82 TRANSACTIONS, NATURAL HISTORY SOCIETY OF GLASGOW. 
Therefore, to find that nine out of eleven, chosen without any 
idea of this relationship, fit into the usual phyllotactic spirals, 
seems to me encouraging. Of course, some of them, e.g., Vac- 
cinium and Arctostaphylos, are not plants with their leaves in 
rosettes, 
The above idea is not original, for the suggestion occurs in the 
work mentioned above. Sir John Lubbock goes on to point out 
a principle which is of great importance. If the angle or plane 
of the leaf to incident light is not exactly transverse or at right 
angles, but more or less inclined, it is obvious that, to understand 
its shape, the projection or shade in the plane at right angles to 
incident light must be studied. In the paper referred to, Drosera 
intermedia, Hayne, is shown to be comparable to the Common 
Drosera, and Plantago lanceolata, Linn., to P. media, Linn. (p. 
134). Thus the leaf of Hypocheeris is very nearly the theoretical 
leaf of the ;5, phyllotaxis. The ordinary treatment in the best 
text-books is misleading on this point. Green, Manual of 
Botany, vol. ii., p. 493, says—‘‘They place themselves so as to 
present their upper surfaces at right angles to the incident rays.” 
Vine’s Student's Text-book, p. 7T48—“ Dorsiventral members 
(morphologically upper ... surface)... lie in a plane per- 
 pendicular to the direction of incidence of the rays.” This is 
probably founded on Frank’s researches, Bot, Zeitung, 1873, p. 
17 ; but both De Vries and Darwin have shown that this rule, or 
rather tendency, is modified both by the weight of the leaf and 
the tendency to grow upwards. (Cf. Movements of Plants.) 
In fact, the usual history of a leaf in this country is as follows :— 
In the bud condition it is either vertical or curved inwards. As 
it matures, it first straightens itself, and then gradually curves 
outwards, bending over until it may either be in a direction at 
right angles to incident light, or even hang below that position. 
It may be fixed at any point in this series of changes. The very 
slightest observation in the field shows that the transverse posi- 
tion is neither universal nor even usual. This course of develop- 
ment explains the necessity of taking into account the ‘shade 
projection ” of leaves, or their inclination to ineident light. 
Taking next the palmate type of leaf, such as the Ivy, it is at 
first sight impossible to get a definite geometrical idea underlying 
its shape. After I had several times given up the attempt, I 
