HYDRODYNAMICS. 



47$ 



mation and the recession of the floating bodies are not 

 produced by any attraction or repulsion between the 

 two; for if the bodies, instead of floating on the fluid, 

 are suspended by long and slender threads, it will be 

 found that they have not the slightest tendency either 

 to approach or recede when they are brought extremely 

 near each other. From these experiments the following 

 laws are deducible: 



1 . If two bodies, floating on the surface of a fluid, and 

 capable of being wetted by the fluid, are placed near 

 each other, they will approach as if they were mutu- 

 ally attracted. 



2. If the two bodies are not susceptible of being 

 wetted by the fluid, they will still approach each other 

 when brought nearly into contact, as if they were mu- 

 tually attracted. 



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

 wetted and the other not, they will recede from each 

 other as if they were mutually repelled. 



Explanation of ike fir* lam. If two plate* of glass 

 AB, CD, Fig. 8. are brought so near each other that 

 the point H, where the two curves of elevated fluid* 

 meet, is on a level with the rest of the water, they will 

 remain in perfect equilibrium. If they are brought near- 

 er each other, however, as in Fig. 9. the water will rise 

 between them to the height G. The mass of water 

 which is thus raised attracts the sides of the glass 

 plates, and causes them to approximate in a horizontal 

 direction, the mass of water having always the same 

 elect as a curved chain hung to the two plates. The 

 same thing is true of two floating bodies, when they 

 come within such a distance that the fluid is elevated 

 between them. This case is shewn in Fig. 10, where 

 the bodies A, B, placed at a capillary distance, hare 

 the water raised between them, and are therefore 

 brought together by the attraction of the fluid upon the 

 sides of the globules. 



Explanation of tht itcond late. If the two floating 

 bodies A, H, Fig. 1 1 , are not capable of being wetted 

 by the liquid, the liquid will be depressed between 

 them at H, below its natural level, when they are pla- 

 ced at a capillary distance. The two bodies, therefore, 

 are more pressed inwards by the fluid which surrounds 

 them, than they are pressed outwards by the fluid be- 

 tween, and in virtue of the difference of these pressures 

 they mutually approach each other. 



E-rplanaJion of ike third I**. If one of the floating 

 bodies A, Fig. If. is capable of being wetted, while the 

 other B is not, the fluid will rise round A, and be de- 

 pressed round B : Hence the depression round K will 

 not be symmetrical ; and therefore the body B, being 

 placed a* it were on an inclined plane, its equilibrium 

 u destroyed, and it will more towards the right hand, 

 where the pressure is the least. 



The results of U. Mange's experiments have been cm- 

 ' pletely confirmed by the theory of capillary attraction gi- 

 ven by La Place. From thb theory it follow*, that what- 

 ever be the nature of the sssbstaaos of which the floating 

 planes are made, the tendency of each of them to one ano- 

 ther is equal to the weight of aprum of fluid whose height 

 is the elevation of the fluid between the planet, measured 

 to the extreme points of contact of the interior fluid with 

 the plane, minut the elevation e,f the fluid on the ex- 

 terior sides of the tube, whose depth is half the sum 

 of these elevations, and whose width is the horizontal 

 distance between the planes. The elevation must be 

 reckoned negative when it changes into a depression a* in 

 r. If the product of the three preceding dsmuv 



sions is negative, the tendency of the planes becomes re- 

 pulsive. La Place also concludes, that when the planes ' r > 

 are very near each other, the elevation of the fluid be- c {^on O f 

 tween them is in the inverse ratio of their mutual dis- fluids. 

 Unce, and is equal to half the sum of the elevation ^-y-'' 

 which would have taken place, if we suppose the first 

 plane of the same matter as the second, and the second 

 of the same matter as the first. 



It follows from these theorems, that the repulsive 

 force of floating planes i much more feeble than the 

 attractive force which is developed when the planes are 

 very near each other, and which occasions them to ap- 

 proach each other with an accelerated motion. In this 

 case, the elevation of the fluid between the planes is 

 very great, relative to its elevation on the outside of 

 the same plane. In neglecting, therefore, the square 

 of this last elevation in relation to the square of the 

 first, the fluid prism, whose weight expresses the mu- 

 tual tendency of the plane*, in virtue of the first of the 

 two preceding theorems, will be equal to the product 

 of the square of the elevation of the interior fluid, by 

 half the horizontal distance of the planes. This eleva- 

 tion being, by the second theorem, reciprocally pro- 

 portional to the mutual distance of the planes, the 

 prism will be proportional to their horizontal distance 

 divided by the square of that distance. The tendency of 

 the two planes to each other will consequently be in the 

 inverse ratio of the square of their distance ; and there- 

 fore, like the farces of electricity and magnetism, it 

 will follow the law of universal attraction. 



When the two planes are of such a nature that the 

 one is capable of being wetted with the fluid, while the 

 other is not capable of being wetted, then, in conse- 

 quence of these two opposite actions, the surface of the 

 intermediate fluid will have a point of inflexion ; and 

 it follows, from the theory, that they will repel each 

 other at every distance. But if they are brought near 

 each other by force, the point of inflexion will approach 

 more and more to one of the planes, and will at last 

 coincide with it. If the planes arc then brought still 

 nearer each other, the fluid will begin either to ascend, 

 er be depressed between them. From this arises ano- 

 ther force which pushes the planes towards each other, 

 and which, when it come* to surpass the pressure of 

 the exterior fluid, causes the plane* to approach each 

 other with an accelerated motion. This change of re- 

 pulsion into attraction appeared to M. La Place so sin- 

 gular, that he requested M. Hauy to examine the sub- 

 ject experimentally. In order to do this, he employed 

 planes of ivory and talc, the first of which is capable 

 of being wetted with water, while the other pos*essei 

 that kind of unctuosity which prevents the water from 

 adhering to it. 



M. Hauy suspended, by a very fine thread, a small 

 square plate of talc, so that the lower part of it was im- 

 mersed in the water. Into the same vessel, at the dis- 

 tance of some centimetres, he immersed the lower part 

 of a parallelnpiped of ivory, so that one of its faces was 

 parallel to the plate of talc. The ivory was made to 

 advance towards the talc in this state of parallelism, 

 and wan stopped at short intervals, in order to shew 

 that the effect of the motion communicated to the fluid 

 was insensible in the experiment. When the paral- 

 leloprped of ivory, moving with great slowness, ap- 

 proached very nearly to the talc, the latter moved sud- 

 denly into contact with the ivory. In separating the 

 two bodies, the ivory was wetted to a certain height 

 above the level ; and in repeating the experiment be- 



