352 MORPHOLOGY OF THE CEREBRAL CONVOLUTIONS. 



the two films is half that of the larger, in other terms, if we have p 1 =2 p the 

 formula gives r = p, in this case consequently the curvature of the partition 

 will be equal to that of the larger film. 



In order to complete the study of our laminar system it remains only to 

 inquire under what angles the two films and the partitions intersect one another. 

 With this view, let us remark that the small mass of the junction which pre- 

 vails along the entire common edge of these angles, and which was spoken of in 

 the preceding paragraph, must of itself have its equilibrium of figure. Now as it 

 has three surfaces, it is necessary that the curvatures of these should have to 

 one another a ratio which permits of this equilibrium. Hence it is evidently 

 requisite, for the equilibrium of the small mass, and consequently for the whole 

 system, that if we conceive this small mass cut by a plane perpendicular to its 

 axis, the three concave arcs which will limit the section shall be closely identical. 

 Now from this near identity it necessarily results that the two films and the par- 

 tition terminate at the small mass under angles either strictly equal or very 

 nearly so — angles consequently each of 120°, or which will differ from this value 

 by an unappreciable quantity. By considering liquid films as stretched mem- 

 branes we should equally arrive at the equality of the angles between three 

 films which join one another by the same liquid edge. We shall presently see 

 this result and those of the preceding paragraph verified by experiment. 



We have seen that the radius r of the partition is determined, when we 

 know the radii p and p 1 of the two films, by considering the relative value of the 

 pressures respectively exerted by these three portions of spherical caps on the 

 two quantities of included air. On the other hand, the consideration of the 

 conditions of equilibrium of the small mass of junction has led to this conse- 

 quence, that the two films and the partition must intersect one another under 

 angles of exactly or very near 120° ; and it is evident that this necessity of inter- 

 secting each other under angles of 120° may equally serve to determine the 

 radius of the partition. Now no relation between the two principles which 

 serve as the basis of these two determinations is to be seen a priori, and it may 

 be asked whether the two results coincide ; this I propose to examine. 



I will suppose two films forming originally two complete spheres, spheres 

 which have afterwards partially penetrated each other so as to give rise to a par- 

 tition, and shall imagine this whole system intersected by a plane passing through 

 the centre of the two films : it is clear that the centre of the sphere to which the 

 partition pertains will be found on the right line which contains the two above 

 centres. 



This being premised, it is plain that if the angles under which the two 

 films and the partition meet are of 120°, the radii of the two films brought 

 to a point of the line of intersection of the latter will form between them 

 an angle of 60°, and it will be readily seen that the radius of the partition 

 brought to the same point will also form an angle of 60° with that of the two 

 others to which it is nearest. 



