THE ORDER OF CELL-DIVISION 



47 



arrangement is of use in studying the divisions and grouping of the cells 

 in the tissues or growing organs. It must, however, always be remembered 

 that all such geometrical constructions are only of value as representations 

 of actual arrangements in the tissues, and do not indicate or explain the 

 organizing activity which produces them in organs of very dissimilar 

 morphological value. The geometric grouping of the cell-walls will never 

 afford any insight into the processes which determine and govern growth 

 and cell-division, and hence only a short account of the commoner modes 

 of arrangement need be given l . 



The simplest cases occur in the cell-filaments of algae and of hairs, in 

 which the dividing walls 

 are at right angles to 

 the side walls. By the 

 concrescence of such 

 cell-filaments with rect- 

 angular outlines to form 

 a plate or quadratic col- 

 umn, we get a tissue in 

 which the dividing walls 

 are parallel to the planes 

 of symmetry in a corre- 

 sponding crystal of the 

 regular system. A simi- 

 lar crystalline arrange- 

 ment, in which the layers 



nf <-^11o rnrr&cmnnA f/-> 



the lamellae of the crys- 



tal, can be produced by the continuous and regular division of a cell and 



its segments into similar halves. 



If the growing end of a filament broadens laterally it will segment 

 at right angles to the transverse walls. This takes place in the fan-shaped 



FIG. II. Melohesia Leiolisii seen from the upper surface. A number of 

 the dividing-walls are omitted on the right. (After Kosanoff and Sachs.) 



1 For details see Sachs, Arbeit, d. Bot. Inst. in Wiirzburg, 1878, Bd. II, pp. 46, 185 ; Lectures on 

 Physiology (Clar. Press), 1887, pp. 431, 448; also Goebel, Entwickelungsgesch. d. Pflanzenorgane, 

 1883, p. 136; Schwendener, Monatsb. d. Berl. Akad., 1880, p. 412 ; Haberlandt, Physiol. Anat., 

 1896, 2. Aufl., p. 67. [Church (Annals of Botany, Vol. xv, 1901, p. 482) has recently endeavoured 

 to establish an explanation of phyllotaxis upon a similar geometrical basis. He considers that the 

 leaf-primordia primitively arise in the spaces formed by the intersections at right angles of oppositely 

 winding logarithmic spirals, and that the adult phyllotaxis (Archimedean spirals reduced on elongated 

 stems to practically parallel straight lines or orthostichies'} is produced by secondary modification of 

 the primitive arrangement. The latter is supposed to be the direct physical result of the mechanical 

 distribution of energy within the protoplasmic substance of the plant-apex (I.e., p. 488), and is 

 considered to be the natural corollary to the orthogonal intersection of the dividing-walls in 

 growing tissues. There are, however, exceptions to the latter, and similarly it has yet to be shown 

 that the above theory applies to the arrangement of all leaf-primordia. Cf. Church, On the Relation 

 of Phyllotaxis to Mechanical Laws, 1901-2. See also Vochting, Ueber den Sprossscheitel derZz'ar/<z 

 ^ulgaris, Jahrb. f. wiss. Bot., Bd. XXXVIII, 1902, p. 83.] 



