CH. VIl] 



PHYLLOTAXY. 



97 



This plant may be used to demonstrate the fact of some 

 general importance, that the leaves also form a continuous 

 spiral line round the stem. This double arrangement may 

 be illustrated by a diagram, fig. 43, in which the dots are 

 arranged both in vertical and in oblique rows, the former 

 being the more obvious. 



FIG. 43. 

 DIAGRAM ILLUSTRATING PHYLLOTAXY. 



Take a shoot of groundsel and mark the base of any 

 leaf-stalk with a spot of ink by which it may be recog- 

 nized : the next leaf above will be slightly to the left and 

 the third again to the left, so that a line passing through 

 the 1st, 2nd, 3rd, 4th, &c. leaves in order of height will 

 make a spiral travelling upwards and in the direction 

 of the hands of the clock. When the 6th leaf has been 

 reached it will be found to be vertically over the 1st, 

 which must necessarily be the case when the leaves are in 

 five vertical rows. One other point must be noted; in 

 passing from the 1st to the 6th, the spiral goes twice round 

 the stem. These two facts are expressed numerically by 

 the fraction f . In the same way the fraction f means 

 there are eight vertical rows arranged in a spiral which 

 D. E. B. 7 



