822 
MECHANICS OF GROWTH, 
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 the stems of annual plants, 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 be permissible to ascribe a special energy of growth to each separate 
zone of an organ, it becomes possible to understand how it is that, as is actually 
the case, every zone has its separate period of growth, and that a grand period for 
the whole organ itself may be determined. 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, until 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 investi- 
gation 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 
from one to three hours or more. These phenomena I call irregular variations 
of growth ^ They appear to result from the plant being subjected to continual 
small variations of temperature, air, light, and moisture of the soil, which alter the 
turgidity, and therefore the extensibility and elasticity of the growing cells. I come 
^ 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 occurs. 
^ Jahrb. für wissensch. Bot. 1872, vol. VII. p. 402. By a 'constant' size of the w^ood-cells I 
understand that which they possess in the later annual rings ; in the inner annual rings they 
gradually increase, until in the following ones they attain a constant size. 
^ For further details see Reinke, Verhandl. des bot. Vereins für die Provinz Brandenburg, 
Jahrg. VII ; and Sachs, Arbeit des bot. Inst, in Würzburg, Heft II. p. 103. [See also Drude, Die 
stossweisen Wachsthumsaenderungen in der Blattentvvickelung von Victoria regia, Halle i88t.] 
