202 On the Horizontal Motion of Floating Bodies, 



will be horizontal, and we may replace the horizontal effects 

 of the interior meniscus by that of the horizontal tangent 

 plane. There then remains to be considered only the hydro- 

 static tension (fig. 3) or pressure (fig. 4) due to the liquid 

 between the free horizontal surface and the tangent plane, by 

 which, in either case, the plates will be urged together. The 

 amount of the action is known when the elevation of the 

 tangent plane is known. 



In the remaining case, in which the nature of one plate (A) 

 on the interior side is such that if it alone were present the 

 liquid would be depressed, while at the other plate (B) it is 

 raised, the difficulty lies, not in applying the principle we 

 have obtained, but in previously ascertaining the configura- 

 tion of the liquid between the plates to which we have to apply 

 it. It will be observed that in the cases just dealt with a 

 knowledge of this configuration has been taken for granted. 



It is easy, however, by following in the steps of Laplace, 

 and more particularly of Poisson, to obtain this preliminary 

 information. 



If the acute angle of contact a> at the plate A is equal to 

 the corresponding angle w! at the plate B, then there must 

 always be a line F of contrary flexure in the surface midway 

 between the two plates whatever their distance apart ; and 

 this line must be at the level of the exterior free surface, 

 since at this level there is no hydrostatic pressure, and there- 

 fore no curvature of the surface. When the plates are far 

 apart the surface at F is horizontal, and there will be neither 

 attraction nor repulsion of the plates. When the plates are 

 near together the surface will be inclined at F (as in fig. 5); 

 and from what has been said we know that the hydrostatic 

 effect of the depression and elevation on either side of F is 

 exactly such as to counterbalance the diminution of the hori- 

 zontal component of the surface-tension at F, so that the 

 plates may be regarded as drawn together by that component, 

 whereas they are drawn apart by the full amount of the sur- 

 face-tension. Consequently they recede from each other. 

 There is no residual hydrostatic force involved. 



(The apparent repulsion of a wetted floating object from 

 the edge of a glass of water filled above the brim is a com- 

 mon instance in which the obliquity of the surface at one side 

 of the object is very obvious and the effect very striking.) 



If one of the acute angles of contact, say co, at the plate A 

 (fig. 6) be greater than the other, &/, at the plate B, then, if 

 we begin with the plates far apart, we see that, as in the last 

 case, there will at first be neither attraction nor repulsion, 

 but that the line of contrary flexure F must be nearer to the 



