586 PLATEAU ON THE PH/EXOMENA OF A FREE LIQUID MASS 



of gravity, would belong to a perfectly free liquid mass ; thus 

 our processes will partially realize the figures of equilibrium of a 

 mass of this kind. The latter are far from being confined to the 

 sphere; but among them the sphere alone is capable of being 

 completely formed, the others presenting either infinite dimen- 

 sions in certain dii'ections, or other peculiarities which we shall 

 point out, and which equally render their realization in the com- 

 plete state impossible. 



Moreover, the results at which we shall arrive will constitute 

 so many new and unexpected confirmations of the theory of the 

 pressures exerted by liquids upon themselves in virtue of the 

 mutual attraction of their molecules, a theory, upon which the 

 explanation of the phaenomena of capillarity is based. 



Lastly, in our liquid figures we shall discover remarkable pro- 

 perties, which will lead us to some important applications. 



2. In order to guide us in our experiments, and also to enable 

 us to comprehend their bearing, we shall first consider the 

 question in a purely theoretic point of view. The action of 

 gravity being eliminated and the liquid mass being at rest, the 

 only forces upon which the figure of equilibi'ium will depend 

 will be the molecular attraction of the liquid for itself, and that 

 exerted between the liquid and the solid system to which we 

 cause it to adhere. The action of the latter force ceases at an 

 excessively minute distance from the solid ; hence in regard to 

 any point of the surface of the liquid situated at a sensible distance 

 from the solid, we have only to consider the first of the two 

 above forces, i. e. the molecular attraction of the liquid for itself. 



The general effect of the adhesive force exerted between the 

 liquid and the solid, is to oblige the surface of the former to pass 

 certain lines ; for instance, if a liquid mass of suitable volume 

 be caused to adhere to an ellij)tic plate, the surface of the mass 

 will pass the elliptic outline of the plate. At every point of 

 this surface, situated at a sensible distance from this mar- 

 gin, the molecular attraction of the liquid for itself alone is in 

 action. 



Let us now examine into the fundamental condition which all 

 points of the free surface of the mass must satisfy, in virtue of 

 the latter force. 



The determination of this condition and its analytical ex- 

 pression, are comprised in the beautiful theories upon which the 

 explanation of the phaenomena of capillarity are based, although 



