306 Dr. P. Groom. [Jan. 24, 



the successive branches, commencing at the base of the plants and ascending 

 the main stem, gradually change from the ascending-descending curve to a 

 purely descending one (see Curves 2 — 6 in fig. 1), or tend to do so. It is this 

 gradual change in the internode curve of the successive branches that explains 

 the two maxima in the internode lengths (and possibly in the rate of growth) 

 met with in branches. 



By reference to plants of different habit, and growing under different 

 climates or in different habitats (including water), it is proved that these 

 internode curves are characteristic of the species, and inherent though liable 

 to disturbance by external conditions. 



Alternate-leaved Chenopodiacece, both in the main axis and in the branches, 

 display a remarkable periodic zig-zag in the internode curve (see the curve 

 printed plain in fig. 2). By connecting the alternate ordinates, this can be 

 analysed into two consistent and often regular sub-curves (see the dotted 

 curves in fig. 2) ; one of these sub-curves is the " internode sub-curve," and 



Fig, 2. 



the other the " displacement sub-curve." By comparison of the curves of the 

 main axis and branches of Chenopodiacese and typical herbs, also between 

 those of alternate-leaved and opposite-leaved Chenopodiacese, as well as by 

 other means, it is shown that the displacement sub-curve represents the 

 distances up which one leaf at each successive node has been relatively 

 displaced from a primitively opposite arrangement. Both sub-curves of the 

 main axis assume the ascending-descending form, but in the successively 

 higher branches the internode sub-curve changes from the ascending-descend- 

 ing form to a purely descending one, while the displacement sub-curve tends 

 to do likewise, or does so, at a later stage. This inherent peculiarity of the 

 chenopodiaceous internodes sheds light upon the affinity of the family to the 

 Caryophyllacese, whose opposite leaves do not develop simultaneously ; and 

 there are indications that at least several, if not all, of the families comprising 

 the Centrospermse are opposite-leaved in reality, or, like the Chenopodiaceae, 

 in design. 



To test this theory of displacement, reference was made to the admitted 



