224 A Biometrical Study of Conjugatio7i in Paramecium 
of a pair of conjugants to he measured was recorded as A, and the second 
measured as B. Since the order of measurement was entirely I'andom, it is 
clear that with reference to size, both A and B groups are random samples 
out of the whole conjugant population A+B. Their constants then should be 
sensibly equal. 
III. Fundamental Constants. 
For the sake of convenience in reference, the constants for variation in the 
various series are collected and shown together in Table I. In the first column 
of the table is given the letter designating the series ; in the second column 
the class, i.e. conjugant or non-conjugant ; in the third column the character, 
i.e. length, breadth, index or difference ; in the fourth column the number of 
the correlation table in the Appendix, from which the values of the constants on 
the same horizontal line were deduced ; in the fifth, sixth and seventh columns 
respectively the means, standard deviations and coefficients of variation, and their 
probable errors ; and finally, in the eighth column, the number of individuals 
included in the frequency distributions from which the constants were calculated. 
The means and standard deviations for length, breadth and difference are given in 
microns ; for the index in per cent. 
IV. Variation in Paramecium. 
Before considering especially the specific problems of the paper it will be 
of interest to compare our results as to variability in this form with those 
obtained from other series. To this end Tables II. and III. have been formed. 
Table II. gives the means, standard deviations, and coefficients of variation for the 
character length in the total series of the present paper in bold faced type, together 
with the same values for (a) Simpson's* series of 100 individuals; (6) a series of 
250 individuals taken from a culture at Ann Arborj- ; (c) three "control" series of 
500 individuals each, all descended from a common ancestor, and kept in a small 
volume of culture fluid for 100, 200 and 300 hours respectively!; {d) three series 
of 500 individuals each, all descendants from the same ancestor as gave rise to 
the control series enumerated under (c), but reared for 100, 200 and 300 hours 
respectively in a very weak solution of cane sugar J. 
This table brings out a number of points of intei'est. In view of the rather 
large total number of individuals we may safely conclude I think that it gives a 
fairly trustworthy representation of the degree of variability of Paramecium in 
respect to the character length of body. It is obvious that generally with an 
increase in the mean there is associated an increase in the standard deviation 
* Biometrika, Vol. i. p. 405. 
t Pearl, B., and Dunbar, F. J. : Seventh Report, Michigan Academy of Science, pp. 77—86, 1905. 
% Ibid. An account of the experiments on which these series are based will be found in the 
paper referred to. 
