140 
the light and air, and impede each other's functions ; or that 
the alternate arrangement is an obviously wise method of 
securing a larger development of “blade'' and conditions 
equally favourable to all. Nevertheless, it is fact that when 
leaves are crowded, or verticillate, they very often appear less 
capable of sustaining much development of surface.* But this 
might presumably have been attained without the. strictly 
mathematical positions which alternate leaves have assigned to 
them. , , _ . . , , 
We may, then, ask two questions, both of which are at 
present unanswerable. First, why does a leaf of any spiral 
amongst ordinary plants stand at an angular distance varying 
from 120° to 180° from the next to it on the stem? Secondly, 
why does it take up an accurate or definite position on the arc 
between those limits, and is not to be found anywhere along 
tticit arc ^ 
All that can be said is, that such is the case in nature, and 
that when the angles between any two successive leaves of all 
the different generating spirals are measured, and represented 
as fractional parts of the circumference, they are found to bear 
such relations to one another when written down in succession, 
as obtain between the successive convergents of a continued 
fraction of the general form : — 1 + l 
T + i 
1 + &c. 
Whatever our speculations, as to the cause of Phyilotaxis, 
may he, the fact nevertheless remains, and, like the beautiful 
structure of the bee-cell, testifies to the truth that God s 
ways are past finding out,” though bearing witness the while by 
its general invariability to the prevalence of law, ana by its 
exactness and functional value to the power and wisdom ot the 
Law- Giver. 
A discussion ensued, in which Mr. J. Reddie, Mr. A. V. Newton, the Rev. 
C. A. Row, Dr. J. A. Fraser, Mr. Hubert Airy, and the Chairman took part : 
the Rev. G. Henslow replied. 
The Meeting was then adjourned. 
* e.y. The “orders” Com/era, Galiacew, and in the genera Hippuris, 
Myriophyllum, and Gcdlitriche. 
