104 
Miscellanea 
II. On DifTerentiation and Homotyposis in the Leaves of Fagus sylvatica. 
By KARL PEARSON, F.R.S., with the assistance of MARION RADFORD. 
(i) If an examination be made of a beech tree there will be found to be a distinction 
l)etween the nature of the growth at the free higher parts of the tree and at the lower more 
accessible portions. Botanists have distinguished these two types as 'sun ' and 'shade ' branches. 
How far these differences of growth are entirely due to differences merely of light oi' even of air 
environment may be legitimately doubted. The free south side of a large beech tree does not 
as a rule abound in sun liranches, while the north side exhibits only shade branches. There 
appears to be not only some factor beyond the light and air enx'ironmeut controlling the dcA elop- 
ment of the tree, but the age of the tree and the age of the part of the tree considered seem also 
influential. Sun branches at any rate occur where the growth of the tree is most rapid, and 
shade branches where it is less rapid. Our experience is that with old and large beech trees, 
even if they are growing freely on a common, the sun branch is confined to the upper portions of 
the tree, and a random collection of sprays will result in shade branches only. The accompanying 
photographic reproductions which I owe to the kindness of Professors F. W. Oliver and 
A. G. Tansley will illustrate the difference between the two kinds of growth. We have collected 
a considerable number of sprays from beech trees this autumn and examined a considerable 
number collected by other persons, and it is safe to assert that a random gathering round the 
accessible parts of a large beech tree will result in a collection consisting in great bulk or more 
probably entirely of 'shade' branches. 
(ii) If a spray representing a year's growth be cut from a shade branch of a beech tree, there 
will according to our experience generally be found to be four, occasionally only three, more 
rarely five leaves upon it. The accompanying Plate II. represents a number of such sprays, 
the typical forms being I. and II. Looked at from the back we shall call the leaves that fall on 
the right of the stem of the spray, right-hand leaves, and on the left of it, left-hand leaves. 
Measuring from the top of the spray down it, the leaves will be called first, second, third, etc., 
leaves. The lea\ es are almost in\ ariably — in 99 per cent, of the cases observed — on alternate 
sides of the stem. 206 such sprays were gathered from the beech trees growing on Highmorc 
CouHuon, not far fi-om Nettlebed on the Chilterns, by Dr Alice Lee and myself —the bulk fi'om 
\ ery large forest trees. Of these sprays 98, instead of 103 the half, had the first leaf on the 
right-hand side. In one case the third leaf was the first on the right-hand side; in the remaining 
107 cases the second leaf was the first on the right-hand side. On the left-hand side there were 
108 cases of first leaf and 98 cases of second leaf. We think we may therefore assert that the 
first leaf is as likely to be on the right as on the left side of the stem of the spray. The first and 
second leaves of the spray are both much larger than the third and fourth leaves, and there is 
a marked difterentiation between the first pair and the second pair. This dififerentiation 
is so obvious, the second pair being in many cases quite dwarfs, that for the first paper* dealing 
with beech leaves we did not collect this secondiiry pair, and such pairs were therefore not 
included in the countings of the veins. The object of the present note is to test (i) whether 
serious error was introduced by disi-egarding the differentiation of the members of the first pair, 
and (ii) what effect the inclusion of the secondary leaves would have upon the homotyposis. 
(iii) Investigating first the diflerence between the first leaf on the right and the first on the 
loft without regard to order, and dealing with the same character as in the earlier investi- 
gation, i.e. the total number of veins on both sides of the main ridge of the leaf, we find : 
Mean Standard Deviation 
First Left-hand Leaf. . . 15-432 ± -075 1 -589 ± -053 
First Right-hand Leaf 15-495 + -074 1-585 ±"053 
" "Homotyposis in the Vegetable Kingdom." Phil. Trans. Vol. 197, A, p. 324. 
