196 Mr. J. T. Riley on Capillary Phenomena. 



directions, so that they can produce no horizontal motion. 

 The resultant force on A is thus the tension between the 

 liquid surface SQ and the solid ; and this force tends to move 

 A towards B. Similarly, the resultant force on B is the 

 tension between the liquid surface S' Q' and the solid ; and 

 this force moves B towards A. The two bodies are thus drawn 

 together. 



Case II. (fig. 2). In this case the liquid surface is de- 

 pressed in the neighbourhood of both bodies, and, as before, the 

 horizontal components of the surface-tension where the me- 

 niscuses touch the solids cancel out. It is at once evident 

 that the hydrostatic pressures from S to Q and from S' to Q' 

 on the external faces of A and B are unbalanced ; and they 

 therefore press the bodies together. 



Case III. (fig. 3). Here we find a depression of the 

 surface near one plate, and an elevation near the other. The 

 horizontal components of the tensions on both sides of A and 

 B will respectively destroy each other: the resultant hydro- 

 static pressure from P to S forces A towards the left, and the 

 resultant tension from M' to W pulls B to the right, and the 

 plates tend to separate. 



Case IV. (fig. 4). We have now to consider the equi- 

 librium of a single floating plate, with its surfaces so prepared 

 that they produce different degrees of capillary elevation. It 

 is very easy to see that, in an indefinite surface of the liquid, 

 no movement can take place. For the potential energy of 

 the surface cannot be diminished by any movement of the 

 plate; and therefore we conclude that the plate must be in 

 equilibrium, for otherwise its kinetic energy when moving 

 would have been produced without any diminution of potential 

 energy. But it is important to show that we arrive at the 

 same conclusion from an examination of the effects of the 

 capillary forces brought into play. The case does not offer 

 any ground for objection to Laplace's theory, as Dr. Thomas 

 Young insisted it did, nor to any mathematical theory from 

 which the fundamental equation given previously can be 

 deduced. 



Let the surfaces of the compound plate (fig. 6) be such 

 that we have on one side a capillary depression and on the 

 other a capillary elevation. For the equilibrium of the plate 

 we must have the horizontal component of tension H at Q + 

 hydrostatic tension from S to Q = horizontal component of 

 tension H at P + hydrostatic pressure from S to P. In 

 order to determine the hydrostatic tension and pressure, we 

 first find the pressure at any point in the curved surface. As 

 R' is infinitely great, the general equation reduces to p>—gpz 



