16 PART I. MORPHOLOGY. [ 6 



which are not included in this series, e.g. , f , f , etc. In some 

 cases the construction of a spiral with a constant divergence is 

 impossible, as in Salvinia. 



The causes of this regularity of arrangement of the leaves lie 

 partly in the mode of origin of the leaves at the apex of the stem, 

 and partly in the displacements which they undergo in the course 

 of their subsequent growth. 



Instances of the divergence : all Grasses, and the smaller branches of 

 the Elm,-the Lime, the Hornbeam, and the Beech ; in these, particularly in 

 the last, the leaves undergo displacement, so that on the under side of the 

 branch the divergence is less, and on the upper side it is greater than . 



Divergence of is found in all the Sedges, and in the branches of the 

 Alder and Aspen. 



Divergence of f may be regarded as the most frequent ; it occurs in 

 many herbaceous plants and in most of the smaller branches of the Willow, 

 the Poplar, the Oak, the Rose, the Cherry, and the Apple. 



The acicular leaves of the Firs and Spruces usually have a divergence of 

 jj and ^ 3 : jf r occurs very commonly in the cones. 



Finally, it may be observed that the genetic spiral turns sometimes to 

 the right and sometimes to the left on the stem ; in botanical terminology, 

 a spiral is said to be right-handed when it runs in such a direction that if 

 the observer ascended along it he would have the axis on his right ; and 

 left-handed, when it runs in the contrary direction. 



It has been already pointed out that these laws of position stand 

 in the closest relation to the progressive development of the lateral 

 members. It can be demonstrated that the relation of position, when 

 once established, is maintained, because each new lateral member 

 arises just at the spot on the growing-point where there is the 

 greatest amount of space between the members already formed, 

 and it thus falls into the order which its predecessors have es- 

 tablished. So long as the relation of size between the rudiments 

 of the lateral members and the surface of the common axis remains 

 constant, the divergence will likewise remain constant ; but if this 

 relation be altered, if, for example, the newly developed members 

 are smaller than their predecessors, it will be readily understood 

 that the number of orthostichies and parastichies must be in- 

 creased. Hence we find changes in the divergence taking place 

 just in those regions in which the size of the lateral members 

 alters, for instance, at the base and at the apex of Pine-cones, and 

 at the base of the inflorescences of Compositse. Furthermore, sub- 

 sequent alterations may be induced by the growth either of the 

 axis or of the developing lateral members. 



