WIXnORAAVN FROM THE ACTION OF GRAVITY. 593 



gravity ; the analytical condition of paragraph 5 would then be 

 satisfied as regards this mass. Now at each point of the common 

 surface of the two media, the radii of curvature p and p' have the 

 same absolute values, both in the case of the immersed mass 

 and of the hollow figure of the surrounding liquid, except that 

 their signs are contrary, according as they are considered as re- 

 ferring to one or the other of the two liquids. To pass from one 

 of the two figm"es to the other, we need therefore only change 

 the signs p and p', or, what comes to the same thing, change 

 the sign of the constant C. Changing the sign does not destroy 

 the condition of equilibrium ; and consequently, if the immersed 

 mass is in equilibrium as regards its own molecular attractions, 

 the same will hold good in the case of the hollow figure of the 

 surrounding liquid. The pressures of the latter liquid cannot 

 therefore by themselves produce any modification in the figure 

 of equilibrium of the immersed mass. 



Let us now introduce the second kind of molecular actions, 

 i. e. the mutual attraction of the two liquids, and see what will 

 be its effects. Let us imagine, for an instant, that the immersed 

 mass, or, for the sake of fixing the ideas, the mass of oil in our 

 experiments is replaced by the same kind of liquid as that which 

 surrounds it, i. e. by the alcoholic mixture. In other words, 

 supposing the vessel to contain only the alcoholic mixture and the 

 solid system, let us limit, in the imagination, a portion within 

 the liquid, of the same figure and dimensions, and situated in the 

 same manner as the preceding mass of oil. It is then clear that 

 the molecules of the mass near its surface being, like those of 

 the interior, completely surrounded by the same kind of liquid 

 beyond their sphere of activity, these molecules will no longer 

 exert any pressure upon the mass; consequently the pressures 

 which would exist if this mass could be isolated, must be con- 

 sidered as destroyed by the attractions emanating fi-om the sur- 

 rounding liquid. The latter forces are therefore all equal and 

 opposite to the pressures in question. Now as these are all 

 equal to each other in accordance with the figure which we have 

 attributed to the imaginary surface of the mass, the attractions 

 emanating from the surrounding liquid w ill also all be equal to 

 each other. If we now replace the mass of oil, the attractions 

 emanating from the surrounding liquid may certainly alter in 

 absolute value, but it is evident that they will retain their direc- 

 tions, and that they will remain equal to each other ; we there- 



