406 DISTRIBUTION OF THE GEEEN LEAVES ON THE STEM. 



stems without doubt take place according to rule, although they may be in part due 

 to external causes. Numerous comparative observations have shown that the 

 building, and especially the lengthening of the growing stem, does not always 

 follow the direction of a straight line; that, rather, a spiral torsion of the cells and 

 tissues not infrequently occurs, so that the idea that such a stem by its growth 

 bores its way through the air is quite justified. This does not, indeed, refer to the 

 twining of the stem, which will be discussed later, but to the torsion of the tissue 

 mass of a straight stem which remains straight after the torsion has been effected, 

 and which may best be compared to the twisting of a bundle of rectilineal strands 

 to form a string. In every bud from which a leafy branch arises, the points 

 of origin of the leaves may be seen on the periphery of the still very short 

 conical axis; frequently, also, the shape and outline of the leaves are perceptible, 

 and the position and divergence of the leaf - insertions can be geometrically 

 established. If the axis has elongated, and an extended branch been produced 

 from the bud, the arrangement displayed by the fully-formed, displaced leaves does 

 not always coincide with that in the bud. The phyllotaxis has become altered 

 by reason of the pressure which the individual groups of cells exercise on one 

 another in their increase in length and breadth, and in consequence of displace- 

 ments connected with these pressures, i.e. torsions arise. If the torsion is restricted 

 to one portion of the stem only, an actual transition of one phyllotaxis into another 

 is seen, and occasionally it is very pronounced. 



In order to make clear the alterations arising in this way, it is only necessary 

 to remove the leaves from a herbaceous leafy stem, to hold it by the two ends, 

 and to twist it as a bundle of threads might be twisted into a string. The points 

 of insertion of the leaves are thus mutually displaced, parastichies are formed 

 from the orthostichies, and new, often very complicated, leaf-arrangements come 

 into view. The alterations produced by the torsion of the stem may also be 

 rendered evident by a consideration of fig. 102. Let us suppose that the black 

 dots on the three thick lines of the young conical stem, horizontally projected 

 in this illustration, indicate leaf-positions which are separated from one another 

 by a distance of ^ of the circumference of the circle (120°). Suppose now that 

 the stem has undergone a torsion as it lengthened, which is quite definite and 

 equally distributed over all portions of the stem. Each portion of the stem 

 between two consecutive leaves, following one another in age, is twisted through, 

 say jig- of the circumference (24°), and in consequence of this the divergence of the 

 leaves is no longer ^ of the circumference, i.e. 120°, but 120° -f 24° =144°, or, as 

 much as f of the circumference. By reason of this the points of origin of the 

 leaves come to lie in the positions indicated by the thinner lines, and a two-fifths 

 is produced from a one-third phyllotaxis. In the same way the three-eighths 

 arises from the one-third phyllotaxis if the consecutive dots are displaced -^ of the 

 circumference (15°) by the torsion, and the horizontal divergence no longer amounts 

 to ^ of the circumference, but to f. The one-third becomes changed into the 

 one-half phyllotaxis if the second leaf of a story, which in the bud was separated 



