THE MECHANISM OF CURVATURE 239 



It depends upon circumstances as to whether the total length of the 

 concave side increases or decreases during curvature. A shortening of the 

 concave side always occurs during the variation movements of pulvini, and 

 usually also during the nutation curvatures of thick and slowly growing 

 organs, whereas the concave side may in some cases actually lengthen 

 during the curvature of stems and roots capable of active growth. This is 

 due to the fact that during the relatively slow progress of the reaction 

 the general elongation of the curving zone is sufficient in amount to be per- 

 ceptible. Hence rapid curvatures might be expected to produce a shorten- 

 ing of the concave side, and this is absent or hardly perceptible in tendrils 

 because the thigmotropic excitation simultaneously awakens a pronounced 

 general acceleration of growth. On the other hand, during geotropic and 

 heliotropic curvature, the convex side grows more rapidly than normally 

 in spite of the general retardation of growth. It is, however, possible that 

 organs may exist in which stimulation produces a retardation of growth on 

 all sides, the convex side being merely that in which growth is least 

 retarded. 



Hofmeister l attached both ends of a straight piece of stem to the 

 under side of a horizontal sheet of glass. The resultant geotropic curvature 

 caused the concave side to be raised away from the glass, showing that 

 elongation had taken place on both sides. The same applies to heliotropic 

 curvature. Another method is to cover the surface with indian ink, the 

 cracks which appear showing that the geotropic curvature of some stems 

 involves an elongation of both sides, whereas in a grass-node only the 

 convex side elongates 2 . 



Sachs 3 placed marks of indian ink 2 mm. apart on roots and grew 

 them in various positions in loose earth behind glass plates. By means of 

 protractor scales marked on mica-plates, the radius of curvature and the 

 length of the marked segments of the concave and convex sides can be 

 determined. In the case of a vertical radicle of Vicia Faba the terminal 

 8mm. increased by 10-5 mm. in fourteen hours, and when placed hori- 

 zontally the root curved through an arc of 135, the concave side becoming 

 6-1 mm. longer, and the convex 108 mm., so that the growth of the middle 

 lamella was 8-4 mm. The geotropic curvature hence involved an accelera- 

 tion of growth of 0-3 on the convex side, and retardations of 4-4 and 2-1 mm. 

 on the concave side and in the middle lamella respectively. 



In the case of stems Sachs 4 measured the elongation by applying 



1 Hofmeister, Jahrb. f. wiss. Bot., 1863, B d. In > P- 86. 



2 Pfeffer, Druck- u. Arbeitsleistungen, 1893, p. 408. 



3 Sachs, Arb. d. bot. Inst. in Wiirzburg, 1873, Bd. I, p. 463; Noll, ibid., 1888, Bd. Ill, p. 507; 

 Macdougal, Botanical Gazette, 1897, Vol. xxni, p. 361. 



* Sachs, Flora, 1873, p. 324; Arb. d. bot. Inst. in Wiirzburg, 1872, Bd. n, p. 193. No 

 measurements have been made of the curvature of unicellular organs. 



