(3) The length of the arc _MP_ is equal to _a_ θ cot θ; and the value of this for the given angle is ·8751. This is as much as to say that the curved partition-wall which we are considering is shorter than a radial partition in the proportion of 8¾ to 10, or seven-eights almost exactly. But we must also compare the length of this curved “anticlinal” partition-wall (_MP_) with that of the concentric, or periclinal, one (_RS_, Fig. 147) by which the quadrant might also be bisected. The length of this partition is obviously equal to the arc of the quadrant (i.e. the peripheral wall of the cell) divided by √2; or, in terms of the radius, = π/2√2 = 1·111. So that, not only is the anticlinal partition (such as we actually find in nature) notably the best, but the periclinal one, when it comes to dividing an entire quadrant, is very considerably larger even than a radial partition. [Illustration: Fig. 147.] The two cells into which our original quadrant is now divided, while they are equal in volume, are of very different shapes; the {363} one is a triangle (_MAP_) with two sides formed of circular arcs, and the other is a four-sided figure (_MOBP_), which we may call approximately oblong. We cannot say as yet how the triangular portion ought to divide; but it is obvious that the least possible partition-wall which shall bisect the other must run across the long axis of the oblong, that is to say periclinally. This, also, is precisely what tends actually to take place. In the following diagrams (Fig. 148) of a frog’s egg dividing under pressure, that is to say when reduced to the form of a flattened plate, we see, firstly, the division into four quadrants (by the partitions 1, 2); secondly, the division of each quadrant by means of an anticlinal circular arc (3, 3), cutting the peripheral wall of the quadrant approximately in the proportions of three to seven; and thirdly, we see that of the eight cells (four triangular and four oblong) into which the whole egg is now divided, the four which we have called oblong now proceed to divide by partitions transverse to their long axes, or roughly parallel to the periphery of the egg. [Illustration: Fig. 148. Segmentation of frog’s egg, under artificial compression. (After Roux.)] ――――――――――