DISTRIBUTION OF THE GREEN LEAVES ON THE STEM. 



401 



another -fa of the circumference; in the other case by J; and from this it follows 

 that in the one instance there are twenty-one, and in the other thirty-four orthostichies. 



If we place these actually-observed instances together, we have the series 

 4, 4, * t A, A, 4* 



But the variety of the conditions on which the leaves are arranged is not 

 exhausted by a long way. Although but seldom, still cases have been observed 



which can be placed together in the series i, 1, , A A , and also in the series 



i> f A A ^ n a ^ these series this very remarkable peculiarity occurs, that 



Fig. 100. Plan of Five-thirteenths Phyllotaxia. 



in each individual fraction the denominator is equal to the sum of the denom- 

 inators, and the numerator is equal to the sum of the numerators of the two 



preceding fractions. 



Moreover it must be here particularly mentioned that the divergence, by which 

 the leaves following one another in age are separated in a horizontal d.recl 

 the more difficult to establish the smaller it becomes. The one-third, two-fi 

 three-eighths arrangements are the most easily demonstrable on the full-gro 

 shoots, although occasionally doubt arises as to whether the three, five, and e.gh 

 orthostichies represent completely straight lines. But the demonstrate of A a 

 the tf arrangements, especially in green herbaceous stems, is very < 



uncertain. 26 



VOL. I. 



