129 
PHYLLOTAXIS ; OR, THE ARRANGEMENT OF 
LEAVES IN ACCORDANCE WITH MATHEMA- 
TICAL LAWS. By the Rev. George Henslow, M.A., 
F.L.S., F.G.S. 
Introduction. 
T HE subject of the present paper is one which generally 
proves void of much attraction, except to those botanists 
who are interested in mathematical calculations. It may, 
therefore, be advisable to preface a few words in explanation of 
its appearing in the Transactions of the Victoria Institute. 
The Rev. Walter Mitchell’s interesting lecture on the Bee- 
cell, delivered at the Anniversary Meeting of 1870, drew from 
the writer a few remarks tending to show that the fact of 
organic forces acting under some impulse, and producing exact 
results, though rare under any circumstances, was not confined 
to the animal kingdom, but occurs also in the arrangement of 
leaves. 
It was in consequence of these remarks that I was requested 
to bring before this Society some more detailed account of the 
principles of this remarkable phenomenon, or, as it has been 
called, Phyllotaocis, and so furnish the members of the Victoria 
Institute with a paper as companion to, though by no means 
so equally attractive as that of Mr. Mitchell on the bee-cell. 
That an insect should possess the power of practically, yet un- 
consciously working out for its own purposes a high mathe- 
matical problem is probably the most mysterious of Nature’s 
gifts to her creatures. The bee knows nothing of geometry, 
and we can only say that it acts instinctively under direction. 
The cell is one of the rare examples of the issue of organic 
forces being rigidly demonstrable by aid of the exact sciences. 
In the mineral kingdom, on the other hand, it is the rule, 
rather than the exception, to find the issue of natural forces, 
either singly or in their resultant, to be capable of mathematical 
expression ; e.g., the crystallographic forms of minerals. 
But when we turn to the vegetable kingdom, we are again 
amongst organic forces, and we look about almost in vain for 
results which can be tested by mathematics or which can be 
represented by their formulae. The most remarkable instance is 
probably the arrangement of leaves, and which forms the sub- 
ject of the present paper. 
