S64 FOURTH REPORT 1834. 



of the concavity or convexity as the principal cause of the phse- 

 nomenon of elevation or depression, a mode of speaking to 

 which some have objected apparently because it does not expli- 

 citly point to the nature of the forces to which the observed ef- 

 fects are due. This manner, however, of referring capillary ef- 

 fects to the concavity or convexity of the fluid surface, is con- 

 venient in the explanation of phaenomena ; for we may say in 

 general, that wherever the fluid is bounded by a curve surface, 

 it is acted upon at each point by a force tending from the surface 

 towards the centres of the curvature at that point. 



In this way Laplace explains the well known fact, that a drop 

 of water put in a slender conical tube, having both ends open 

 and its axis horizontal, will move towards the smaller end. The 

 surface of the drop will be concave towards both ends of the 

 tube, but with a greater curvature on the side directed to the 

 smaller end than on the other. The drop will therefore be urged 

 by two forces in opposite directions ; but the forces being pro- 

 portional to the curvatures, the greater force will be that which 

 urges it towards the vertex of the cone. If a drop of mercury 

 were inserted, its surface would be convex towards both ends 

 of the tube, and the greater curvature would again be at that 

 part of the drop which is nearer the smaller end. Therefore, of 

 the two forces directed from the curved surfaces to the centres 

 of curvature, that will prevail which urges the drop towards the 

 base of the cone. It follows from the constancy of the angle of 

 contact, that the surfaces of the two ends of the drop, whether 

 it be of mercury or water, are similar segments of spherical sur- 

 faces. Their curvatures are therefore inversely as their distances 

 from the vertex of the cone ; and the difference of the curvatures, 

 to which the diiference of the forces which urges the drop is pro- 

 portional, will vary inversely as the product of these distances, 

 if the length of the column into which the drop is formed be 

 given, that is, this length being small, nearly as the square of 

 the distance inversely of the middle of the drop from the vertex 

 of the cone. 



As the fundamental equation obtained above admits of being 

 successfully treated whenever the surface of the fluid contained 

 in a capillary space is one of revolution, it may be employed to 

 determine the capillary action which takes place between two 

 cylindrical surfaces having a common axis and distant from each 

 other by a small interval ; for the surface of the inclosed fluid 

 will evidently be in this case a surface of revolution. The re- 

 sult of the analj'tical calculation is, that the fluid will be raised in 

 this space to the same height as in a tube of which the radius is 

 equal to the interval between the cylindrical surfaces. If the 



