31G 
Dr Ludwig on Variation 
Dr Ludwig on Variation and Correlation in Plants. 
By ALICE LEE, D.Sc. 
A NUMBER of points arise from Dr Ludwig's paper in the October uumber of Biometrika 
which deserve to be considered from the standpoint of statistical theory. I have accordingly 
worked ovit the statistical constants of the material given by him, with the following results. 
Ficaiia veriui 
Greiz A (1000) 
Greiz B (1000) 
Greiz C (1000) 
Greiz D (300, in 1900) 
Greiz E (300, in 1901) 
Greiz F (400, in 1901) 
Greiz G* (1000) 
Mean (A, B, C and G) 
jPetals 
(Sepals 
rPetals 
[Sepals 
Petals 
Sepals 
Petals 
Sepals 
Petals 
Sepals 
Petals 
Sepals 
Petals 
Sepals 
Petals 
Sepals 
Mean 
8-286 
3-695 
8-401 
3-669 
8-486 
3-649 
8-597 
3-556 
8-467 
3-753 
8-4175 
3-640 
8-232 
3-437 
8-351 
3-650 
S. D. 
33821 
8524j 
26601 
8174] 
27611 
8417J 
43421 
8267) 
24591 
8539] 
16181 
8349j 
99541 
7033J 
21891 
8037] 
CorreLation 
-2439 ± -0201 
•2181 ±-0203 
■2705 ±-0198 
•2540 + -0364 
•2586 ±-0363 
•3379 ± 0299 
•2480 ±^0200 
•2451 
The probable error of the petal means for A, B, C or G=^026 about, and of their standard 
deviation = •018. 
The probable error of the sepal means = -017 about, and of their standard deviation ^012 for 
the same series. We may tlicrofore conclude that there will be a sensible difference in the petal 
means when they differ by two to three times •04, and in petal variabilities when they 
differ by two to three times •OS. In the sepals the means must differ by two to three times 
•024 and the variabilities by two to three times ^02. 
We see that sensible diflFereuces occur, especially between the A and G series, as to the 
variability of both petals and sepals and as to the mean of the latter. But these changes, 
while demonstrating that the four series are not random samples of the same population made 
at the same time, are not by any means greater than the same plant in the same locality at 
different periods of its season or the same plant in different districts at the same period has 
been known to give. They are well within even the limits of local environmental or seasonal 
changes t. 
A similar remark applies to the divergencies between the components D, E, F of the series C. 
* The reduced variabilities of this series indicate that it was gathered in a different place or at a 
different season from A, B and C. 
t Compare for example the divergencies for Papovcr Rhaeas given by Pearson, Phil. Trans. 
Vol. 197, A, p. 312, for neighbouring districts, and by MacLeod for Ficaria ranunculoides during the 
flowering season, Biometrika, Vol. i. p. 125. 
