WITHDRAWN FROM THE ACTION OF GRAVITY. 415 



formation of the liquid ring by the action of the centrifugal force, it was said 

 that during the first moments this ring remains united to the metallic disk by a 

 very thin pellicle or sheet of oil. We now see to what order of facts this pel- 

 licle pertains. It is evidently of the same kind with all the films which we 

 have been considering in the preceding paragraphs of the present memoir. It ' 

 may be remarked here that this pellicle further establishes a difference between 

 the phenomena produced in my apparatus, phenomena which depend on mole- 

 cular attraction, and those which belong properly to the domain of astronomy, 

 and which depend on universal attraction. I shall show in another series that 

 the liquid figures of my first series differ essentially, by the equation of their 

 surfaces, from those which would be assumed by a planetary mass supposed to 

 be fluid. I will repeat, then, what I have already said in note 2 of § 62 of the 

 second series, namely, that from the experiment in question no induction can 

 be drawn in favor of a cosmogonic hypothesis. 



§ 9. It results from facts previously described that liquid films withdrawn 

 from the action of gravity affect, like full masses, determinate figures of equili- 

 brium. Now, it is easily demonstrable that these figures must be the same in 

 both cases. 



If, at a point of one of the two surfaces of such a film, we imagine a right 

 line perpendicular to that surface, it is clear that, considering the slight thick- 

 ness of the film, this line may be also regarded as perpendicular to the other 

 surface. Further, if a plane be made to pass by this common perpendicular, it 

 will cut the two surfaces by curves which may, without appreciable error, be 

 taken as identical. Consequently, at the points where the perpendicular pierces 

 the two surfaces, the curvatures of the two curves will be the same ; only, in rela- 

 tion to the liquid which f(5rms the film, one of these curvatures will be convex 

 and the other concave. If, then, the radius of the first be designated by p, that 

 of the second will be — p ; and as this result is general, it is equally applicable 

 to the principal curvatures, that is to say, to the greatest and to the smallest ; so 

 that if R and R' represent the two principal radii of curvature at one of the two 

 points considered, the two principal radii of curvature at the other point will be 

 — R and — R'. Hence the capillary pressures respectively corresponding to 

 these two points, and referred to the unity of surface, are (2d series, § 4) for 



the first, P+— i -f7"f~p-, I and for the second, P — -—a -p+p, |» P being the 



pressure which a plane surface would occasion, and A a constant which de- 

 pends on the nature of the liquid. 



Now, these two pressures being opposed, they give a resultant equal to their 



difference, namely, to A a -p+77, V Then if the laminar figure is such that, 



in its whole extent, the above resultant is null, it is clear that equilibrium will 

 exist. If this condition is not fulfilled, the resultants corresponding respec- 

 tively to the different points of the figure will tend to drive these points in one 

 direction or the other, but in this case again equilibrium will be possible if the 

 laminar figure is closed, like the bubbles of § 7, and hence imprisons in its in- 

 terior a limited mass of alcoholic liquid ; for if the figure has then such a form 

 that the resultants in question have everywhere the same intensity, these forces 

 will evidently be destroyed by the resistance of the interior alcoholic mass. We 

 shall express, therefore, the general equation of equilibrium of laminar figures 

 by establishing the condition that the resultant is null or constant ; and for thia^ 



as the co-efficient A is constant and finite, it will suffice to put p+T7/=C!, 



Xv Xv 



where the quantity C may be null or constant. Now, this general equation 



