110 Scientific Proceedings, Royal Dublin Society. 



then the effect of the ringing ought to have resulted in an acceleration in the rate 

 of growth. This, however, was not the case, for the banking np of organic substances, 

 which was indicated by the relatively greater weight of the basal segments of the 

 stem of the ringed plants (cf. Table 2), did not increase the rate of growth. From 

 this it seems legitimate to conclude that the rate of growth was not influenced by 

 the supply of organic nutrients available. It will be therefore evident that no 

 correlation can exist between the rate at which the subterranean storage organs 

 increased in weight and the activity of the cells of the apical meristem. 



It would seem that for a given complex of external conditions the rate of growth 

 in Bitter Cassava is determined by autogenous changes within the cells of the 

 apical meristem ; possibly, as suggested by Eeed, by the catalytic activity of these 

 cells. The experimental results are, in fact, in harmony with this view, provided 

 it be assumed that growth proceeded in two cycles, each of which followed the 

 course of an autocatalytic reaction, and provided also it be assumed that these two 

 cycles ran concurrently over a considerable portion of the latter period of growth. 

 The differential equation 



-zr = kx (a - x), 

 at 



which is characteristic of an autocatalysed reaction (cf. Robertson (7)), has been 

 employed in making the computations shown on Table 3. In this equation x repre- 

 sents the height of the stem, a the final height which would have been attained in 

 each cycle, and h is a constant. "When integrated the above equation becomes 



log. -^ = K{t-n 

 a - X 



where K= ah, and t' is the time at which the stem has grown to half its final 



height for each cycle, that is to say, when x = -. By means of tables prepared by 



Eobertson, the constants K and the theoretical values of x are obtained for each 

 cycle from the observed values. The values taken for a and t' and the values of 

 ^derived from the observations made on the unringed group of plants will be seen 

 in Table 3, the logarithms being reduced to the base ten and K modified accordingly. 

 It will be observed that the calculated and the experimentally obtained values of 

 X are on the whole in good accord. 



