and Repulsions of Small Floating Bodies. 55 



bounding film which envelops such a floating composite plate 

 must necessarily be exactly the same in all parts of its peri- 

 meter ; so that it is impossible for the forces due to capillary 

 actions to disturb the equilibrium of such a body while float- 

 ing in the liquid so long as its component plates are main- 

 tained at a fixed distance apart. It is obvious that the tensile 

 reaction can only tend to press the plates together ; it cannot 

 produce a motion of translation. It is almost needless to add 

 that in the cases previously considered, where the floating solids 

 were separated and movable, the conditions of equilibrium 

 were disturbed by the modifications of the interfering menis- 

 cuses due to their proximity; and these conditions of equili- 

 brium could only be realized by mutual contact, or by reces- 

 sion beyond the reach of disturbing influences. 



It is likewise evident that in cases 1 and 2 the interfering 

 and modified united bounding films tend in each case to assume 

 a minimum perimeter, which is only secured when the two 

 bodies are brought into contact. In the composite plate above 

 considered this condition is instantly realized upon partial im- 

 mersion in the liquid. This principle explains why it is prac- 

 tically so much more difficult to experimentally verify case 3 

 than cases 1 and 2. For in case 3, when the floating bodies 

 are brought so near to one another that the interfering menis- 

 cuses form a common enveloping film, the principle of mini- 

 mum bounding perimeter prevails, and the verification of 

 apparent repulsion fails; for the two bodies are drawn together 

 as in cases 1 and 2. The fact that in such cases floating bodies 

 apparently repel one another at a certain distance ; but on 

 nearer approach apparently attract, is noticed both by Laplace 

 and by Poisson as a deduction from their respective theories 

 of capillarity, and was experimentally verified by the Abbe 

 Haiiy and others. 



Finally, it may be proper to add that the reaction of the 

 surface-tension of liquids always tends to reduce the surface to 

 the smallest area which can be enclosed by its actual boundary. 

 This fundamental principle of the tensile reaction tending to 

 reduce the bounding area or bounding perimeter to a minimum 

 affords a very simple and elegant explanation of the whole 

 class of phenomena under consideration*. As already inti- 

 mated, cases 1 and 2 evidently come under this principle; for 

 the common bounding perimeter produced by the union of the 

 meniscuses, in tending by virtue of its elastic reaction to become 



* This principle is very elegantly deduced by the great geometer Gauss 

 by the application of the principle of mutual velocities. He shows that 

 the condition of capillary equilibrium is that the expression for the force- 

 function shall be a minimum {vide op. cit. ante). 



