MORPHOLOGY OF THE CEREBRAL CONVOLUTIONS. 351 



In this paper Plateau discusses the laws of the formation of partitions formed 

 by spherical liquid films such as are formed by the meeting of two or more soap 

 bubbles. Evidently as far as regards a general mathematical discussion the 

 expanding liquid films may represent the expanding cerebral substance as it 

 aggregates around certain centres of growth, whilst the partitions as formed by the 

 meeting of the liquid films will indicate the planes of fissuration. A brief outline 

 of the theory of Plateau will serve to show how the application may be made and 

 also as to whether, by means of it, any advance may be hoped for in establishing a 

 mathematical theory to explain the convolutional configuration of the cerebral 

 surface. 



Plateau's experiments were made with soap bubbles floating on water or 

 brought together when attached to a glass plate. Everyone is familiar with the 

 peculiar partition structures produced by inflating a number of bubbles of different 

 sizes upon the surface of some cohesive liquid, such as a mixture of soap suds 

 and glycerine. In a somewhat similar way we may consider the cerebral convex 

 as consisting of numbers of swellings growing from different centres, when the 

 fissures will represent the partition planes produced by their joint meeting. Of 

 course the conditions are vastly more complex in the case of the brain surface 

 than in those involved in the union of hemispherical liquid films, still the funda- 

 mental relations of the forces, leaving out secondary and tertiary complications is 

 of the same general nature ; and we shall be surprised to find the general unifor- 

 mity in results produced in some of the least interfered with regions of the cereb- 

 ral surface. 



Plateau first considers the case of two spheres of unequal size meeting each 

 other. 



Let p, p 1 and r be the radii of the spheres to which respectively appertain 

 the larger film, the smaller film and the partition, and let p, p 1 and q be the 

 respective pressures which they exert, in virtue of their curvatures, on the air 

 which bathes their concave faces. These pressures being 1 in the inverse ratio of 



their diameters and consequently of the radii, we shall have -i- = — and J-- = — r 

 but according to what has been seen above it is necessary for equilibrium, that 



we should have q = p' — p ; whence, 1 = i- ±- . Substituting for this 



q q 



last equation the above values of ±- and of — and solving for r, there results 



q q 



r = l P , a formula which gives the radius of the partition when we know 



p— p' 



those of the two films. If, for example, these two films pertain to equal spheres, 



we have p = p', and the formula gives r = infinity ; that is to say the partition 



is then plane, as we have already found it to be. If the radius of the smaller of 



1 5th Series U 22 and 28 

 44 JOTJRN. A. N. S. PHILA., VOL. X. 



