24 DEVELOPMENT OF SIUM CICUTAEFOLIUM. 



As further evidence that this is the correct interpretation of the pin- 

 nate leaf, the diagrams shown in figs. lo and ii were constructed as 

 follows : All the leaves of a single stem of Sium cicutaefolhim (omitting 

 several which had disappeared at the base) were arranged in their 

 normal sequence, but side by side, with their rachises parallel and at 

 equal intervals. These rachises are represented by the horizontal lines 

 of the figures. The point of origin of each pair of leaflets was then 

 marked, and the figures were completed by connecting with lines the 

 points of origin of leaflets assumed to be homologous. In fig. lo the 

 proximal leaflets, and in fig. ii the distal leaflets, are assumed to be 

 homologous. The basis for the interpretation of these figures is to be 

 found in the demonstration by Fraulein Tammes (1903) that the law 

 of periodicity underlies all morphological phenomena in such a way 

 that serially homologous characters increase regularly to a maximum 

 and then decrease, decrease regularly to a minimum and then increase, 

 or that they form a half period, i. e., they begin with the maximum and 

 end with the minimum, or vice versa. Even a most superficial inspec- 

 tion of the two figures discloses the fact that in one there is a simple 

 underlying law which would lend itself to ready formulation, while in 

 the other all is confusion. The characters which are represented in 

 these figures are the interfoliola or portions of the rachis between suc- 

 cessive pairs of leaflets. Homologous interfoliola are represented by 

 the portions of the horizontal lines included between any two consecu- 

 tive curves. In fig. 10 these interfoliola are seen to reach a definite 

 maximum length in the second leaf from the base of the figure and to 

 diminish continuously from that maximum upward until each in turn 

 is reduced to zero, as required by the law of periodicity. The only 

 irregularities appear in the two distal interfoliola of the third leaf from 

 the base of the figure and in the distal interfoliolum of the first and of 

 the fifth leaves from the base, these variations in the distal interfoliola 

 being in full accord with my view that this is the region of active dififer- 

 entiation and reintegration in the leaf. In fig. 11, on the other hand, 

 there is not a single instance in which a series of interfoliola assumed 

 to be homologous shows an increase to a definite maximum followed by 

 a continuous decrease. The law of periodicity is beautifully exemplified 

 in fig. 10, which is based on the assumption that the proximal leaflets 

 of one leaf are homologous with the proximal leaflets of every other leaf 

 of the same stem, while there is no indication of that law in fig. ii, in 

 which the distal leaflets are assumed to be homologous. Certainly no 

 more conclusive proof of the truth of my proposition could be asked. 



As in the case of the juvenile and senescent leaves, the sole basis for 

 the assumption that the base and apex of a leaf exhibit conditions which 



