Floating Bodies under the Action of Capillary Forces. 199 



principles of (1) a definite surface-tension, (2) a definite 

 contact-angle, (3) a hydrostatic pressure within the liquid 

 increasing continuously with the depth and having the value 

 zero at the level of the free horizontal surface, so that any 

 liquid raised above this level is in a state of tension. 



We will consider the forces acting on one surface of a 

 vertical floating plate so broad that it is not necessary to take 

 into account the action at the edges. We will take first the 

 case in which the liquid is depressed at its contact. 



Fig. 1 represents this case. The level surface F G is 

 depressed to E. 



Produce the horizontal surface F G to meet the plate 

 inK. 



It is easy to show that the sum of the horizontal forces 

 acting on the plate is precisely the same as if the angle of 

 contact were a right angle and the surface were not de- 

 pressed, but left the solid at K. 



We need only consider points above the level of E ; and our 

 remarks will have regard to a strip of the surfaces whose 

 width in the direction perpendicular to the plane of the paper 

 is one unit. Let T be the surface-tension per unit of length. 

 If the liquid were not depressed, the plate would be pulled 

 to the left by a tension T, applied at K, and would be pushed 

 to the right by the hydrostatic pressure due to the depth of 

 liquid KE. 



The surface-layer between G and E may be regarded as 

 a smooth, weightless, perfectly flexible coherent sheet. The 

 hydrostatic pressures due to the depth of liquid between K and 

 E are applied everywhere at right angles to this surface, and 

 may be resolved into vertical and horizontal components. 

 The vertical components may be regarded as applied to the 

 solid at E where the surface-sheet on which they act is 

 attached to the solid. 



The sum of these vertical forces is obviously equal to the 

 weight of the liquid which would fill the space GKE; and 

 the solid is accordingly buoyed up precisely as if it were so 

 shaped as to displace this liquid, and the hydrostatic pressure 

 were exerted on the solid itself. 



In the same way the sum of the horizontal components 

 may be regarded as applied to the coherent plane surface F G 

 at G, whereby the effective pull of the free horizontal surface 

 on the solid is diminished by the precise amount of the hydro- 

 static pressure in question; so that the result of the depression 

 of the surface is to diminish the hydrostatic pressure on the 

 plate to the right by precisely the same amount as the surface- 

 pull to the left is diminished. 



