MTSCELLANEA. 
I. Change in Organic Correlation of Ficaria ranunculoides during the 
Flowering Season. 
Among the numerous statistical studies we owe to Professor Julius MacLeod is one which 
deals with the change in con-elation between the number of stamens and the number of pistils 
in Ficaria ranunculoides during a single flowering season [Over de Correlatie tusschen het 
aantal meeldraden en het aantal stampers bij het Speenkriiid {Ficaria ranuncxdoides) : Botaniscli 
Jaarboek, Jaargang xi. 1899]. The number of stamens, and the number of pistils, were deter- 
mined in each of a series of flowers borne by certain plants at the beginning of the flowering 
season, and again in a series of flowers from the same plants at the end of the season. The 
correlation between the number of stamens and the number of pistils differed widely in the 
two cases. The observations were made on the same plants (or their asexual offspring) during 
two successive seasons, and similar results were obtained on each occasion. The coefficient 
of correlation was in each case lower at the beginning of the flowering season, higher at the 
end ; so that the same plants are shown to exhibit a rhythmical change in the amount 
of correlation between two impoi'tant sets of organs. This fact is of very great interest in its 
bearing upon our knowledge of organic correlation in general : and it is to be regretted that 
Professor MacLeod should have expressed his valuable result in a manner which fails to 
exhibit its full impoi-tance, through his adoption of Verschaft'elt's method of stating correlation. 
Dr Verschafl^elt has always failed, so far as I am acquainted with his writings, to distinguish 
between correlation and regression, so that he is unable to find a single constant, expressing 
the correlation between two variables, except in very special cases. It also follows that his 
estimate of the amount of correlation is generally erroneous. 
The notation introduced by Mr Galton, when he first used the conceptions of correlation 
and regression in biological work, enables us to express the important result obtained by 
Professor MacLeod with great ease : and in order to show this, the Tables relating to the 
flowers observed in 1899 are here reprinted. 
Table 11. shows the frequency of flowers with a given number of stamens and pistils among 
the "late" flowers, which appeared from April 17 to 23, 1899. The column at the extreme right 
of the Table gives the whole number of flowers with a given number of stamens, the line at the 
foot gives the whole number with a given number of pistils. From these we find that the 
mean number of stamens (J/j) was 17'863271, the mean number of pistils {M^) was 12-147453*. 
The Standard Deviation or Error of Mean Square of the number of stamens, which we will call 
o-g, was 3-29840 ; that of the number of pistils (o-,,) was 3-38776. Now if we call Ap a deviation 
from the mean number of pistils, and Aj a deviation from the mean number of stamens, the best 
value of the coefficient of correlation is 
where n is the number of observations, and <S'(ApAs) is the sum of the products of all associated 
deviationst. The value of this expi-ession, for Table IL, is 
3121;520053^ 
4167-97287 ' 
* I have to thank Miss M. A. Lewenz, of University College, London, for going over the com- 
putations connected with these Tables. 
t See Pearson; Phil. Trans, a. 1896; and Yule; Roy. Soc. Proc. lx. 
