of Floating Bodies under the Action of Capillary Forces. 201 



0=6 . With the origin at the level of the free horizontal 

 surface the equation becomes 



T COS 6 — T COS 0= «2— . 



We will now apply the principle to all possible cases. Of 

 the case of a single floating plate, whose sides are of different 

 materials so that the liquid is raised at one side and depressed 

 or less raised at the other, the explanation is obvious. There 

 can be no horizontal displacement, since the total horizontal 

 force on either side is the same as if there were no capillary 

 elevation or depression at all. 



Consideration, however, of the position of the points of ap- 

 plication of the surface-tension, and of the centres of hydro- 

 static pressures or tensions, shows that the plate will tend to 

 topple towards the side on which the liquid is elevated or 

 more elevated. 



When two parallel plates are concerned, we see then that the 

 nature of their exterior surfaces is immaterial, since we may 

 always imagine the exterior meniscus replaced by a plane 

 horizontal surface. 



If the interior surfaces are such that the liquid would be 

 {a) raised or (b) depressed by either alone, then, whatever the 

 value of the interior contact-angles, the lowest portion of the 

 meniscus (as in fig. 3), or the highest portion (as in fig. 4), 



the usual form of the differential equation to the surface very shortly as 

 follows. 



This equation referred to an origin at an elevation H above the free 

 surface is 





T Ir 



l "o' : 



= - JJ(M+y), 





and becomes 



W 



T 

 P 



= -D(H+y) 





when one curvature vanishes, 

 for p its value 



, as in the case under consideration. 



ds _ dy 

 d6 sin 6 d& 



Writing 



we get 



Tsin$dd= - 



-DCHdJH-ycfc), 





or 



TCOS0 



=0- 



-(H+!)yD; 





and when y=0, 











tcos0=tcos0 o =C; 

 .-. tcos^ -tcos^ = (H-J-|Kd. 

 Phil. Mag. S. 5. Vol. 15. No. 93. March 1883. 



