Raymond Pearl 
229 
conjugants, + •2377, (c) for length of non-conjugants, + "SSGS, and (d) for breadth 
of non-conjugants, + "3346. 
It will at once be noted that the skewness is positive in three out of the four 
cases, or in other words, that the mean falls at a higher value than the mode 
in these distributions. Having regard to the probable errors, however, the skew- 
ness and difference can be regarded as certainly significant in only one distribution 
— that for the breadth of conjugants. For the length of the conjugants both 
these constants have values sensibly equal to zero. For both of the non-conjugant 
distributions it is somewhat doubtful whether the skewness and ditference are to 
be considered to have significant values, but probably they are. It should be 
said, however, that so far as symmetry is concerned all the curves are not far 
from the normal type. 
If we examine the degree of kurtosis*, measured by the deviation of ^2 from 3 
in comparison with the probable error of 13^, it is evident that all the distributions 
except that for the breadth of the conjugants are mesokurtic within the limits of 
error from random sampling. The value of S — ^2 in the case of the breadth 
of the conjugants is almost certainly significant and indicates that the dis- 
tribution is platykurtic, or in other words, is more " flat-topped " than the 
normal curve. 
The value for V/3i differs from zero by an amount which is certaiidy significant 
in the breadth distribution of conjugants, and probably significant for the breadth 
of non-conjugants. For the length distributions the values are insignificant. It 
should be noted that though in several cases the constants are insignificant in 
comparison with their probable errors when considered singly, yet the skewness, 
difference, and V/Sj for all but one the distributions show a deviation in the same 
sense. When we have a number of constants all pointing towards skewness rather 
than symmetry in the distributions we cannot safely say that as a whole the distri- 
butions are normal, even though each observed constant taken singly differs by 
something less than its probable error from its theoretical value. There is a 
cumulative effect of a number of like results, though each may be insignificant by 
itself. 
We conclude then that while all these distributions deviate from the normal 
law the length distributions do not diverge greatly. The breadth distributions 
clearly demand skew curves for graduation. The breadth distribution of the 
conjugants belongs to Pearson's (loc. cit.) Type IV., while the same distribution for 
non-conjugants is of Type I. 
It will be understood that these conclusions are not intended to be sfeneral but 
to apply only to the four cases discussed. As has been mentioned above, I hope 
later to discuss the whole question of variation in Paramecium with much more 
extensive material. 
* For the introduction of this term to express, in connexion with the prefixes lepto-, meso-, and 
platy-, the conditions as to the shape of a fre(inency curve in the region of the mode, cf. Pearson, K., 
Biometrika, Vol. iv. pp. 1G9— 212. 
Biometrika v 30 
