234 



IIOFMEISTER, ON 



the angles at the base is 69° 13' 50-765''; the relation of 

 the base to one of the sides is 1 : 1*4067. The divergence 

 of these numbers from the measurement falls within the 

 limits of probable error.* The conformity of the angle of 

 the apical cell of the stem with the divergence of the appen- 

 dicular organs is not limited to the £ arrangement. The 

 calculated relation of the shorter side of the triangular apical 

 surface of the terminal cell to one of the longer sides is • 



i the | arrangen 



ent 1 



1.618 



I 



1 



1.307 



3 



1 



1.4067 





1 



1.3683 



1 3 



1 



: 1.3799 



2 1 

 3, 6 6 33 



1 



1.3294 



The observed relations are— 



— 



Base. 



Side. 



Relation of 

 the two. 



As2}.filixmas% arrangement, Spiral right . 

 ,, (seedliug) 



33 33 33 33 33 



A 33 3, right . 



13 



33 TJT 33 33 33 



M.M.M. 



56.9738 



27.8558 

 36.1298 



M.M.M. 



74.2464 

 36.6814 

 47,7134 



1 : 1.307 

 1 : 1.316 

 1:1.3216 



63.161 

 63,4386 



86.1052 

 90.23 



1 : 1.363 



1:1.381 



It would be natural to attempt to explain this pheno- 

 menon by the supposition, that the angle which a new 

 septum of the apical cell forms with the next older side 

 wall, bears a relation to the angle of divergence of the 

 frond arrangement, inasmuch as it equals the half of the 

 latter angle. The necessary result of this would be, that 



* I considered it much better to calculate the angle of the apical surface 

 from the length of its sides than to measure it directly with the goniometer, 

 as the former process gives a more certain result. The credibility of each, 

 method depends upon the same circumstances as those upon which, in the 

 determination of phyllotaxis, the relative credibility of the results obtained by 

 the direct measurement of the augle of divergence and by the calculation of the 

 latter from the number of the turns, depends. The number of measurements 

 might easily have been increased, but it seemed advisable to exclude all the 

 cases in which the imperfect parallelism to the apical surface of the stem of 

 the section separating the outermost apex of the flat bud from the remaining 

 tissue, might have given rise to mistakes. 



