Miscellanea 
105 
There is clearly then no sensible differentiation between the number of veins or its variability 
when we pass from the right to the left-hand side of the stem. 
Next dealing with the leaves taken in order down the stem, and without regard to their right 
or left-handed position, we have : 
Number 
Mean 
Standard Deviation 
First Leaf 
206 
15-684 + -071 
1-505 + -0.50 
Second Leaf 
206 
15-257 + -076 
1-612 + -054 
Third Leaf 
205 
1.3-098 + -096 
2-034+ -068 
Fourth Leaf ... 
145 
10-559+ -110 
1-968+ 078 
Fifth Leaf 
23 
8-348 + -204 
1-448 + -144 
The mean of all the fii'st and second leaves together may lie compared with the Great 
Hampden series of 1900, also from the Chilterns : 
Mean Standard Deviation 
Highmore Beeches ... 15*471 1-574 
Great Hampden Beeches 16-106 1-735 
Considering the difference of localities, of season and class of tree, these results appear to be 
in reasonably close agreement, and enable us to judge how far any serious error was introduced 
into the Hampden results by the hypothesis that the large, i.e. first or second leaves on the 
spray, were undifferentiated. The Hampden leaves have clearly more veins, there is a sensible 
difference of -6 in the mean, not very great, but sufficient to show that we had properly excluded 
the third and fourth leaves, when we collected. In the next place there is a sensible differentiation 
as we go down the stem, most marked when we pass from the first two leaves to the third, fourth 
and fifth, but hardly of great importance when we consider only the first and second. 
If we treat as we did in the Hampden series the first two leaves as homotypes and work out 
their correlation we find : 
Homotypic Correlation of first two leaves 
p = -.504 ±-025. 
Now let us work this out, allowing for the differentiation between the two leaves. Using the 
formula given in R. S. Prov. Vol. 71, p. 302, i.e. : 
"■^ Cm" 
~^ a'^- (T ( m - 1 ) ( - o-j/'') ' 
we have : p = -5042, 
0-2 = 2-47731, (r,;2= -045582 
0-2 -o- ,,2 = 2-34839. HI = 2. 
Whence we find : )- = -5513. 
The actual value given for homotyposis in beech leaves of the Hampden series being -5699, 
it will be seen that only a small change has been made by allowing for differentiation in 
the present results from the Hampden value. The simple explanation of this undoubtedly 
being that our leaves were almost entirely, owing to our method of gathering, the first and not 
the second leaves of the year's growth. 
But the present investigation allows us to go a stage further, and to find the homotyposis in 
beech leaves supposing we take all leaves and not merely the two first leaves of the year's 
growth. We have 144 sprays* with four leaves on, five leaves are so i-are that we cannot use 
* In the case of the 145 sprays with fourth leaves recorded, there was one in which a third leaf was 
not available for counting. 
Biometrika iii 14 
