THE GROWING POINT 



275 



the leaves of higher plants. Interruptions in the alternation are (as in Dasy- 

 cladus), however, always found if the number of the branches in the whorl be 

 altered and an increase takes place in proportion to the vigour of the plant. 

 The whorls in Dasycladus are especially worthy of notice in this relation because 

 they are laid down at a considerable distance from each other. The case figured 

 at Fig. 66 is much commoner ; here also the whorls alternate, but they are crowded 

 so closely together that the lateral branches in successive whorls are in actual 

 contact with each other. 



Another type of arrangement is met with when we pass from the ' whorled ' 

 to the ' spiral ' distribution of lateral members. The characteristic feature of 

 this type is that at any definite level on the axis only one lateral branch is 

 developed, not two or more. We will select a very simple case and represent 

 it diagrammatically. In Fig. 67, /, the bases of the leaves are represented in the 

 usual way, so as to show their relation to each other and to the central axis. 

 The lowest leaf is indicated by the figure /, the highest by 6. It is easily seen 

 that the leaves lie in five longitudinal planes (' orthostichies '). and that, by pro- 

 ceeding from leaf / to the next, one passes round two-fifths of the circumference 

 of the axis. Looked at sideways, as shown in Fig. 67, 2, one sees that the leaves 

 may be united by a spiral line (the so-called 'fundamental spiral ') and that 



Fig. 66. Growing point o{ Hif>pttris I'lil- 

 garis. After Sachs (Vorlesungen iiber 

 Pflanzenphysiologie, ist ed., Fig. 307). 



Fig. 67. Diagram of a two-fifths spiral. 1, in ground 

 plan ; -', seen laterally. 



leaf 6 stands exactly above /, 7 above 2, and soon. This very common arrange- 

 ment is described as a ' two-fifths spiral ' and from this description it will be 

 readily understood what is meant by a one-third, three-eighths, or a five-thir- 

 teenths spiral respectively. In simple arrangements, such as the one-third or 

 two-fifths spiral, the numbers indicate for the most part the order of development 

 of the members. It is possible even in such complicated cases as, for example, 

 the succession of the flowers in the inflorescence of the sunflower, to number the 

 lateral members in accordance with certain geometrical rules, and from the 

 numbers to construct a ' fundamental spiral.' In the latter case, however, this 

 has no significance, since we are not entitled to assume that the development of 

 the branches takes place in the order in which the numbers follow each other. 

 The formation of the lateral members frequently takes place more rapidly on 

 one side of the growing point than on the other, and the successive appearance 

 of the young branches is not indicated at all by the position of the member 

 preceding it in the numerical series but arising far from it. The position of 

 the new member depends, for the most part, far more on its immediate neigh- 

 bours, and hence ' oblique lines ' (parastichies) are determinable, of which 

 there are often in Helianthus fifty-five in one direction and eighty-nine in 

 the other, so long as growth is regular. Their regularity disappears, however, 

 if the space relationships at the growing point alter, and if the relation between 

 the diameter of the lateral axes and that of the growing point varies (com- 

 pare SCHWENDENER, 1878 ; HOFMEISTER, 1868). 



It is not possible for us to go further into the question of the arrangement 



T 2 



