PROFESSOR DICKSON ON SOME ABNORMAL CONES OF PINUS PINASTER. 507 



however (under which they include such arrangements as those in fir cones), 

 they are disposed to admit the occurrence only of such transitions as take 

 place by way of " convergence " of secondary spirals, resulting in diminu- 

 tion of number. For example, after referring to the possible derivation of an 



arrangement with 5 and 7 secondary spirals (series -, -=, --, — , &c.) from an 



ordinary one with 5 and 8, by abortion of one of the spirals by 8, and adding 



that " the series 1, 4, 5, 9 . . . . J-, -, -, — -, -—, &c.~l, does not admit of 



L4 5 9 14 23 J 



explanation by the way of abortion, and that one can deduce it from the 

 ordinary series only by supposing a superfcetation, or addition of a new spiral, 

 among the secondary spirals by 8," they continue, " This hypothesis appears 

 to us altogether improbable, since, in the face of an immense number of 

 instances where two spirals converge into one, we cannot, on the other hand, 

 cite one (apart from rectiserial stems), where one spiral diverges into two 

 similar and parallel ones." "• 



Not having any strong belief in the fundamental distinction between the 

 " curviserial " and " rectiserial " forms of these authors, and knowing that 

 " divergence " or bifurcation of vertical rows (which are, in one sense, to be 

 regarded only as the steepest secondary spirals) is not very rare in " recti- 

 serial " Cacti and succulent Euphorbice, I have not been surprised to encounter, 

 as I have done, cases of " divergence " of secondary spirals in fir cones. In 

 the following remarks, however, I shall treat chiefly of the " convergence " of 

 secondary spirals, a phenomenon which, I think, I shall be able to explain 

 more definitely than has hitherto been done ; reserving to a future occasion 

 more extended reference to the phenomenon of " divergence " of spirals. 



For some of the cones to be described, I am indebted to the kindness of R. 

 Smyth, Esq., Emyvale, county Monaghan, Ireland ; others I obtained in the 

 woods at Muirhouse (seat of H. Davidson, Esq.), near Edinburgh ; further, I 

 am indebted to Professor Balfour for permission to examine the collection of 

 cones in the Museum at the Royal Botanic Garden, Edinburgh, where I found 

 the remarkable cone of P. lambertiana, which was lately exhibited before the 



Society,t and to which I shall recall attention in the following remarks, as also 



5 

 a cone of P. Pinaster, with — spiral, which was exhibited on the same occa- 

 sion, and of which I give an outline figure in Plate XX. fig. 8. 



I shall, in the first place, give a brief description of the cones forming the 

 subject of the present paper; after which we shall be in a position to judge of 

 and discuss the bearings of the abnormal phenomena. 



I. Cone of P. Pinaster— Mr Smyth— (Plate XX. figs. 1 and 2 ; Plate XXI. 



Q 



fig. 1). Length of cone 5| inches. At the base there is a right-handed - 



* L. c. pp. 104, 105. + See Proceedings R. S. Edin., vii. pp. 398, 399. 



