7o6 MECHANICAL LAWS OF GROWTH. 



and where (so long as direct observations are wanting) the most vigorous growth in 

 length or at least the commencement of its decrease may, from other indications, 

 be inferred. Both above and below, i. e. on older as well as younger parts of the 

 shoot (or of the single internode), the curvature is less, the radius of curvature 

 greater, and the regions of least pass insensibly into those of greatest curvature. 

 It follows that a long portion of a curved internode cannot in these cases be con- 

 sidered as an arc of a circle, and must not be treated as such in measurements 

 of length. It follows also that the radii of curvature spoken of in paragraphs b and c 

 represent only approximate values which can give but a rough idea of the curvature 

 observed in those cases. 



In the primary roots of seedlings of Vicia, Faba, Pisum, Zea, &c. from 5 to 

 15 cm. in length, I convinced myself by a similar series of experiments that the most 

 flexible and least elastic regions lay far below those where growth in length had 

 already completely ceased ^ 



{e) Sudden curvature of growhig shoots from a bloiu or concussion. If upright 

 growing shoots ^ are suddenly and violently struck below at a point where growth 

 has ceased, the curvature thus caused advances upwards in the form of a wave, so 

 that immediately after the blow which has been given to the lower part the apex 

 of the shoot is strongly bent, the concavity of the curvature lying on the side from 

 which the blow was received. The elasticity of the bent part causes the apex to 

 spring back immediately ; but when, as we have seen, the elasticity is very imper- 

 fect, the shoot retains a part of its curvature. As soon as the shoot has come to 

 rest after some oscillations, it may be observed that below the apex, where the 

 shoot is most flexible to an ordinary passive curvature, a permanent curvature is 

 established, the apex bending over, and always on that side from which the blow 

 was received. In many cases this phenomenon is produced by a single blow from 

 a stick, as e. g. in Fagopyrum, Lythrum, and Senecio, flower-stalks of Digitalis, 

 Cimicifuga, Aconitum, &c. ; in more rigid stems and the parts of those that are 

 less flexible and elastic, the bending over of the apex does not take place till after 

 three or four or even from twenty to fifty blows have been given to the lower 

 w^oody part ; the amount of curvature also varies in difl'erent plants. If shoots are 

 cut off low down so that a woody piece the growth of which has ceased can be 

 taken in the hand, and the shoot made to oscillate rapidly backwards and forwards, 

 it assumes, when it comes to rest, a distinct curvature below the apex in the region 

 of greatest flexibility. The plane of curvature coincides with that in which the 

 oscillations take place, and the apex may bend to either side; but the permanent 

 curvature will always be concave on the side on which the oscillations were 

 strongest. If finally a rooting shoot or one firmly held in the hand receives 

 repeated lateral blows at its summit, that is, above the most flexible part, a perma- 



^ Further details will be found in the Arbeiten des Bot, Inst, in Wiirzburg, Heft 3. 



- The phenomenon here described was first observed and studied by Hofmeister (Jahrb. fiir 

 wissensch. Bot. vol. II, i860); and a few important corrections of his description were given by 

 Prillieux (Ann. des Sci. Nat. vol. IX, sheet 2). The statements here made, which confirm the 

 previous observations in all essential points, while differing from them in a few others, are entirely 

 based on my most recent observations. 



