200 Mr. A. M. Worthington on the Horizontal Motion of 



Consider next the case of a plate of such a nature that the 

 liquid is elevated. This case is represented by figure 2; and 

 we can deal with it in exactly the same way. 



The surface-layer between Gr and E may again be regarded 

 as a smooth flexible coherent sheet; and it sustains a hydro- 

 static tension due to the liquid elevated above the surface and 

 equal in amount to the weight of the liquid that fills the 

 space Gr K E. The surface-sheet is attached to the solid at E, 

 which is therefore weighed down by a force equal to this 

 weight, and which is the vertical component of the surface- 

 tension at E. The effect of the horizontal components of the 

 hydrostatic tension exerted on the surface-sheet E G is ob- 

 viously equal to that exerted on the solid in the opposite 

 direction ; so that while the effective pull of the free hori- 

 zontal surface beyond Gr is diminished by this amount, an 

 equivalent hydrostatic tension is substituted. Hence, in either 

 case, whatever the value of the contact-angle, the total horizontal 

 force is the same as if there were no capillary elevation or de- 

 pression of the surface. 



It is to be observed also that the reasoning we have just 

 made use of is applicable to any portion of the liquid surface 

 of unit width enclosed between horizontal lines parallel to the 

 plate, and that the difference of the horizontal components of 

 the surface-tensions at the two lines is equal to the horizontal 

 hydrostatic pressure or tension on the surface between them. 



If the distance from the free horizontal surface of the nearer 

 bounding line be H, and of the further H + ?/ (perpendicular 

 distances being reckoned positive when measured away from 

 the free horizontal surface), and if D be the weight of unit 

 volume of the liquid, then the horizontal hydrostatic force in 

 question, being equal to that on a vertical rectangle of unit 

 width and height y and whose centre of gravity is at a dis- 

 tance H + ~ from the free surface, is 



(H+|),D; 



and if we designate by 6 the acute angle between the surface 

 and the horizontal at the level H, and by 6 the corresponding 

 angle at the level H+y, we may write the equation to the 

 surface 



t cos O -t cos 6= ( H + |)yD*, 



the origin being taken in the surface at the level H, where 



* It is a special case of this result that Pro f. Quincke makes use of in 

 his treatment of large flat drops and bubbles. It may be deduced from 



