BOTANY 



PART I 



When the arrangement of the leaves is alternate the divergence may be \ (Fig. 

 107), i (Fig. 144), | (Fig. 105), T 5 T (Fig. 104), etc. Here also, owing to the 

 uniformity of the angle of divergence, the leaves will stand in orthostichies on the 

 stem. With a divergence of \ leaf 4 will stand vertically over leaf 1 (5 over 2, 



6 over 3, 7 over 1, etc.) ; with a f divergence (Fig. 105) leaf 6 comes over leaf 1, 



7 over 2, 8 over 3, etc. If one imagines the insertions of successive leaves connected 

 by the shortest line passing round the circumference of the stem, this line will be 

 a spiral. The alternate arrangement of leaves is therefore also spoken of as 

 SPIRAL ARRANGEMENT. The segment of this genetic spiral passing from leaf to 

 leaf till one vertically over the starting point is reached is called a CYCLE of the 

 spiral (e.g. in Fig. 105 from 1-6 or 3-8). In the case of i divergence the cycle 

 consists of three leaves and passes once round the stem. In | divergence (Fig. 

 105) the cycle consists of five leaves and passes twice round the stem. In the 



fraction expressing a divergence the 

 numerator shows how often the cycle 

 passes round the stem, and the denomi- 

 nator how many leaves the cycle in- 

 cludes. The latter also indicates how 

 many orthostichies there are and which 

 leaf will next be found in the same 

 orthostichy. For example, in a T 5 -j 



FIG. 106. Diagram of the decussate arrange- 

 ment of leaves. The dotted lines are the 

 orthostichies. (Modified after STRAS- 



BURQER.) 



FIG. 107. Diagram of two-ranked arrange- 

 ment of leaves. The dotted lines are 

 the orthostichies. (Modified after 

 STRASBURGER.) 



divergence the stem will be passed round five times before the next superposed leaf 

 is met with, there are 13 orthostichies, leaf 16 stands over leaf 3 (3 + 13), and over 

 leaf 8, leaf 21 (8 + 13). Since the denominator always indicates the number of ortho- 

 stichies, the ^ divergence is also spoken of as two-ranked, the ^ divergence as three- 

 ranked, etc. When the leaves on a stem are crowded and in contact another series 

 of ascending spirals becomes more prominent ; these are the PARASTICHIES. They 

 come about by the contact of those leaves the lateral distance between which on the 

 axis is the least. The parastichies appear very clearly on pine-cones from which 

 Fig. 108 is prepared as a somewhat diagrammatic view from the base. In this view 

 the parastichies appear as spiral lines. Several systems of parastichies running in 

 the same direction are clearly apparent. One of these (indicated by the unbroken 

 lines I-VIII) goes in the direction of the hands of a clock ; two cross this system, 

 one being a flat and the other a steep spiral, and these are marked by the two types 

 of dotted lines. Two systems of equivalent parastichies that cross, can be used to 

 determine the divergence (cf. Fig. 108). Denoting any particular leaf by 1, the 

 number of the next leaf in the parastichy is obtained by adding to 1 the number 

 of the oblique ranks of that system which pass round the stem. There are 8 



