452 
Proceedings of the Royal Society 
look at the above-mentioned cone of Pinus Lambertiana , where the 
arrangement in the middle region results from an augmentation of 
parts as compared with the base of the cone; while the spiral at 
the top, which is the same as that at the base, is, of course, 
the result of a diminution as compared with the middle. It has 
been already observed by authors, moreover, that in such plants 
as Cacti and succulent Euphorbias* one vertical row may be split 
into two, or, conversely, two run into one, thus changing the 
spiral. Now, as vertical rows are, in one sense, only to be regarded 
as the steepest secondary spirals (a slight torsion readily con¬ 
verting them into actual spirals), such cases are in all essentials 
comparable to the above-described cones. 
The arrangements above indicated will be rendered very readily 
intelligible by the accompanying tabular views .7 
Table A. — Gone of Pinas Pinaster (Mr Smyth — No. 1 ). 
s 
D 
S 
D 
S 
D 
S V 
13 
34 
Top, 1 
2 
3 
5 
8 
13 
21 34 = 
Middle. — 
j 
— 
2 
6 
8 
14 
22 36 - 
5 
18x2 
Bottom, — 
1 
4 
0 
9 
14 
23 37 = 
8 
37 
Table B.— 
-Cone of P. 
Pinaster (Mr Smyth — No. 2). 
D 
S 
D 
S 
D 
V 
q 
Top, 
— 
2 
4 
6 
10 
16 = 8 x: 
2 
Bottom, 
1 
3 
4 
7 
11 
»- A 
The greater number 
of these plants would be 
reckoned as truly recti- 
serial by MM. Bravais. Dr Dickson lias no hesitation in referring to such 
cases in this argument, as he is strongly disposed to douht as to there being 
any fundamental distinction between the “ rectiserial” and the so-called 
“ curviserial” spirals of these authors. 
f In these tables, under S, are indicated the numbers of spirals, generating 
as well as secondary, running to the left; under D, the numbers of those run¬ 
ning to the right; while under V are indicated the numbers of vertical rows. 
