee that article in Vol. VII. 



The knowledge of the centre of preflure is required, in 

 order to apply this calculation to wooden veflels, fuch as the 

 large backs ufed by brewers ; or to find the preffure againft 

 the gates of a fluice or lock, or in any other cafe where the 

 wood planks, or the ftones of the mafonry are fo united to- 

 gether into one mafs, that the whole fide of the veffel muft 

 be removed together. If the plane againft which the water 

 afts rifes up as high as the furface of the water, and is of a 

 reftangular figure ; that is, if all its horizontal dimenfions, 

 whether taken at the bottom of the veffel or at the top, are 

 equal, then the centre of preiTure is fituated at fd? of the 

 greateft depth beneath the furface. 



Example — A wooden vat is 18 feet long, and contains 

 water 6 feet deep ; required the force which the water ex- 

 erts againft the fide of the vat to force it outwards. Two- 

 thirds of 6 feet is 4 feet, which is the depth of the centre of 

 prefTure: 4 x 62.5 = 250 lbs. is the mean prefTure upon 

 each fquare foot of the plane, 1 8 feet long x 6 feet deep 

 = 108 fquare feet of area x 250 lbs. 27,000 lbs., wliich is 

 the force exerted againft the fide of the vefTel, and muft be 

 refifted by the ftrength of the materials. 



On the Means of meafur'mg or gunning the Quantity of run- 

 ning Water — The ancients feem to have had no other mea- 

 fure of running water than that uncertain and fallacious one, 

 ■which depended wholly on the perpendicular feftion of a 

 ftream, without confidering the velocity of the motion. The 

 firft who opened a way to the truth was Benedift Caftelli, 

 an Italian, and friend of Galileo. He firft (hewed that the 

 quantity of water, flowing through a given feftion of a ftream, 

 is proportional to the celerity with which the water is carried 

 through that feftion. This obfcrvation engaged philofo- 

 phers to ftudy the doftrine of the motion of fluids with 

 much diligence, and after Caftelli's time there was fcarcely 

 any mathematicians who did not endeavour to add fomething 

 thereto, either by experiments or by reafoning and argu- 

 ment. 



But few of them, until the illuftrious fir Ifaac Newton, 

 had any fuccefs, becaufe of the exceeding difficulty of the 

 fubjeft. 



Thofe who ftudied the theory laid down fuch theorems as 

 were found to be falfe, when brought to the teft of experi- 

 ments, and thofe who laboured in making experiments fre- 

 quently omitted to obferve fome minute circumftances, the 



'mportance of which they had not yet perceived. Hence 



they differed greatly from one another, and almoft all of 

 them erred from the real meafure. 



The theory of hydraulics has never been carried to a vei-^ 

 high degree of perfeftiou upon mathematical foundatic 

 alone, nor has it hitherto, even with the afiiftance of exper: 

 ment, been rendered of much praftical utility. NewtOi 

 began the inveftigation of the motions of fluids on tri.^ 

 principles. Daniel Bernouilh added much valuable mattci 

 to Newton's propofitions, both from calculation and expe- 

 riment. D'Alembert, and many later authors, have exer- y 

 cifed their analytical talents in inquiries of a fimilar nature, li 



Dr. Robifon obferves that thefe, and other mathema- ' 

 ticians of the firft order, feem to have contented themfelve- 

 with fuch views as allowed them to entertain themfelves with 1, 

 elegant applications of calculus. They rarely had any op- | 

 portunity of doing more, for want of a knowledge of fafts, 

 but they have made excellent ufe of the few which have 

 been given them. 



It requires much labour, great variety of opportunities, 

 and great expence, to learn the multiplicity of things which 

 are combined, even in the fimpleft cafes of water in motion. 

 Thefe advantages feldom faU to the lot of a mathema- 

 tician, and he is without blame when he enjoys the pleafure. 

 within his reach, and cultivates the fcience of geometry in 

 its moft abftrafted form. Here he makes a progrefs which 

 is the boaft of human reafon, being almoft infured from 

 every error, by the intelleftual fimplicity of his fubjeft. 

 But were we to turn our attention to material objefts, we 

 know neither the fize and (hape of the elementary particles, 

 of water, nor the laws which nature has prefcribed for their 

 aftion. We cannot, therefore, prefume to forefee their 

 effetts, calculate their exertions, or direft their aftions, with 

 any reafonable expeftations of certainty. 



A different and more praftical mode of attaining hy- 

 draulic knowledge, has been attempted by a diftindl clafs 

 of inveftigators. Thefe have begun from experiment alone, 

 and have laborioufly deduced, from very ample obfervations 

 of the aftual refults of various particular cafes, the general 

 laws by which the phenomena appear to be regulated, or 

 at leaft the formulas by which the effeft of new combina- 

 tions may be predicted. But it muft be confefled, that 

 thefe formulas, however accurate, are almoft too intricate 

 to be retained in the memory, or to be very eafily applied to 

 calculations from particular data. 



There are two gentlemen whofe labours in this refpeft 

 defenc very particular notice, profefTor Michelotti, at Tu- 

 rin, and abbe Boftut, at Paris. The firft made a pro- 

 digious number of experiments, both on the motion of 

 water through pipes and in open canals. The experi- 

 ments of BolTut are alfo of both kinds, and though on 

 a much fmaller fcale than thofe of Michelotti, they feem 

 to deferve equal confidence. The chevaher de Buat, who 

 has taken up this matter where the abbe Bofliit left it, 

 has profecuted his experiments with great affiduity and fin- 

 gular fuccefs. 



Mr. Eytelwein, a gentleman honoured with feveral em- 

 ployments and titles relative to the public architefture of 

 the Pruffian dominions, made a tranflation of Buat's works 

 into German, with important additions of his own ; and he 

 alfo publiflied " Handbuch der Mechanik und der Hydrau- 

 lik," Berlin, 1801. In this compendium of mechanics and 

 hydraulics, he has coUefted the principal fafts that have 

 been afcertained, as well by his own experiments as by thofe 

 of former authors, efpecially fuch as are the moft capable 

 of praftical application. He appears to have done this in 

 fo judicious a manner, as to njake his book a moft valuable 



abftraft 



