318 
Dr Lmlwig on Variation 
their environments were interchanged, they would not at once interchange also their statistical 
constants. Dr Ludwig, however, gives a double correlation table for pistils and stamens for 
Gais and Greiz, and considers that the difference here confirms his view of a difference of local 
race. I have worked out the correlation in the two cases, and find the following results : 
Ficaria verna 
(Pistils 
(Stamens 
Gais (80) 
Mean 
18-1125 
23-8250 
13-2635 
20-3682 
S. D. 
4-2885] 
2- 8872j 
3- 0606| 
3-8234j 
Correlation 
-3913 ±-0639 
•5328 + -0290 
Now compare these results, obtained, indeed, from very small inimbers, with Professor 
Weldon's results for MacLeod's statistics of Ficaria rammculoides. 
Ficaria ranunculoides 
fPistils 
Mean 
S. D. 
Early Flowers (268) 
Late Flowers (373) 
17-4478 3-89421 _ 
tstamens 26-7313 3-7609) 
fPistils 12-1475 3-38781 
1 Stamens 17-8633 3-2984] 
Correlation 
5065 + -0306 
•7489 ±-0153 
It will I think be clear that the differences between the means and correlations in the second 
table are sensibly as great as the differences between the like quantities in the Ficaria verna at 
Gais and Greiz. It is conceivable therefore that a difference in the periods of the seasons at 
either place would well account for the differences in the "correlation-fields" without any 
necessity for supposing difference of race. We require in fact to know how the means, 
variabilities and correlations of the characters of a i)lant change (i) with its season and (ii) with 
the influence of environment, before we can formulate a test for racial differences. 
On p. 25 of his memoir Dr Ludwig gives a table for the correlation of $ and $ flowers in 
the Bliitenkopfchen of Homogyne alpinu. 
I find for the 162 individuals dealt with : 
Homogyne alpina Mean S. D. Correlation 
? flowers 10-537 2-63031 
flowers 31-8333 7-3924} 3'35± 0456 
Here again it would be of much interest to know if this relationship is maintained through- 
out the whole flowering season. 
Finally I have dealt with Herr Heyer's elaborate system of measurements of 12000 needles 
from Pinus silvestris. I find 
Pinua silvestris 
Mean 
S. D. 
Coefficient of 
Variation 
Lower Branches 
22-163 + -048 
4-474 + -034 
20-19 
Middle Branches 
26-524+ -055 
5-167 ±-039 
19-48 
Upper Branches 
25-949 + -062 
5-858 + -044 
22-57 
Here the differences in the means and variabilities of needles from different parts of the tree 
are quite sensible. The variability of the needles as judged by the S. D. increases as we go 
upward, but the length of the needles does not. It would be of great value, as bearing upon 
the growth of the tree, to ascertain whether the above relations are due (i) to the special 
