Karl Ppurson 
371 
offspring to grandparent. Warren and Johannsen himself* are the only investi- 
gators who, so far as I am aware, have hitherto provided material in sufficient mass 
for approximately answering such a question, and what do we find : 
Johannsen : Phaseolus vulgaris. 
Correlation Regression 
Offspring and parent ... .. 'So + '01 "27 
Offspring and grandparent .. "24 + '01 '11 
Warren : DapJniia. 
Offspring and parent ... ... '47 + '0.5 "62 
Offspring and grandparent ... -27 f '12 "50 
Warren : Hyalopterus. 
Offspring and parent -40 + '03 '47 
Offspring and grandparent ... "24 + '04 -25 
In every one of these cases, although, as the probable errors show, not based 
on sufficient numbers to be absolutely final, the parental is higher than the grand- 
parental correlation. The ratio of the two is almost exactly the 3/5 found for 
the same ratio in mammals with bisexual generation. Pearl and Jennings put 
such results — and many others of the Biometric School — on one side, without even 
reference; on what bases? The former on the foundation that fertility is not 
inherited in hens — an interesting result but one that might be predicted from what 
we know of mice and swine. The latter because he has failed under the method 
adopted by him to discover inheritance in Paramecium. From that he argues 
not only to the whole range of possible heredity in Paramecium but apparently 
in every living form, whatever its mode of reproduction. The fundamental con- 
dition of a crucial experiment of this character must be to show (1) on a sample of 
sufficient size that the character is inherited at all, and (2) that if it be inhei'ited 
the relationship between offspring and grandparent is as intense as between 
offspring and parent. Whether the pure line theory be true or not, it cannot be 
demonstrated eitlier by showing that a fertility correlation is zero, or by the mere 
ipse dixit of Jennings that " ' variations ' are mere temporary fluctuations, without 
effect in heredity, so that their relation to evolution is nil" 
No biometrician asserts that every variation is of hereditary value ; on the 
contrary he asserts the very opposite whenever he tables a correlation less than 
perfect in parthenogenetic reproduction. What he does assert is that on the 
average such variations form in a measurable degree the mark of a certain 
associated gametic character. He would not have thought it worth while to 
try and determine the correlation of gametic and somatic charactersf had he 
believed every individual variation capable of direct inheritance. Nor would his 
results be in the least upset if — and some theorists in heredity seem coming to 
that — every individual were in himself a " pure line." He might mildly wonder 
* Elise Hanel's results for Hydra grisca will be discussed at length below; the character of the 
selections made prevents full comparison here, 
t See Biometrika, Vol. vi., pp. 90, 91. 
