Raymond Pearl 
269 
and the cross assortative correlations must arise from the existence of an organic 
correlation between length and breadth in the individual and the direct selection 
of lengths. It would seem that we had here the means of making a conclusive 
statistical test of whether all the assorting in the conjugation is on the basis of 
length alone, by making use of the theorems in selection which Pearson* has 
given. Thus it should be possible to determine what would be the values of the 
coi'relations between the breadths, and between length and breadth after a selec- 
tion of the lengths alone. Unfortunately, however, these theorems cannot be 
applied in the present case because of a fact which has been discussed before in 
the paper, namely that the breadth dimensions of the conjugants are changed as a 
result of the union in conjugation itself. As we have no data on the pro-conju- 
gant population it is impossible to make accui'ate allowance for the effect of this 
flattening of the conjugants upon the variations and correlations. The wh(jle 
matter has been studied carefully from the statistical standpoint, with the general 
result which may be stated without the publication of all the equations and 
figures, that if we assume the assorting in the conjugation to be on the basis of 
length alone we get a system of values for the direct breadth with breadth corre- 
lations and the cross correlations which are not inconsistent with the observed 
values, allowing for the effect of the change in breadth which occurs during the 
union. It may be possible later to make an accurate allowance for this disturbing 
factor, and then the complete evidence can be presented. 
Finally, in bringing the paper to a close, I wish to point out what seem to me 
to be some of the significant theoretical bearings of the results. These, I think, fall 
under two general heads ; namely, first those considerations which arise from the 
fact that the conjugants are differentiated from the non-conjugants and secondly 
those considerations which are implied by the existence of a high degree of 
homogamy in the conjugation. These points will be discussed in the order 
mentioned. 
The results of this work have given clear and indubitable evidence that in the 
different samples and different cultures the individuals which are conjugating at a 
given moment belong to a distinct type, clearly and markedly differentiated from 
the type of individuals which are not conjugating. The facts regarding the details 
of this differentiation have been shown in extenso earlier in the paper (Tables V., 
VI., VII., VIII., X., and XI., and Diagram 1 ), and I think there can be no doubt 
as to its existence in the mind of anyone who will take the pains to examine 
carefully these tables. Thus, unless the results are repudiated on the general 
ground that the material here used was in no way representative of Paramecia 
in generalf, these facts mean that there is in Paramecium what may be called 
* Phil. Trans. Vol. 200 A, pp. 1—66. 
t That such a criticism cannot fairly be made is sufficiently evidenced by the fact, which every 
comparative table in the paper clearly shows, that there is a very good agreement between the results for 
different series taken from different cultures in different ways. Table II. by itself demonstrates that the 
material here used cannot be considered abnormal. 
Biometrika v 35 
