By a similar calculation we can shew that a _spherical_ wall, cutting off one solid angle of the cube, and constituting an octant of a sphere, would likewise be of less area than a plane partition as soon as the volume to be enclosed was not greater than about {350} one-quarter of the original cell[387]. But while both the cylindrical wall and the spherical wall would be of less area than the plane transverse partition after that limit (of one-quarter volume) was passed, the cylindrical would still be the better of the two up to a further limit. It is only when the volume to be partitioned off {351} is no greater than about 0·15, or somewhere about one-seventh, of the whole, that the spherical cell-wall in an angle of the cubical cell, that is to say the octant of a sphere, is definitely of less area than the quarter-cylinder. In the accompanying diagram (Fig. 138) the relative areas of the three partitions are shewn for all fractions, less than one-half, of the divided cell. [Illustration: Fig. 138.] In this figure, we see that the plane transverse partition, whatever fraction of the cube it cut off, is always of the same dimensions, that is to say is always equal to _a_^2, or = 1. If one-half of the cube have to be cut off, this plane transverse partition is much the best, for we see by the diagram that a cylindrical partition cutting off an equal volume would have an area about 25%, and a spherical partition would have an area about 50% greater. The point _A_ in the diagram corresponds to the point where the cylindrical partition would begin to have an advantage over the plane, that is to say (as we have seen) when the fraction to be cut off is about one-third, or ·318 of the whole. In like manner, at _B_ the spherical octant begins to have an advantage over the plane; and it is not till we reach the point _C_ that the spherical octant becomes of less area than the quarter-cylinder. [Illustration: Fig. 139.]