414 



HYDRODYNAMICS. 



^lljstory. wrote a very ample work, both theoretical and practi- 

 S ""Y"~"*' cnl, entitled DC Motu Aquarum, which contains many 

 Frisi. excellent practical observations. Frisi composed a work 



on the method of regulating rivers and torrents, in 

 which he has endeavoured to prove that gravel and 

 sand are original productions, and not the detritus of 

 pre-existing materials. A selection of practical ob- 

 servations from the work of /endrini will be found in 

 the 5th volume of the Nuova Raccolia, and the whole 

 of Frisi's work in the 7th volume of the same collec- 

 tion. 



K ri- One of the most celebrated writers on Hydraulics 



ments of tna * Italy produced, was the Marquis Poleni, professor 

 the Marquis of mathematics at Padua. In the year 1695 he pub- 

 Poleni. lished a treatise in 4to, entitled, De Motu Aquae miocto, 

 Born 1693. wn ich, though it contains nothing that possesses much 

 *' novelty, yet the reader will find in it many observa- 

 tions both of local and general utility. He supposes, 

 that the bed of a river is a rectangular canal, and re- 

 garding any perpendicular section of it as an orifice, he 

 gives the name of dead water to that which is compre- 

 hended between the surface, and a point in relation to 

 which all the fluid molecules would have equal momen- 

 ta, and would therefore be in equilibrium, according to 

 the laws which are observed in the equilibrium of solid 

 bodies : The rest of the water which is comprehended 

 between this centre of equilibrium and the bottom of 

 the canal or orifice, he calls the living water. He then 

 considers the motion of the water that flows through 

 the orifice as partly produced by the action which the 

 living water derives naturally from its fall, and partly 

 by the pressure which the dead water exerts upon the 

 living water. Hence arises the title of Poleni's work, 

 De motu mixto Aqua;. After detailing a number of ex- 

 periments, and comparing the results with the theory, 

 he applies the same principles to the motion of rivers, 

 and to the lakes of Venice. His principal work, how- 

 ever, appeared at Padua in 1718, under the title of 

 De Castellis per qua derivantur jlimiorum aquas. This 

 work contains many important observations and expe- 

 riments. From an extensive series of experiments on 

 the quantity of water discharged by an orifice in the 

 bottom of a vessel, he concluded, that, instead of being 

 proportional to 2AH, A being the area of the orifice, 

 and H the height of the reservoir in the vessel, it was 



proportional to 2AH X , which is only a little 

 1.000 



more than one-half of what is discharged, upon the sup- 

 position that the water issues with a velocity due to the 

 altitude H. Poleni was the first person who observed, 

 that a greater quantity of water issued from a small 

 cylindrical tube, fitted into the orifice in the bottom 

 or sides of a vessel, than from a simple orifice of the 

 same diameter. This remarkable fact may be explain- 

 ed by supposing that the fluid vein, instead of suffering 

 a contraction, flows out in a column of the same dia- 

 meter as the orifice, from the viscidity of the water, 

 and its capillary adhesion to the sides of the tube. We 

 are indebted also to Poleni for a new edition of the 

 works of Julius Frontinus, which he enriched with am* 

 pie notes. Poleni is likewise the author of a dissertation 

 on dikes, and of another on the measure of running wa- 

 ters, both of which, along with his first work, are repub- 

 . lished in the 3d volume of the Nuova Raccolia. 



Bernoulli. Hitherto the science of Hydrodynamics was founded 

 upon vague and uncertain principles ; but it was now 

 destined to receive a more scientific form from the la- 

 bours of Daniel Bernoulli. So early as the year 1726, 

 he communicated to the Academy of St Petersburg!! a 



memoir entitled, Thcoria Nova de Motu Aquarum per History. 

 Canales qiio.in/nf/ue fluentes. In this memoir he in- ^~~y~~~* 



forms us, that his father having shewn, that the prin- nan ' c , 1 BeN 



,. " ,". noulli s 



ciple of the viref uric was of great use in the resolution t i, cor y O f 



of problems incapable of being solved by more direct the motion 

 methods, it had occurred to him to employ this prin- of fluids. 

 ciple in discovering a true theory of the motion of run- Born 17(10. 

 ning waters, and that he had found it to answer his ut- Uic(1 * 782> 

 most expectations. After the publication of this me- 

 moir, which contains merely the germ of his theory, he 

 made a great number of experiments at St Petersburgh 

 in order to illustrate his theoretical views, and was thus 

 enabled to produce his great work, entitled, Hydrodyna- 

 rnica sen de viribus el motibus Jiitidontm Commcjttarii , 

 which was published at Strasburg in 1738. In consi- 

 dering the efflux of water from an orifice in the bottom 

 of a vessel, he conceives the fluid to be divided into an 

 infinite number of horizontal strata, which are suppo- 

 sed to move in such a manner, that the upper surface 

 of the fluid always preserves its horizontality ; that the 

 fluid forms a continuous mass ; that the velocities vary 

 by insensible gradations, like those of heavy bodies ; and 

 that every point of the same stratum descends vertically 

 with the same velocity, which is inversely proportional 

 to the area of the base of the stratum. By the aid of 

 these assumptions, which are conformable to experience, 

 Bernoulli obtains an equation from the principle that 

 there is always an equality between the actual descent 

 of the fluid in the vessel, and its vertical ascension, 

 which is the principle of the conservation of living 

 forces. In those cases, where sudden irregularities in 

 the shape of the vessel, or other causes, produce rapid 

 changes in the velocity of the fluid strata, he then con- 

 siders that there is a loss of living force, and therefore 

 the equations founded on the entire conservation of 

 this force require ta be modified. In the whole of this 

 investigation, Bernoulli displays the greatest sagacity 

 and originality of thought, though he has taken it for 

 granted, without sufficient evidence, that the law of 

 the conservation of living forces is really applicable to 

 the motion of fluids (a point which it was reserved for 

 D'Alembert to demonstrate) ; yet his work will be long 

 regarded as one of the finest specimens of mathematical 

 genius. 



The important subject of the resistance of fluids was Daniel Her 

 likewise indebted to the genius of Daniel Bernoulli. In noulli on 

 the Commentaria Pelropolitana for 1727, he modestly 

 proposed a new method of determining the resistance 

 of fluids, founded upon principles different from those 

 of Sir Isaac Newton ; but having found that it gave 

 results quite hostile to experiment, he afterwards called 

 his determination in question in his treatise on Hydro- 

 dynamics, and in the year 1741, in the eighth volume 

 of the Commentaries of St Petersburgh, he proposed a 

 very ingenious and elegant method of determining the 

 impulse of a column of fluid falling perpendicularly up- 

 on a plain surface infinitely extended. He considers 

 the curve described by every filament of fluid as a ca- 

 nal in which a body moves, which experiences at each 

 point the action of a centrifugal force, and which he 

 supposes also to be subjected to the action of a tangen- 

 tial force, varying according to a given law. He then 

 calculates all these forces, and finds, that the impulsion 

 against the horizontal plane is equal to the weight of a 

 column of fluid whose base is equal to the section of 

 the fluid vein, and whose altitude is twice the height 

 of the full due to the velocity of the fluid. Although 

 there are cases in which this proposition may be safely 

 and advantageously used in practice, yet it does not 

 easily apply either to oblique impulses, or to impulses 





