Raymond Pearl 
237 
where B signifies breadth in microns and L signifies length in microns. The 
probable errors of determinations made by these equations are given in microns. 
If now, we substitute, for L in these equations the mean length of the conju- 
gants in series A and G respectively and solve for B, we shall get the probable 
mean breadth of a group of non-conjugants selected to the same mean length as 
the conjugants. This has been done with the following results : 
Series A, Mean Breadth predicted = 47"97l microns, 
„ „ „ observed =44'371 „ 
Difference = 3-800 
Series C, Mean Breadth predicted = 47'8S3 microns, 
„ „ „ observed = 43"158 „ 
Difference = 4725 
Now these differences, which in view of the probable errors of the determi- 
nations are barely sensible, must represent the sum total of decrease in mean 
breadth due to (a) direct selection of breadth, provided it occurs, and (h) shrinkage 
of the breadth dimension measured due to the conjugation process itself. We 
know from direct observation that {h) occurs and, as will be brought out as we go 
on, there is no evidence that (a) occurs at all. Hence it seems to me not unlikely 
that these differences represent practically solely the changes in the oral-aboral 
breadth dimension due to the conjugation process itself as explained above. 
Another interesting point which comes out of Table VI. is that, as we pass 
from Series A to Series G, there is no increase in the mean breadth corresponding 
to the increase in length due to environmental influences. The non-conjugants, it 
is true, show a slight increase (= 1'381 microns), but this is hardly significant in 
view of the probable error. The conjugants show a decrease of about the same 
amount. In other words, it is seen that the environmental change which occurred 
in the culture during the time between the taking of Series A and Series G 
caused an increase in mean length but not in mean breadth, so consequently 
the shape was changed, the individuals becoming more slender. This point will 
be discussed further in connection with the indices. 
We may now turn to a consideration of the length-breadth index for conju- 
gants and non-conjugants. Table VII. has been prepared for this character in 
the same way that Table VI. was for breadths. For the same reasons as before, 
only Series A and G are included. 
This table brings out more clearly several results which have been reached by 
examination of the lengths and breadths alone. In the first place it is seen 
that the non-conjugants have a higher mean index in both cases than do the 
conjugants, but the difference is not great. In other words, as was concluded 
above, the conjugants are narrower in proportion to their length than the non- 
conjugants, due to the flattening of the conjugants as a result of the union. 
Biometrika v 31 
