46 
PHYLLOTAXY 
spiral round the stem, passing by the nearest way through 
all consecutive leaves, to the leaf B exactly above A ; then 
the number of leaves from A to B is the denominator, the 
number of turns of the spiral the numerator, of the fraction 
representing the phyllotaxy. 
In Gramineae the phyllotaxy is i.e. leaves alternately 
on opposite sides of the stem, in Cyperaceae ^ . Nearly all 
other actual arrangements are terms of the continued fraction 
starting from l, If we add the numerators together to 
make a new numerator, and treat the denominators in the 
same way, we get the next arrangement f. This with ^ 
gives §, and then T 5 g and so on. It is rare to find a stem 
that shows the phyllotaxy very clearly ; usually in the course 
of growth more or less twisting occurs (cf. Pandanaceae). 
The benefit of the phyllotaxy is that the leaves are spread 
out to occupy the available space to advantage ; the larger 
the number of ranks the better this is effected, and the less 
shading of the leaves by one another there is 1 . 
The spreading out of the leaves is further assisted by the 
formation of petioles or leaf-stalks which carry the blades 
away from the stem and thus increase the space available. 
The stalk also enables the leaf to move more readily in the 
direction of the wind, so that the risk of tearing is lessened. 
A large leaf is never without a petiole, although small ones 
are commonly stalkless or sessile . 
An examination of a branch, say of a Horse-chestnut 
(Aesculus), from above shows that the leaves, owfing to the 
various lengths of stalk and other points, are arranged so 
that there is but little shading of one another, and hardly 
any space unoccupied. They form what has been termed a 
leaf-mosaic . Such mosaics are common in plants of our cli- 
mate 2 . In dry climates (see Xerophytes, Chap. III.) the case 
is often different. 
Phyllotaxies of these types give shoots of radial symme- 
try (p. 31); there are also bilateral arrangements, especially 
1 Asa Gray, Structural Botany ; Goebel, Organography of Plants , 
p. 74 (mechanical theory) ; Sachs, History of Botany Bk. I. Chap. IV. ; 
Schumann, Morphologische Studien ; De Vries in Prings. Jahrb. f. wiss. 
Bot. xxm. 
2 Kerner, Natural History of Plants, I. ; Lubbock, Flowers , Fruits 
and Leaves. 
