Apparent Attraction and Repulsion of Floating Bodies. 349 



equal to the distance of the plates. The cause which determines 

 this ratio is to be found in the above theory. For, in the case 

 of tubes, the action of the concave or convex surface upon 

 the elevated or depressed column is half of the action of two 

 spheres which have for radii the greatest and least radii of the 

 osculating circles to the surface at the lowest point. The tube 

 being flattened in any direction, the radius of the corresponding 

 curvature augments, and finally becomes infinite, when the flat- 

 tened sides of the tube become parallel plane surfaces. The 

 first part of the attraction of the surface being inversely as this 

 radius, will become zero, and there will remain only the term 

 depending on the other osculating radius, and the attractive force 

 is accordingly reduced one half. Such is the simple and rigor- 

 ous result furnished by the theory of Laplace. 



463. This theory serves to explain also, and with the same 

 simplicity, all other capillary phenomena. Thus, the ascent of 

 water between concentric tubes, and in conical tubes ; the curva- 

 ture which water assumes when adhering to a glass plate ; the 

 spherical form observed in the drops of liquids ; the motion of a 

 drop which takes place between plates, having a small inclination 

 to each other and to the horizon ; the force which causes drops 

 floating on the surface of a liquid to unite; the adhesion of plates 

 to the surface of a liquid, which is in many cases so great as to 

 require a considerable weight to separate them ; these effects, so 

 various, are all deduced from the same formula, not in a vague 

 and conjectural way, but with numerical exactness. 



On the apparent Attraction and Repulsion observed in Bodies float- 

 ing near each other on the Surface of Fluids. 



464. (1). If two light bodies, capable of being wetted, be 

 placed at the distance of one inch from each other on the surface 

 of a basin of water, they will float at rest, and without approach- 

 ing each other. But if they be placed at the distance of only 

 a small part of an inch, as two or three tenths, they will 

 together with an accelerated motion. 



