478 



HYDRODYNAMICS. 



PLATE 

 CCCXVI. 

 Fig. 7. 



OnCapillary The approximation of these results gives the true 



Attraction cause o f the ascent or descent of fluids in capillary 



nd the tu j, eg j n t f, e i nverse ratio of their diameter. If in the 



Cohesion of . . . . , 



Fluids. axis * a R'IS* tube we conceive a canal infinitely nar- 

 s ^v ^ row, which bends round like the tube ABEDC in Fig. 

 7. the action of the water in the tube in this narrow 

 canal, will be less on account of the concavity of its 

 surface, than the action of the water in the vessel on 

 the same canal. The fluid will therefore rise in the 

 tube to compensate for this difference of action ; and as 

 the concavity is inversely proportional to the diameter 

 of the tube, the height of the fluid will be also inversely 

 proportional to that diameter. If the surface of the 

 interior fluid is convex, which is the case with mercury 

 in a glass tube, the action of this fluid on the canal 

 will be greater than that of the fluid in the vessel, 

 and therefore the fluid will descend in the tube in the 

 ratio of their difference, and consequently in the in- 

 verse ratio of the diameter of the tube. 



In this manner of viewing the subject, the attraction 

 of capillary tubes has no influence upon the ascent or 

 depression of the fluids which they contain, but in de- 

 termining the inclination of the first planes of the sur- 

 face of the interior fluid extremely near the sides of the 

 tube, and upon this inclination depends the concavity 

 or convexity of the surface, and the length of its radius. 

 The friction of the fluid against the sides of the tube 

 may augment or diminish a little the curvature of its 

 surface, of which we see frequent examples in the ba- 

 rometer. In this case the capillary effects will increase 

 or diminish in the same ratio. 



The differential equation of the surfaces of fluids in- 

 closed in capillary spaces of revolution, conducts La 

 Place to the following general result ; that if into a cy- 

 lindrical tube we introduce a cylinder which has the 

 same axis as that of the tube, and which is such that the 

 space comprehended between its surface and the inte- 

 rior surface of the tube has very little width, the fluid 

 will rise in this space to the same height as in a tube 

 whose radius is equal to this width. If we suppose 

 the radii of the tube and of the cylinder infinite, we 

 have the case of a tube included between two par- 

 allel and vertical planes, very near each other. This 

 result has been confirmed, as we have already seen, by 

 the experiments of Newton, Hauy, and Gay Lussac. La 

 Place then applies his theory to the phenomena pre. 

 sented by a drop of fluid, either in motion or suspend- 

 ed in equilibrium, either in a conical capillary tube, or 

 between two plates, and inclined to each other, as dis- 

 covered by Mr Hawksbee ; to the mutual approxima- 

 tion of two parallel and vertical discs immersed in a 

 fluid ; to the phenomena which take place when two 

 plates of glass are inclined to each other at a small 

 angle ; and to the determination of the figure of a large 

 drop of mercury laid upon a horizontal plate of glass. 



In the application of his theory to the experimental 

 results obtained by Hawksbee respecting the angles re- 

 quired for suspending a drop of oil of oranges at diffe- 

 rent stations between two inclined planes of glass. * 

 La Place obtained the results contained in the following 

 Table. 



Column 1st contains the number of the first column 

 of Hawksbee's table, subtracted from 20 inches; and co- 

 lumn 2d contain* Hawksbee's 3d column, diminished by 

 5' 22". 



Attraction 

 and the 



Cohesion of 

 Kluids. 



SECT. II. OH the Approximation and Recession of Bo* 

 dies floating near each other in a Fluid. 



IT was long ago observed by philosophers, that when On the ap. 

 bodies floating on the surface of a fluid approached ei- proximatioi 

 ther one another or the sides of the vessel, they mo- a . nd reees - 

 ved rapidly into contact, as if they had been two float- ?' oi - 

 ing magnets. This phenomenon, which was in gene- w"^,. 01 

 ral ascribed to the mutual attraction of the floating bo- each other 

 dies, was tolerably well explained by M. Marriotte in in a fluid. 

 his Traite du Mouvement dcs Eaux. It was reserved, 

 however, for M. Monge to describe and explain these 

 phenomena with accuracy, which he has done in his 

 Memoirs xur quelqties effets d' attraction ou de repulsion 

 apparenle enlre les Molecules de Matiere. 



The following are the principal experiments upon 

 this subject : 



1. If two light bodies, capable of being wetted with 

 water, are placed one inch distant on the surface of 

 water perfectly at rest, they will float at rest, and ex- 

 perience no motion but what is derived from the agita- 

 tion of the air ; but if the distance at which they are 

 placed is only a few lines, they will approach each 

 other with an accelerated motion. If the vessel which 

 contains the water is capable of being wetted by it, 

 such as glass, and if the floating body is placed within 

 a few lines of the edge of the vessel, it will move to- 

 wards the edge with an accelerated motion. 



2. If the two floating bodies are not susceptible of 

 being wetted with fluid, such as two balls of iron in a 

 vessel of quicksilver, and if they are placed at the dis- 

 tance of a few lines, they will move towards each other 

 with an accelerated motion ; and if the vessel is made 

 of glass, in which the surface of the mercury is always 

 convex, the bodies will move towards the sides when 

 they are placed within a few lines of it. 



3. If one of the bodies is susceptible of being wetted 

 with water, and the other not, such as two globules of 

 cork, one of which has been carbonised by the flame of 

 a taper, then if we attempt, by means of a wire or 

 any other substance, to make the bodies approach, 

 they will fly from each other as if they were mutually 

 repelled. If the vessel is of glass, and if the carbon, 

 ised piece of cork is placed in it, it will be found im* 

 possible to bring the cork in contact with the sides of 

 the vessel. 



In these experiments, it is obvious that the approv- 



These result! are given in p. 487, top of col, 1. 



