DIV. 



MORPHOLOGY 



parastichies indicated by unbroken lines, so that the next leaf in this parastichy 

 is 1 + 8 = 9 and the next to this 9 + 8 = 17, etc. Taking the opposite system of 

 spirals there are 5 marked by broken lines (13 marked by dotted lines), and thus 

 the leaves in the system with broken lines are 1 + 5 = 6, 6 + 5 = 11, and so on. In 

 the dotted parastichies, on the other hand, they are 1 + 13 = 14, 14 + 13 = 27, etc. 

 This regularity depends on the fact that in every system of parastichies there must 

 be as many leaves between the successive leaves of one parastichy as the remainder 

 of the parastichies of that system. (This, in the system indicated by unbroken 

 lines in Fig. 108. is 7, and seven leaves intervene between 1 and the next leaf of 

 the parastich}-. This leaf must follow on 1 + 7 and therefore be number 9.) If 

 all the leaves are numbered in this way the successive numbers 1, 2, 3, 4, etc., give 

 the genetic spiral and the 

 divergence. The pine-cone in 

 Fig. 108 has the leaf arrange- 

 ment -/i, and in accmxlance 

 with this the leaves 1, 22, 

 43 come above one another 

 i.e. in the same orthostichy. 

 When the divergences are 

 determined in diverse plants 

 with alternately - arranged 

 leaves it is found that certain 

 divergences are particularly 

 common. The series ^, , -|, 

 I, T\, -nr, H, etc., can thus be 

 arrived at. These fractions 

 have an evident connection 

 with one another ; the numer- 

 ator and denominator of each 

 are the sums of the numer- 

 ators and denominators re- 

 spectively of the two preceding 



fractions. The divergences Fl0 ' 108.-Semi-dia g rammatic view of a pine-cone seen from 



c , , . . below. Divergence of scales / T ; I-VIII, system of para- 



this series all he between sticMes running in the direction of the hands of a watch . 



and | of the circumference of 1-5, system of parastichies running in the opposite direc- 

 the stem. They deviate the tion. For further description see the text, 

 less from one another as the 



start of the series is departed from and approach more and more an angle of 

 1-37 30' 28". This scries is termed the main series of leaf arrangements. There 

 are also other similar series, but the main series is characterised by the fact that 

 by its divergences the most uniform spacing of the leaves on an axis is attained 

 with the smallest number of leaves. The discoverers of this series -were CARL 

 SCHIMPER and ALEXANDER BEAUX. 



Erect radial shoots with elongated intemodes or with broad leaves have usually 

 few orthostichies, while those with short internodes and narrow leaves have many. 

 In the latter case the divergences belong to the higher members of the series. 



Changes in the original position of the leaves may be caused by torsions of the 

 axis. Thus the leaves at the growing point in species of Pandanus are laid down 

 in three vertical series, but subsequently come to be arranged by the torsion of the 

 stem in three spiral lines. In this way the leaves can better utilise the light. 



The arrangement of the leaves on inclined dorsiventral stems is relatively 

 simple. A divergence of % or a similar arrangement is the most common ; by this 



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