30 MORPHOLOGY OF SPECIES 



From this leaf starts a i/3rd cycle of leaves, which may pass into 

 the ^/S cycle. 



In the second case, the median leaf, as above, initiates at once 

 a 3/8 arrangement without passing through the 1/3 cycle. I find, 

 however, that this arrangement is not constant. It varies as the 

 length of the spine and the number of leaves it produces. There 

 is a tendency to the production of leaves arranged in whorls or 

 groups of two or three, which modifies considerably any given 

 cycle. 



The arrangement of the leaves on the accessory branches 

 differs somewhat from this. According to Wydler there are two 

 cases. In the first case, the four first leaves are produced in pairs 

 at right angles to one another; then follows a 1/3 cycle, suc- 

 ceeded by the 3/8 arrangement. In the second case, the 3/8 

 arrangement follows at once on the two pairs of leaves. My own 

 observations generally support Wydler's, but in some cases the 

 number of pairs of leaves at the base is more than two, and in 

 other cases the leaves are not developed in pairs at all, but start 

 at once with a spiral arrangement. 



The general structure and arrangement of the leaves are the 

 same in I/, nanus, var. Gallii, as in U. EuropcBus, and calls for no 

 detailed description here. For comparison, I will shortly describe 

 a branch, 80 mm. long, taken from among about sixteen others, 

 growing in a group on the main axis of a fairly strong plant of 

 several years' growth. Starting at the base were six short spathu- 

 late leaves, about 3 mm. long, with no branches in their axils. 

 These were growing in a shady position. Then followed a number 

 of spathulate leaves, with a slightly developed spine at the apex. 

 On following these leaves upwards, they were found to vary in 

 length from 4*5 mm. to 7 mm., at the same time becoming more 

 distinctly spiny, and were succeeded by leaves gradually decreas- 

 ing to 2 '5 mm. in length, with a well developed spiny character 

 and the ordinary structure of a spiny leaf. Of these leaves 

 twenty-nine had well formed spines in their axils, on the upper 

 five of which flowers were produced. Above these twenty-nine 

 leaves were thirteen others close to the apex with rudimentary 

 spines in their axils, one only possessing a flower. The lowest 

 spine on the branch was 6 '5 mm. long and had two lateral lea/es. 



