DISTKlliLTKiN OF THE GKEEX LEAVES ON THE STEM. 



403 



signiticance iu the life of tlie plant, the attempts to explain them must not be 

 passed over. First of all, it must be pointed out that the number of orthostichies, 

 i.e. of the leaf-members of a .story, as well as the number representing the circuits 

 made by the genetic spiral in each story, is connected with the extent of the 

 horizontal divergence between consecutive leaves. In order to make this clear, let 

 us draw a spiral line on the surface of a cone, as shown in fig. 99, and let us place 

 dots on this line at regularly recurring intervals. The length of the interval 

 between the dots is quite immaterial, it is only of importance that the successive 

 dots shall remain separated from each other by the distance originally fixed upon. 



Fig. 101.— Parastichies of a Pine-cone 



The eight parastichies turning steeply to the left, start from the points 1, 6, 3, 8, 6, 

 2, 7, 12 ; the five turned less steeply to the right, from the points 4, 1. 3, 6, 2. 



Suppose that the dots are placed on the spiral line at intervals of ^V of the circum- 

 ference of the circle (36°), then in each revolution of the spiral there will be 10 

 dots, separated by equal distances from one another. With the tenth -^, however, 

 the spiral line has completed the circuit of the cone, i.e. of the axis. The eleventh 

 dot lies vertically above the first dot, and with it begins a new revolution and a 

 new story. On such a stem ten orthostichies would necessarily be produced, and if 

 we substitute actual leaves for the dots, the phyllotaxis will be represented bj^ ^. 

 As another example, let us place the dots on the spiral line at horizontal distances 

 of i of the circumference. How will the dots then be arranged? Dot 2 is f of the 

 circumference of the circle from dot 1; dot 3, f+f = ^; dot 4:, ^+^+f = f; dot 5, 

 •f + t + T+f = T of the circumference from dot 1, measured along the genetic spiral. 

 Dot 4 is not quite vertically above dot 1, and dot 5 lies beyond it, neither of the 

 two, therefore, coming exactly above 1. More dots are now placed at the same 

 intervals on the second revolution of the spiral line; first dot 6, which is i^, then 



