HYDRODYNAMICS. 



469 



OB(><nvr In a subsequent memoir, entitled, Explicatio Diffici- 

 /rum erperimentontm circa tucensum eqiue in titbit Copil- 

 " rf larilna, published in the ( ommentarii Acad. Pelropoiila- 

 na, for 1737, M. Weitbrechl resumes the subject He 

 ^ shews that Muschenbroek was mistaken in considering 

 the height of ascent as affected by the length of the tube. 

 He |ioints otit the effects produced by interposing bub- 

 bles of air between the different parts of the elevated co- 

 hunn ; he CT*H>* the phenomena exhibited by coni- 

 cal tubes, and tubes where the diameter of the bore 

 changes rapidly ; and he terminates his memoir with se- 

 veral interesting experiments on the effects of capillary 

 syphons and bent capillary tubes. 



Hitherto mercury was the only metallic fluid which 

 had been employed in capillary experimentis. M. Gel- 

 lert, however, communicated a memoir to the Academy 

 of Science* at St Petersburg!), entitled, De Phenomena 

 f*ti in Tutu CapiUaribta. In making these 

 he employed the thinnest glass tubes he 



ipcri- 



procure, and heated them gradually before he 

 rsed them into the melted lead. In this way he 

 found, that melted lead always stood below its level in 

 a tube of glass, and that the altitudes in different tubes 

 were nearly in the reciprocal ratio of their diameters, 

 When the diameter of the tube was 10 SI of an Eng- 

 lish inch, the lead sunk 0.-J7 of an inch, whereas in a 

 tube 0.07 it sunk 0.73 of an inch. These results give 

 567 and 510 for the constant quantity, the roieji of which 

 is 5385. In another paper, entitled, De TVsst Cestlfe. 

 ntnti Pntmalictt, 14. Gellcrt treats of the a*cent of war 

 tor in prismatic tube* of a triangular and quadran- 

 gular form made of iron. He found, that they gave 

 tese.1** perfectly analogous to those which were made 

 of glass. See p. 477. col. 1 . 



Before the time ef Clairant, no attempt had been 

 made to analyse with accuracy the different fa 

 1 which concur in the elevation of water in capillary 

 tithe*, and to subject the phenomena to a rigorouA cat 

 relation The merit of doing this belongs wholly to 

 this eminent mathematician, who has published his in- 

 vestigation* in the tenth chapter of his Tkroriede la Fi- 

 gure dt If Ttrrf tiree det Principe* dt tHydrotUUufne, 

 hich was published at Paris in 1743, and of which a 



appeared in 1808. In this chapter, 

 rEimuHim * At tAbaimtmt* oW 

 Liquevri dam it* luuanj CapiUaircs. be begins by 

 pouting out the mistake in the reasoning employed by 

 DrJuhn inth*e*tablisheatofhi*hyi>othws.aiidhe 

 then proceed* to the analysis of the force* by which the 

 water is elevated and iiupended. An account of this 

 analysis ha* already been given in our article or. 

 riLLAHV ATTRACTION, p. HI. The resulting formula 

 which he obtain* for the altitude It, (Plate CX. Fig. 9.) 



u i, - 



c*. *. Q. oa 



where 



() = intensity of the attraction of the glass. 



Q' = the intensity of the attraction of the water. 

 b = the interior radiu* of the tube. 

 p = the fora of gravity. 



The function of the instance which expresm the law 

 ef attraction both for glass ad water U nippoMii givwa, 

 and be employs t to denote the distance of a particle 

 from the plane MN, (Vj the force at which this par. 

 tick is attracted by a body, of which this plane i* the 

 exterior surface, supposing the intensity of the attrac. 



and the 

 Cohesion of 



tion of this body to be unity. The function 6*3 On Capillary 



expresses the force with which a particle Q, placed at -Attraction 



the distance QO or JT from the surface CH is attracted 



by the tut>e or bulb cylinder CDABGHEF, and 



\J), x, Q, Qf^ the force with which a corpuscle p ^*-y 



placed at the distance j- from VX is attracted by the 



small mass of water Y\ XX. 



" Without pu-!iin<* the calculation farther," says M. 

 Clairaut, " in order to find what will be the quantities 

 &, i^ and T6, JT, Q, Q'] according to the different 

 functions of the distances by which the law of attrac- 

 tion may be expressed, we may easily see that there 

 will be an infinity of laws of attraction in which the 

 preceding expression of I i will give a sensible altitude 

 when the diameter b of the tube is very small, and on 

 the contrary, a height almost insensible when the tube 

 is very wide." It follows from the value of I i, that if 

 the attraction of the capillary tube is less than that of 

 water, provided it is not twice as small, the water will 

 still ascend ; for it is obvious from the term (2 Q Q') 

 J'd i [6, *2, that while Q' i* less than 2 Q, I i will be 

 positive. 



In the Transactions of the Royal Society of Gottin- Segner, 

 gen for 1751, M. Segner has referred all the phono- 17.51. 

 mena of capillary attraction to the attraction of the su- 

 perficial particles of fluids. Considering the resemblance 

 at the surface of the drops of fluids and of fluids con- 

 tained in capillary tube* to the surfaces, which geome- 

 ters have named linteariaor clastic, he was led to consider 

 fluid* a* enveloped in such surfaces, which, by their 

 tension and elasticity, gave to fluids the form indicated 

 by experiment. It appears, however, that Segner con- 

 sidered this only a* a fiction which might represent 

 the phenomena, but which ought only to be admitted 

 in so far a* it belonged to a law in which the nttr.u - 

 tieq is insensible at sensible distance*. Segner tried to 

 this dependence; but in the opinion of La 



Place, " in following this reasoning it i* easy to dis- 

 iU inaccuracy, which i* also proved by the incor- 

 rectness of the result* to which he arrives. He finds, 

 for example, that we ought to consider only the cur- 

 vature of the vertical section of a drop, and not it* 

 horizontal curvature, which U not exact ; and betide* 

 this, he did not perceive that the tension of the surface 

 U the same whatever be the magnitude of the drop."* 

 The subject of the adhesion of fluid* to plates of so. M orr u 



W - * 4sUlTdU t 



bodies, which was first investigated by our country. 1773. 



man Dr Brook Taylor.t was now resumed with great 

 success by M. Guy ton Morveau, in 1773. The name 

 subject was prosecuted by M. Achard of Berlin, ami M. 

 Dutour, the last of whom made a great number of 

 experiments, both on the adhesion of discs, and on the 

 ascent of fluids. An account of the general results 

 which they obtained, will be fuuud iu our article ADO 

 ticsiox. 



In the year 17S7, M. Monge published in the Me- Mongr, 

 moirs of the Academy of fjf^*y^^ a paper entitled, &nr 1787. 

 ijurhfutt tjett <f attraction et dt repulsion tpparattr rn- 

 tre lei Moieculei dt Mature. These experiments re-lute 

 principally to the apparent attraction and repulsion 

 which are exhibited by floating bodies when they ap- 

 proach within a certain distance of each other ; to the 

 phenomena of drop* ; and to the ascent of water be- 

 tween two plane* of glass. An account of hi* experi- 

 ment* will be found in the present Chapter. 



The subject of capillary attraction has been ably inves- Dr Tbooiai 

 tigated by Dr Thomas Yuung, in his paper the (Joke- Young., 



MML 





1741, lorn. L p. 301. 



t Sss rkil. 7V*u. ITU. 



