WITHDRAWN FROM THE ACTION OF GRAVITY. 231 



nature as tliose which we have cousidered throup;hout the preceding details, 

 towards the interior of tlie liquid to Avhich they belong, and these pressures 

 must consequently also impart a figure of equilibrium to the surface in intaglio ; 

 so that if the immersed mass of itself had no tendency to assume any one iigure 

 rather than anotlier, the surrounding liquid would give it a determinate one, by 

 compelling it to mould itself in the above hollow figure. This is why a bubble 

 of air in a liquid assumes the globular form, solely in consequence of the pres- 

 sures exerted by the liquid upon it. Kow let us suppose that the immersed 

 mass has assumed that figure which it would acquire in vacuo if really deprived 

 of gravity; the analytical condition of paragraph 5 would then be satisfied as 

 regards this mass. Now at each point of tne common surface of the two media, 

 the radii of curvature p and />' 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 referring to 

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

 the other, we need therefore only change the signs p and />', 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 efiects. 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. c, 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 Avithiu 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 Avill no longer exert any pressure upon the 

 mass ; consequently, the pressures which would exist if this mass could be 

 isolated must be considered as destroyed by the attractions emanating from 

 the surrounding 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 ac- 

 cordance with the figure which we have attributed to the imaginary surface of 

 the mass, the attractions emanating from the surrounding liquid will 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 evi- 

 dent that they will retain their directions, and that they Avil! remain equal to 

 each other. We therefore see that they Avill only diminish, by the same quan- 

 tity, all the pressures exerted by the mass of oil upon itself; consequently, as 

 all the differences remain equal to each other, the condition of equilibrium will 

 still be satisfied as regards that mass. It is evident that the same mode of 

 reasoning may be applied to the pressures exerted by the surrounding liquid 

 upon itself — pressures which will retain their directions, all of which will only 

 be diminished to the same extent by the attractions emanating from the oil, so 

 that the condition of equilibrium will still be satisfied as regards the hollow 

 figure of the surrounding liquid. Thus the whole of the molecular actions due 

 to the presence of the surrounding liquid will not tend in any way to modify 

 the figure of equilibrium of the immersed mass, which figure will, consequently, 

 be idetitically the same as if that mass were really void of gravity and were 

 placed in vacuo. We can, therefore, leave the surrounding liquid completelj' 



