H Y D R O D Y N A M I C S. 



413 



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this error in the edition of the PrtHcifjia which appear- 

 ed in 171* ; ami, considering the area of the section of 

 the tea/I i-oxtracta as the true area of the orifice from 

 which the water should be conceived to flow, he made 

 the velocity equal to that of the height of the fluid, and 

 obtained results more agreeable to experience. Not- 

 withstanding this additional accuracy to which Newton 

 had brought his theory, it was still liable to the very seri- 

 ous objection*, which have been urged against it by suc- 

 ceeding authors. Giannini has written a dissertation 

 against it in his O/rutcitla, and John Bernoulli, in the 

 Hh volume of his works, fws demonstrated, that, if such 

 a cataract existed, the part of the fluid without the ca- 

 taract would be stagnant, and consequently would ex- 

 ert a pressure, in virtue of its gravity, against the cata- 

 ract iUelf in which the fluid ought to experience no 

 pressure. But, independent of this specie* of argu- 

 ment, it may be shewn, as Bossut has done, by direct 

 experiment, tliat whin a vessel of water empties itself 

 by an orifice in the bottom, every fluid |wutide descends 

 vertically, whether it is si'uatcd near the axUor the side 

 of the vessel ; and that this vertical motion is not chan- 

 ged into a lateral one till the particles are very near the 

 orifice itself. 



The subject of the resistance of fluid*, one of the 

 most important and difficult in Hydrodynamics, was 

 likewise investigated by Sir Isaac Newton. He first 

 considers the fluid as a rare medium, composed of equal 

 parts, situated at equal distances from each other, and 

 possessing the prwperty of perfect intermobility , so that 

 !ie solid, without being pre- 

 vented by any of the adjacent ones. Hence he find*, 

 that : f a globe and a cylinder, of equal diameters, more 

 in such a medium with equal velocities, the resistance 

 of the globe will only he one half of that of the cylin- 

 der. He next proceeds to determine the absolute re. 

 sistance which il.r K I..U- m i!l experience, whether the 

 parts of the fluid are perfectly elastic, or absolutely in. 

 elastic. In the case of perfect elasticity, he shews, that 

 the resistance of the globe is to the force by which its 

 total motion may be produced or destroyed in the time 

 that it takes to describe two-thirds of iu diameter by 

 a uniform velocity, as the density of the medium u to 

 the density of the globe. In the case of abstain' 

 elasticity, he shews that the resistance is twice as email. 

 After examining the resistance in different mrdisjeae, 

 as water, mercury, oil, &c. be advances another theory 

 suited to tho*c mediums in which the globe doe* not 

 immediately strike all the resisting parts of the fluid, 

 but only communicates to the neighbouring particles a 

 pressure whuh M inn in tt.d to aJI the rest From 

 this theurv it follows, that the resistance of globe is 

 equal to that of the circumscribed c) linder. 

 pothetic.tl theory, though it exhibits much 

 characteristic inpn ity. is still founded on false prin- 

 ciples, and is radically inconsistent w ith the results of 

 experiment. 



With the exception of a few observations by Galileo 

 . in bis Sytc a Cotmicum, we are indebted to Sir Isaac 

 I Newton for all that wa* known in hit time respecting 

 tfssts" the oscillation of waves. In order to investigate this 

 diffi. ult subject, he considers the fluid as at rest in the 

 two vertical branches of a syphon connected by a ho- 

 rizontal branch. If the one column is raised to a greater 

 height than the other, and is then permitted to descend, 

 it ill olnimi-ly fill liciow .t* original Uvel, and raise 

 the other column to a greater height than that at which 

 column will in like manner 

 descend, ar^l the opposite column will rise, till, after a 



certain number of oscillation?, the fluid will return to History. ^ 

 a state of rest. In order to determine the time in which ^ ">"" 

 these oscillations are performed, Newton considered 

 the water as in the same state with a pendulum vibra- 

 ting in a cycloid, and he >h<:\v -. by a very simple de- 

 monstration, that a pendulum, whose length is equal 

 to half the length of the column of water in the syphon, 

 will perform ita oscillations in the same lime with the 

 fluid. Hence it follows, that all the oscillations of the 

 fluid will be isochronous, whatever be the intensity of 

 the motions of the fluid ; and that the velocity of waves 

 will vary as the square roots of their breadth. 



The motion of fluids was treated, both experimentally Labours of 

 and theoretically, by Michelotti, a celebrated Italian Michdotti. 

 physician, in his work entitled, I)f Sfparatione Fluido- A. D. 17*0 

 rum in (' r/> rr Animali, published in 1719 or 17-0. 

 He rejects Newton's idea of a cataract, and considers 

 the water in a vessel as all frozen, excepting a small 

 part of it immediately above the orifice. This thin 

 plate of water is pressed by the superincumbent solid, 

 which is supposed to melt gradually as the water is 

 discharged. In this work Michelotti criticises, with 

 rather too much severity, a paper " On the Motion of 

 Running Water," published by Dr Jurin in the Vhil.- 

 tapfiical I'raniacticns for 1718. Jurin replied to this 

 criticism in the /'A/7. Trant. for 1722, and successfully 

 defended Sir Isaac Newton against the charge of in- 

 consistency which was rashly brought against his doc. 

 trine of effluent water by the Italian philosopher. 



A aeries of valuable experiments on the motion of Couplet. 

 water in conduit pipe*, were made on a very large Dud K.n. 

 scale by M. Couplet, on the water-pipes at Versailles. 

 These experiments, though not sufficiently varied, shew 

 the great effect which is produced by trictiori on the 

 motion of water. A full account of them is published 

 in the Memoirs of the Academy for 1732, in the paper 

 entitled Dtt ItecJtrrchet ntr le mouremrnt da Eaux /ci 

 let tttymut de co*<luitr. The theory which he has found- 

 ed upon his experiments, and also that which M. Be. 

 lidor has substituted in its place, are not deserving of 

 notice. 



Italy produced about this time several authors on c,mA 

 I (ydrodvnamics, that have acquired considerable cele- Grandi 



The most distinguished of these was Guido 

 Grandi, who wrote a geometrical treatise on the motion 

 of water, deduced from the theorems of Galileo and To- 

 ricelli. He invented also a method of measuring the 

 velocity of a river at different depths by a tin parallelo- 

 piped, which had an aperture that could be opened 

 and shut by a moveable plate. The box was sunk to 

 the required depth, and the orifice opened. After a 

 certain time had elapfd, the orifice was again shut, 

 and the % elority was determined from the Quantity of 

 water in the box. Grandi was also the author of se- 

 veral dissertation*) on the river Km, and on other small 

 Italian rivers. All these works are published in the 

 Afcoeo RmcctUa, already referred to. Eustnchio Man* 

 fredi, another Italian author, contributed to the pro- Mtnfr *"- 

 grese. of Hydrodynamics. He added valuable notes 

 to Gttglicknini's work on rivers. He published a dis- 

 sertation in conjunction with /endrini, on the means 

 of preventing the inundations of the Ronco and the 

 Montone in the town of Ravenna ; and he was the 

 first person who proved, by decisive experiments made 

 on several of the ancient buildings of Ravenna in 1751, 

 that the bottom of the Adriatic Sea was continually ri- 

 sing. The names of /endrini, and Frisi, deoerve to 

 be mentioned among the Italian writers on Hydrody- 

 namics. Bernard Zendrini, a Venetian mathematician, 



