358 THE FORMS OF TISSUES [ch. 



tension^ both external and internal to the cell, play their part 

 in the determination of its partitions, and that the answer to 

 our problem is not to be given in a word. How fundamentally 

 important it is, however, in spite of all conflicting tendencies and 

 apparent exceptions, we shall see better and better as we proceed. 



But let us leave the exceptions and return to a consideration 

 of the simpler and more general phenomena. And in so doing, 

 let us leave the case of the cubical, quadrangular or cylindrical 

 cell, and examine the case of a spherical cell and of its successive 

 divisions, or the still simpler case of a circular, discoidal cell. 



When we attempt to investigate mathematically the position 

 and form of a partition of minimal area, it is plain that we shall 

 be dealing with comparatively simple cases wherever even one 

 dimension of the cell is much less than the other two. Where two 

 dimensions are small compared with the third, as in a thin cylin- 

 drical filament Uke that of Spirogyra, we have the problem at its 

 simplest; for it is at once obvious, then, that the partition must 

 lie transversely to the long axis of the 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 Berthold's 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. 



