842 
MECHANICS OF GROWTH. 
like W\ the part S on the contrary the upward curvature, as S'. It is self-evident 
that each of these curvatures can only result from the growth, equal on all sides 
when the organ is erect, having now become unequal on the upper and under sides, 
the convex growing in both cases more quickly than the concave side. 
If we now apply the results of my experiments on internodes and nodes of 
Grasses which curve upwards to the simple tube, the growth is found to be more 
rapid on the convex under side, less rapid on the upper side of the upwardly curved 
part, than when it grew erect. It may be assumed, from Ciesielski's measurements of 
roots, that when the filament curves downwards the growth has been more rapid on 
the convex upper side, less rapid on the concave under side, than if the curved part 
had grown onwards in a vertical direction. In other words, when the filament is 
placed in a horizontal position the growth is accelerated on the upper side of the 
positively geotropic part and on the under side of the negatively geotropic part, but 
always retarded on the opposite sides. 
If therefore we assume that in Fig. 482 ^ the two side walls of a transverse disc 
of the part S of the filament when in an upright position had lengthened in a definite 
time to the equal lengths 0 0 and u u, it would have remained straight ; but if the 
Fig. 482.— Diagram for illustrating geotropic upward and downward curvature. 
tube had been placed horizontally during this time, the lower side would have attained 
the greater length u u, the upper side the shorter length 0' o\ and the piece must in 
consequence become curved. Exactly the opposite would be observed, as shown in 
Fig. 482 C, if the growing piece belonged to the part W oi the filament. 
If now the unicellular filament A were supposed divided by transverse and lon- 
gitudinal divisions into a tissue consisting of a number of layers of cells ; or if, what 
amounts to the same thing, a stem of a seedling were supposed to be substituted for 
the part -S" of the filament, and a root for the part the same phenomena would 
occur, as experiments have shown, in every cell of the growing part, as those pre- 
viously observed in the filament. In the part 6" every cell would grow more rapidly 
on the under side, less rapidly on the upper side than if the part were upright, the 
reverse in the part W. We should find that in S both the upper and under sides of 
any cell e. upper and under in relation to the radius of the earth) are longer than 
those of the cells situated above it, the reverse in PF; in other words, that every indi- 
vidual cell of a part which shows geotropic curvature behaves in the same way as if 
the part previously straight were held firmly by the two ends and then bent. This 
will be made clearer to the student if in the portion of the curved part included in 
