DISTRIBUTION OF THE GREEN LEAVES ON THE STEM. 405 



bud, in the most advantageous manner, quite independently of external influences, 

 without the knowledge, so to speak, of the conditions to which its foliage-leaves 

 will he exposed in the future, can only be explained by the specific constitution 

 of its protoplasm. Just as crystals are formed from the aqueous solution of a 

 salt which, according to the nature of the salt, are sometimes six-sided, sometimes 

 three-sided, whose surfaces are always the same in outline, and whose edges always 

 form exactly the same angles, so bands, bars, and partition-walls arise in the 

 growing cells, by which these cells become articulated and divided; and the shape 

 and position of these intercalated walls and their geometrical ratios are no less 

 definite in the most diverse plant species than are the surfaces of the crystals 

 arising from the salt solution. But that which applies to the plan of construction 

 of the individual cells must also apply to the plan according to which a group 

 of cells — a tissue, a growing shoot, a stem with its leaves, even the entire plant — 

 is constructed. The position on the circumference of the stem at which a leaf 

 originates is certainly not determined by chance, but is based upon the molecular 

 constitution and composition of the protoplasm of the species of plant in question; 

 and if the leaves on an oak-branch always arrange themselves in f phyllotaxis, 

 the constancy of the arrangement is neither more nor less remarkable than the 

 constancy of the size of the angles in an alum octahedron. 



It should be noted here, in this connection, that the geometrical arrangement 

 of the cells in simple elongated tissues, easily accessible to observation, is exactly 

 similar to the arrangement of the leaves on stems. For example, the cells on the 

 hair-like stigmas of grasses follow the one-third arrangement veiy beautifully. A 

 connection between the geometrical arrangement of the cells at the apex of a 

 growing stem, and the geometrical arrangement of the leaves on the same, may 

 now also be considered. A group of cells is formed out of each cell at the growing 

 point of the stem by the repeated intercalation of division-walls. If the position 

 of these dividing cells is geometrically defined, and if the partition-walls resulting 

 from their division assume definite directions in each species of plant, then the 

 arrangement of the cell-groups produced from these cells which build up the stem 

 must also be geometrically defined. Supposing now that from each of these groups 

 of cells which build up the stem a leaf arises, then the distribution of the leaves 

 on the circumference of the stem will be only a repetition of the distribution of 

 the cells at the growing point of the stem. In the simplest of all leafy stems, 

 in that of a moss-plant, this relation is noticeable enough; but in j^lants of more 

 complicated construction it is not so easily demonstrated. In these the constancy 

 of the geometric ratios of the cells at the growing point is beset with many 

 diSiculties, and the groups of cells produced from them are also much displaced 

 and distorted. Nevertheless in each form of plant a uniform plan of construction 

 very probably exists; and it may be taken for granted that in each species the 

 arrangement of the atoms in the protoplasm, the ai-rangement of the cells, and the 

 arrangement of the leaves, are based upon the same symmetrical construction. 



Indeed, even the displacements and torsions of the cells which occur in leafy 



