thread. But even where one dimension only is relatively small, as for instance in a flattened plate, our problem is so far simplified that we see at once that the partition cannot be parallel to the extended plane, but must cut the cell, somehow, at right angles to that plane. In short, the problem of dividing a much flattened solid becomes identical with that of dividing a simple surface of the same form.
There are a number of small Algae, growing in the form of small flattened discs, consisting (for a time at any rate) of but a single layer of cells, which, as Berthold shewed, exemplify this comparatively simple problem; and we shall find presently that it is also admirably illustrated in the cell-divisions which occur in the egg of a frog or a sea-urchin, when the egg for the sake of experiment is flattened out under artificial pressure.
Fig. 144 (taken from Bertholdãs Monograph of the Naples Bangiaciae) represents younger and older discs of the little alga Erythrotrichia discigera; and it will be seen that, in all stages save the first, we have an arrangement of cell-partitions which looks somewhat complex, but into which we must attempt to throw some light and order. Starting with the original single, and flattened, {359} cell, we have no difficulty with the first two cell-divisions; for we know that no bisecting partitions can possibly be shorter than the two diameters, which divide the cell into halves and into quarters. We have only to remember that, for the sum total of partitions to be a minimum, three only must meet in a point; and therefore, the four quadrantal walls must shift a little, producing the usual little median partition, or cross-furrow, instead of one common, central point of junction. This little intermediate wall, however, will be very small, and to all intents and purposes