CELL-DIVISION AND DEVELOPMENT. I 29 



terms the confocal ellipses the periclines, and the hyperbolas 

 anticlines, the division of the protoplasmic disc being produced 

 by an alternation of these two kinds of cleavage planes. The 

 result of this mode of division is a number of cells arranged in 

 definite curves, each cell belonging to two curves which cross 

 one another at right angles, one of the curves being portion of 

 an ellipse while the other is portion of an hyperbola. The 

 periclines and anticlines, in other words, form what geometri- 

 cians term orthogonal trajectories, and if Sachs' law be valid 

 we must expect to discover in plant and animal tissues indica- 

 tions of the occurrence of these trajectories. 



We do not, it is true, find either in plants or animals a mathe- 

 matical regularity of the periclines and anticlines, but an exam- 

 ination of plant embryos, or even of adult individuals of some 

 of the simple plants, shows unmistakable indications of their 

 existence. For instance, in Fig. 4 is shown a specimen of the 

 alga Melobesia, in which the periclines and anticlines, though 

 modified by the fan-like form characteristic of the species, 

 nevertheless are clearly recognizable, and, so far as animals are 

 concerned, orthogonal trajectories are to be found in the early 

 stages of some of the Crus- 

 tacea,^ where the ectodermal 

 cells form a single layer lying 

 on the surface of the yolk, as 

 in the naupliar region of the 

 embryo of the Crayfish. The 

 general form of the embryo 

 here, as in Melobesia, modifies 

 the arrangement somewhat, 

 and is a factor which must 



Fig. 4. (After Sachs.) 



be taken into consideration. 



If, for instance, instead of an elliptical disc, which is not infre- 

 quent in plant forms, a circular one had been taken as a basis 

 on which to estimate the arrangement of the division-planes 

 under Sachs' law, then there being but a single focus, all the 

 anticlines would pass through that focus, and, furthermore, if a 



1 H. Reichenbach : Studien zur Entwickelungsgeschichte des Flusskrebses. 

 Abhandl. Senckenbg. Naturf. Gesellsch., XIV, 1886. 



