510 PROFESSOR DICKSON ON SOME ABNORMAL CONES OF PINUS PINASTER. 



determine in this cone is one with secondary spirals 8D,9 S, = a left-handed 



2 112 



— spiral (series -, -, -^-r. &c). This spiral is continued through between 40 

 17 8 9 17 



and 50 scales of the cone, when two of the eight secondary spirals to the right 



converge into one, giving us the arrangement 7 D, 9 S, = a right-handed 



7 13 4 7 



— spiral (series -, =, -, —> &c), which, after being continued through between 



20 and 30 scales, gives place to a left-handed trijugate of the ordinary series, 



2 

 with divergence - — -, by two of the spirals by 7 becoming replaced by one 



D X o 



of a set by 6. Neglecting the very bottom of the cone, we have the changes 

 represented in the following table : — 



Table D. — Cone of P. Pinaster. 











D 



S 



D 



S 



V 



Top, 









— 



3 



6 



9 



15 = 5—3 



Middle, 









1 



2 



7 



9 



'-"A 



Bottom 



(a 



little above 



the) 



— 



1 



8 



9 



9 



17 = T7 



V. P. Pinaster— Muirhouse — (Plate XIX. fig. 3). Length of cone 3£ inches. 



8 ' 1 ^ 



The upper part of this cone exhibits a left-handed ^- (or possibly ^7) spiral. 



■^1 34 



Carrying the eye downwards, however, we begin to observe, a little below the 

 middle, rudimentary scales of small size and somewhat peculiar shape, inter- 

 calated with considerable regularity among the others, so as to appear as pro- 

 jections placed between the angles of the larger scales. As the base is 

 approached, the scales in the downward continuation of the larger series become 

 gradually reduced in size, till they are practically indistinguishable from the 

 smaller ones ; the general arrangement becoming, at the same time, so 

 crowded and confused as to render precise determination of the spiral 

 impossible. 



In addition to the above, I would recall attention to the abnormal cone ofPinw 

 lambertiana which I exhibited to the Society on a former occasion. This cone is 



noteworthy, not only as showing a transition by convergence from a biiugate of the 



12 3 5 

 system -, -, => — , &c, giving the numbers 4, 10, 14, &c, to a simple spiral of 



112 3 5 

 the system-, -, ± — , — &c, giving the numbers 1, 4, 5, 9, 14, &c, but also 



as showing a transition, conversely, by divergence, from the latter to the 

 former. 



The following table represents the arrangement : — 



