240 



HOFMEISTER, ON 



however cases occurred, though less frequently, of tri- 

 angular upper surfaces with a very acute apical angle. 

 These irregularities possibly depend upon the fact of the 

 occurrence in each internode of a gradual transposition, a 

 deviation of about 90, of those septa of the apical cell of the 

 bud, which are turned towards the surfaces of the leaves. 



Trees with imperfect 3-numeral phyllotaxis always ex- 

 hibited three-sided apical cells with one shorter edge. In 

 Robinia Pseudacacia (phyllotaxis |) the following measure- 

 ments occurred : 



The base of the triangle. 



9.9288 m.m.m. 

 10.121 

 9.875 



One of the sides. 



15.4448 = 1 : 1.555 

 10.2936 = 1 : 1.689 

 15.9975 = 1 : 1.62 



Mean 



= 1 : 1.634 



This result corresponds as nearly with the relation re- 

 quired by calculation, viz. 1 : 1*618, as could be expected, 

 considering the errors in measurement likely to arise from 

 the minuteness of the objects. Even if the first of the 

 above measurements may not be attributed to the dis- 

 placement of the apical cell between two divisions, it would 

 only be necessary to introduce a correction of about ^ 

 millimeter in the first, and the same in the second (where 

 the proportion is too large), in order to make the observed 

 measurements correspond with the calculated ones. 



The following are farther measurements of apical cells : 



