BIPARENTAL INHERITANCE IN PARAMECIUM 429 



others, we may expect to find that there is a positi\'e coefficient 

 of correlation between them, in this respect. To determine the 

 coefficient of correlation is a more accurate and elegant way of 

 discovering whether the two members of a pair are more aUke 

 than strains taken at random, than that which we have thus far 

 employed. I have therefore computed the coefficients of corre- 

 lation for Experiment 1, and also for other experiments, to be 

 set forth. In these cases we shall as a rule not employ the method 

 thus far used, but consider that the determination of the coeffi- 

 cient of correlation suffices for answering the questions in which 

 we are interested. 



In studying the coefficient of correlation in rate of reproduction, 

 we are dealing with integral variates; namely, the number of fissions in a 

 given period; these can be counted exactly. Furthermore, the two mem- 

 bers of the pairs are alike, so that we have the condition for which sym- 

 metrical correlation tables have been used. For determining the co- 

 efficient, I have employed mainly the 'difference method' (Harris '09), 

 which is peculiarly applicable to cases of the present character. The 

 formula for the coefficient of correlation is for such cases by this method 



r = 1 — — 



where x = the number of fissions, and v = the difference in number of 

 fissions between the two members of a pair. 



In this formula it is important to remember that o-v^ is given by the sum 

 of the squares of the positive differences between the members of pairs, 

 divided by the number of pairs. The formula can be written 



= 1 — ^ 



where n is the number of pairs, and v is the positive difference. 



In using this formula, it is not necessary to arrange the data in a 

 correlation table, since all that one requires is, the standard deviation 

 of the number of fissions (for all members together), and the standard 

 deviation of the differences between the two members of pairs. These 

 differences can be readily taken directh' from such a table as table 29 

 of the preceding paper on the effects of conjugation (page 379), and ar- 

 ranged at the same time as in table 39 of the present paper. 



