120 
ORGANOGRAPHY. 
BOOK I. 
is also eight. The position of the several beginnings of the 8 
spirals (viz. on Nos. 1. to 8.) is shown in C; and in D we 
have the numbers (169. 106. 43. &.c.) which respectively 
begin the second series of each spiral. 
To discover the primary spiral, we may fix on any scale 
as a point of departure (No. 1.), and then, by numbering the 
scales on two of the secondary spirals (as 1. 9. 17. &c. and 
1. 6. 11. &c.) which proceed in opposite directions, we may 
afterwards very readily place the numbers on all the scales. 
The easiest method of obtaining the common differences (viz. 
8 and 5), for the purpose of numbering the scales in the tw'O 
cases selected, is to draw a circle round the cone, and count 
the number of each of the two kinds of spirals intersecting it 
(which will be 8 of the first and 5 of the second). When a 
secondary spiral perfects a complete coil (as 1. 9. &c. 161. 
169.), the number of the spirals of the same kind is readily 
seen ; but the former mode for obtaining this number will 
apply equally well to cases where the cone is too short for the 
coils to be completed. 
It is obvious that the hypothesis of the spiral arrangement 
of the foliaceous organs of plants is a mathematical question 
having but little relation to Botany. Those who wish to 
investigate it, will find all that is known of it in SteinheiVs 
Observations upon the Theory of Phyllotaxis, in Ann. Sc. 
n. s. IV. 100. 142, Bravais, sur la disposition des feuilles 
curviseriees, ib. VII. 42. and VUI. 161., Link^ Elementa 
Botanica, ed. 2. II. 448., Dutrocliet, Memoires, I. 238. 
In their normal state leaves are obviously distinct, both from 
each other and from the stem. But, in some cases, adhesions 
of various kinds occur, and give them a new character. Thus, 
in Cardui, and many other thistle-like plants, the elongated 
bases of the leaves adhere to the stem, and become what is 
called decurrent. The elevated lines upon the stem, thus 
formed, are called by Link and Klotzsch sterigmata : vera, 
when traversed by a cord of vessels ; spuria, when mere ele- 
vated cellular plates. In Bupleurum perfoliatum the lobes 
of the base of the leaf not only cohere with the stem, but pro- 
jecting beyond it, grow together, so as to resemble a leaf 
through which the stem has pierced : this is called being 
