647 



XV. On the Variations of the angular divergencies of the Leaves of Ilel 



tuberosus. By the Rev. George HEXSL0*k<i5l/;^., F.L.S. 



(Plate L.) 



Read April 16th, 1868. 



1 HE angular divergences of leaves and their homologous appendages, as represented by 



the different fractions of the well-known series, are for the most part tolerably constant ; 



but it sometimes happens that in following the leaves spirally up a stem, we find 

 vertically over the leaf selected as the first a different one from that which \\ < i should 

 have expected. That cycle, therefore, must be represented by a different fraction to the 

 one preceding. 



Again, in continuing our observations from the point last reached, Ave find perhaps 

 the same number of leaves after the same number of revolutions in the third cycle as in 

 the first; or, on the other hand, the leaf in the same vertical line may be found only 

 after an additional number of revolutions, and the cycle which ends at that point will 

 accordingly be represented by a higher fraction of the series. 



Again, if any number of stems on which the leaves are very numerous and their 

 internodes short, or of cones on which the scales are very crowded, be taken, and wi 

 attempt to make out the angular divergences of their generating spirals, difficulties 



frequently arise — partly because the growth of the leaves or scales may not be exactly 

 the same throughout, partly in consequence of some slight torsion of the axis, or 

 from some unaccountable cause, independently of the fact that the generating spirals of 

 cones very frequently belong to some curviserial form * ; so that we may be at a loss to 

 select the leaf or scale placed actually, or even nearly, vertically above the one selected 

 below, especially as in many cases the spiral does not admit of strict vertically. 

 In examining the arrangements of the leaves on about eighty stems of the Jerusalem 



O "~~ **"«"0 



Artichoke, I found a very considerable amount of variation. The following divergence 

 were especially common : — 



2 



occurred on about .... 28 per cent.f of the stems examined. 



f j, „ • 40 ,, j> » 



7 JJ ,, 23 „ 35 » 



A decussate arrangement 47 



2 



g,^xu.v.j.iu 3 1 5 j 



33 » 



throughout the stem . . 11 



33 " 



33 



8 } , „ 12 „ 33 



A tricussatej arrangement 15 „ 33 



33 



33 



* Curviserial divergences are those, for the most part, represented by the higher fractions of the series, e. g. 



H> &c -, whose denominators are irrational, or no measure of the circumference. 

 T *• e. for one, two, or more cycles only. . , 



t I adopt the word « tricussate » for whorls of three leaves each, in which the leaves of each W horl alternate With 



those of the whorls above and below it. 



