416 



JIY DUO DYNAMICS. 



History, which covers the anterior part of the bocly is, to a cer- 

 s ">~"" >/ tain extent, stagnant. The pressure experienced by 

 the solid, or the resistance which it opposes to the mo- 

 tion of the fluid particles, is occasioned by the loss of 

 velocity which each of these particles sustains. The 

 problem is then reduced to this, to find the velocity of 

 the fluid which slides immediately over the surface of 

 the body, which D'Alembert has done by two different 

 methods, and he then obtains a formula exhibiting the 

 pressure exerted upon the solid. By a little modifica- 

 tion of the general method, D'Alembert determines the 

 action of a vein of fluid which strikes a plain surface, and 

 he finds it to be a little less than the weight of a cylin- 

 der of fluid, the area of whose base is equal to that of 

 the section of the vein, and whose altitude is double 

 of that which is due to the velocity of the fluid; a re- 

 sult which agrees most wonderfully with the experi- 

 ments of Bossut, who found that it was always a little 

 less than that which was due to twice the height which 

 produces the velocity. * The results of this enquiry 

 were published in 1752, in D'Alembert's Essai d'une 

 ttouvellc theorie sur la resistance drs Fluides, and the 

 theory was afterwards extended in his Opuscules Ma- 

 themaliqites. 



Labours of The celebrated Euler, to whom every branch of sci- 

 U ' er 'l7 7 encc owes suc ' 1 ^ ee P obligations, did not fail to exhi- 

 l?ed 1783 ' ki' l ' le wonderful resources of his genius on a subject 

 of such difficult investigation as the theory of running 

 water. In the Memoirs of the Academy of St Peters- 

 burgh, for 1768, 1769, 1770, and 1771, he has published 

 a new and complete theory of the motion of fluids, which 

 is founded on the laws of mechanics and hydrosta- 

 tics, and occupies no less than 513 quarto pages. The 

 first of these memoirs is entitled De Slatu Equilibria 

 Fluidonm, and is divided into four sections : 1 . De Na- 

 tura et varietate Fluidornm. 2. De Equilibria Fluido- 

 rum, remota gravitate aliisque simililius viribus. 3. De 

 Equilibria Fluidorum a viribus quibuscunque solticita- 

 torum; and, 4. De Equilibria Fluidorum a sola gravitate 

 lollicitatorum, in which he applies his reasonings both to 

 compressible and incompressible fluids. The second 

 memoir is entitled, De Principiis Molvs Fluidorum ; the 

 third, De Motu fluidorum lineari poliss imum aquce, and 

 the fourth, De Motu aeris in Tiwis. In the third me- 

 moir, he deduces, from his general theory, explained 

 in the preceding memoir, the solution of a great num- 

 ber of beautiful problems upon a particular species of 

 the motion of fluids, which he calls linear. The 

 same general theory is applied in his memoir De Mo- 

 tu Aeris, to the linear motion of air. In these me- 

 moirs, he reduces the whole theory of the motion of 

 fluids to two differential equations of the second or- 

 der, and he applies the general principles to the dis- 

 charge of water from orifices in vessels, to its motion 

 in conduit pipes, whether their diameters be constant 

 or variable. In extending his investigation to elastic 

 fluids, and particularly to air, he obtains very simple 

 formulae respecting the propagation of sound, and its 

 formation in flutes and in the pipes of an organ. It 

 is much to be lamented, that in all these researches, 

 Euler has proceeded on the hypothesis of a mathemati- 

 cal fluidity, which has no existence in nature. Had 

 he only treated the subject in reference to those resist- 

 ances, such as cohesion and friction, which modify the 

 action of gravity, the solutions which he has given 

 might have been advantageously applied to the motion 

 of water in pipes and canals. 



In the year 1765, a very complete work on the the- History, 

 ory and practice of hydrodynamics was published at 

 Milan, by P. Lecchi, a celebrated Milanese engineer. 

 It was entitled, Jdroslalica esaminata ne' suoi principi, 

 e slaliilita nelle sue reg^/e delta mesnra delle acque cor- 

 rcnti, and contains a complete examination of all the 

 different theories which have been proposed to explain 

 the phenomena of effluent water, and the doctrine of 

 the resistance of fluids The author treats of the ve- 

 locity and the quantity of water, whether absolute or 

 relative, which issues from orifices in vessels or reser- 

 voirs, according to their different altitudes, and he after- 

 wards enquires if this law is applicable to large masses 

 of water, which flow in canals and in rivers, and he de- 

 monstrates the rules which have been found most use- 

 ful in practice for tne division and the mensuration of 

 running water. This work contains several pieces by 

 the celebrated Italian geometer Father Boscovich, by 

 whom the work was revised and corrected. The ex- 

 tensive and successful practice of Lecchi as an engineer, 

 has stamped a high value upon his work. 



A very extensive series of experiments on the mo- 

 tion of water in pipes and canals, was made at Turin 

 by Professor Michelotti, and at the expence of the 

 King of Sardinia. These experiments were performed 

 upon a splendid scale, and with every attention to ac- 

 curacy. The water issued from orifices and tubes of 

 various shapes and sizes, from a tower of the finest ma- 

 sonry twenty feet high and three feet square, supplied 

 by a canal two feet wide, and under pressures, which 

 varied from five to twenty-two feet. A huge reservoir, 

 whose area was 289 feet square, built of masonry, and 

 lined with stucco, received the effluent waters, which 

 were conveyed in canals of brickwork, lined with stucco, 

 and having various forms and declivities. Michelotti's 

 experiments on the motion of water in pipes, are the 

 most numerous and exact that have yet been performed. 

 The trials which he made in open canals are still 

 more numerous, but they are complicated, with many 

 unnecessary circumstances, and seem to have been made 

 more with the view of examining some disputed points 

 in hydraulics, than of furnishing us with rules for cases 

 which are likely to occur in practice. A full account 

 of these experiments was published at Turin in 1774, 

 in Michelotti's Sperienze Idrauliche. Michelotti pub- 

 lished also a memoir on the impulse of a vein of fluid, 

 in which he describes some experiments which do not 

 agree with the common theory. It appeared in the 

 Memoirs of the Academy of Turin for 1778. 



One of the most zealous and enlightened cultivators 

 of hydrodynamics, was the late Abbe Bossut, who has 

 published a full account of his theoretical and experi- 

 mental investigations, in his Traite T/ieorique et Expe- 

 rimental d Hydrodynamique, in 2 vols. 8vo. The first 

 edition was published in 1771; the second edition 

 appeared in 1786, considerably enlarged ; and a third 

 edition, with very considerable alterations, was pub- 

 lished in 1796. The experiments of Bossut, though 

 made on a much less scale than those of Michelotti, 

 have, in as far as they coincide, afforded similar results ; 

 and while they have the merit of equal accuracy, they 

 are much more applicable than those of the Italian 

 philosopher to cases which are likely to occur in prac- 

 tice. In order to determine the motion of the par- 

 ticles of a fluid which was in the act of being dischar- 

 ged from an orifice, Bossut employed a glass cylinder 

 about eight inches high, and six inches diameter, to 



* See Bossut's Hydrodynamijue-, Chap. xir. Exp. 5, 6, 7, 8. 



