354 THE FORMS OF TISSUES [ch. 



is (as in our flattened disc) a median vertical one. And 

 likewise, the hemisphere itself can be bisected by no smaller 

 partition meeting the walls at right angles than that median 

 one which divides it into two similar quadrants of a sphere. 

 But if we produce our hemisphere into a more elevated, conical 

 body, or into a cylinder with spherical cap, it is obvious that there 

 comes a point where a transverse, horizontal partition will bisect 

 the figure with less area of partition-wall than a median vertical 

 one (c). And furthermore, there will be an intermediate region, 

 a region where height and base have their relative dimensions 

 nearly equal (as in b), where an obhque partition will be better 

 than either the vertical or the transverse, though here the analogy 

 of our triangle does not suffice to give us the precise limiting 

 values. We need not examine these limitations in detail, but we 

 must look at the curvatures which accompany the several con- 

 ditions. We have seen that a film tends to set itself at equal 

 angles to the surface which it meets, and therefore, when that 

 surface is a solid, to meet it (or its tangent if it be a curved surface) 

 at right angles. Our vertical partition is, therefore, everywhere 

 normal to the original cell- walls, and constitutes a plane surface. 

 But in the taller, conical cell with transverse partition, the 

 latter still meets the opposite sides of the cell at right angles, and 

 it follows that it must itself be curved; moreover, since the 

 tension, and therefore the curvature, of the partition is every- 

 where uniform, it follows that its curved surface must be a portion 

 of a sphere, concave towards the apex of the original, now divided, 

 cell. In the intermediate case, where we have an oblique partition, 

 meeting both the base and the curved sides of the mother- cell, 

 the contact must still be everywhere at right angles : provided 

 we continue to suppose that the walls of the mother-cell (like those 

 of our diagrammatic cube) have become practically rigid before 

 the partition appears, and are therefore not affected and deformed 

 by the tension of the latter. In such a case, and especially when 

 the cell is elhptical in cross-section, or is still more compHcated 

 in form, it is evident that the partition, in adapting itself to 

 circumstances and in maintaining itself as a surface of minimal 

 area subject to all the conditions of the case, may have to assume 

 a complex curvature. 



