742 MECHANICAL LAWS OF GROWTH. 



by shorter ones. If we designate the energy of growth of the internodes I, II, III, 

 &€., by Ej, Eg, E3, &€., we get the series — 



I II III IV V VI VII VIII 

 E, < Eg < E3 < E, > E, > Eg > E, > Eg. 



With this increase and decrease in the energy of growth of the various inter- 

 nodes of a stem is usually associated a similar relationship between the size of their 

 leaves, the lower ones forming smaller, the upper ones larger leaves, and then a 

 largest of all (or whorl of largest leaves), usually followed again by smaller ones\ 

 The secondary roots also which spring from the same primary root show similar 

 relationships, the first attaining a smaller length than those that follow, and these 

 being again followed by a graduated succession of shorter ones. The same is the 

 case also with the lateral branches of an annual stem, as well as of trees, especially 

 when the order of development is distinctly monopodial. 



It seems probable that an investigation of the zones of a root, stem, or leaf, 

 would also show that the energy of growth of successive zones first increases, then 

 reaches a maximum, and finally decreases. The cells in the zone in which the 

 maximum energy of growth prevails would also be the largest, while their number 

 would be least. This hypothesis is in harmony with Sanio's measurements^ of the 

 wood-cells of Pinus sylvestris ; for he found that the final constant size of the wood- 

 cells of the stem varies, increasing gradually from below upwards, till it attains a 

 maximum at a definite height, and then again decreases towards the apex. The 

 same is the case with the branches. 



If it were possible to predicate the exact energy of growth of every separate 

 zone of an organ, it would also be possible, from the fact that every zone has its 

 separate period of growth, to determine a grand period for the whole organ itself 

 The maxima of rapidity of growth attained in the successive zones first rise and 

 then fall ; the duration of growth also of the zones probably at first increases and 

 afterwards diminishes. Consequently the measurements of the whole organ represent 

 the sum at first of only few and small partial increments, later of more numerous 

 and larger ones ; finally the sum of the partial increments diminishes, because the 

 number of zones growing at any one time and the energy of their growth alike 

 diminish. Further investigation will show whether this hypothesis, which is at least 

 an approximate one, is correct. 



If the increments of length of an internode, stem, or leaf, in short intervals of 

 time such as half-an-hour or an hour, are compared, it is usually found that they do 

 not increase and then decrease regularly, but irregularly, the growth being sometimes 

 greater, sometimes smaller. If the grand curve of growth is constructed directly 

 from them, it does not assume the form of a continuous curve, but shows a number 

 of small zigzags, which however disappear, if, for example, the interval is extended 



' This phenomenon has not at present been sufficiently investigated. In many stems, especially 

 creeping ones, when the leaves have reached a certain size, this size remains constant in a long 

 series of leaves before any decrease occms. 



2 Jahrb. fiir wissensch. Bot. 1872, vol. VII, p. 402. By a 'constant' size of the wood-cells I 

 understand that which they possess in their later annual growths ; in the inner annual rings they 

 gradually increase, until in the following ones they attain a constant size. 



