28 PART I. THE MORPHOLOGY OF PLANTS. [ 4. 



the numbers of the members in any one such line. Thus in Fig. 

 15, again, another parastichy connects the members 2, 5, 8, 11, 

 and so on ; and a third, the members 1, 4, 7, 10, etc. From 

 this it is possible to deduce a simple method for ascertaining 

 the arrangement in complicated cases ; the parastichies which run 

 parallel in one direction are counted, and the members in one of 

 them are numbered according to the above-mentioned rule ; by 

 repeating the process in another system of parastichies which in- 

 tersects the first, the number of each member will be found. 



As an illustration : In Fig. 15 there are three left-hand parastichies ; taking 

 the members of any one of them, we mark the first 1, the second 4, and so 

 on: there are two right-hand parastichies; so begmuiog with the member 

 already marked 1, we mark the next 3, the next 5, and thus complete the num- 

 bering of the members. Having numbered them, it is at once apparent that 

 9 is on the same orthostichy as 1, and that the divergence is f . 



The commonest divergences are the following : 



1, i, f> I. T 5 3 2 8 T> M- 



This series is easy to remember, for the numerator of each fraction 

 is the sum of those of the two preceding, and it is the same with 

 the denominators. There are, however, divergences which do not 

 enter into this series, namely -, f , f , etc. 



As examples of the divergence , the leaves of many Mosses, of the Sedges, 

 and the leaves and branches of the Alder, may be mentioned : is a very 

 common divergence for leaves on herbaceous stems, and those of Willows, Oaks, 

 etc. ; the needle-like leaves of Firs and Spruces have commonly the divergences 

 | and ^ ; ^-, |, occur in pine-cones, in the capitula of many Compositse, 

 etc. ; the leaves of some Algae, such as Polysiphonia, have the divergence J. 



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, for 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 that it thus falls into the order which its predecessors have 

 established. 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 likewise remains constant ; but if the 

 former condition 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 



