CHAP. II. 
LEAVES. 
115 
capellary leaves, which do not fonn, like the floral envelopes of 
other plants, a complete cavity surrounding the sexual organs 
on all sides, but which are slightly concave, and protect them 
on one side only. This point admitted, if we consider atten- 
tively the cone of a Pine, or of a Spruce Fir, we are at once 
led to inquire whether the scales are arranged in spires or in 
whorls. Breaking through its middle a cone of Pinus Picea 
(Silver Fir), we remark three scales, which at first sight ap- 
pear to be upon the same plane ; but a more attentive examin- 
ation shows that they really originate at different heights, and 
moreover, that they are not placed at equal distances from 
each other; so that we cannot consider them a whorl, but 
only a portion of a very close spiral. But, considering the 
external surface of the cone viewed as a whole, we find that 
the scales are disposed in oblique lines, which may be studied 
— 1. As to their composition, or the number of scales requisite 
to form one complete turn of the spire; 2d. As to their in- 
clination, or the angle, more or less open, which they form with 
their axis ; 3d. As to their total number, and their arrange- 
ment round the common axis, which constitutes their co-ordi- 
nation. Finally, we may endeavour to ascertain whether the 
spires turn from right to left, or vice versa. 
He then proceeds to show, that the spiral arrangement is 
not only universal, but subject to laws of a very precise na- 
ture. The evidence upon which this is founded is long and 
ingenious, but would be unintelligible without the plates 
which illustrate it. I must, therefore, content myself with 
mentioning the results. Setting out from the Pine cone above 
referred to, he found that several series of spires are dis- 
coverable in the arrangement of their scales, and that there 
invariably exists between these spires certain arithmetical 
relations, which are the expression of the various combina- 
tions of a certain number of elements, disposed in a regular 
manner. All the spires depend upon the position of a funda- 
mental series, from which the others are deviations. The 
nature of the fundamental series is expressed by a fraction, 
of which the numerator indicates the whole number of turns 
required to complete one spire, and the denominator the 
number of scales or parts that constitute it. Thus /y indicates 
I *2 
