Miscellanea 
249 
I don't think I ever read a passage which shows greater need for biometric training in 
a biologist ! Can Professor Lloyd have the least conception of what are the leading features of 
a multiple frequency surface ? Has he never heard of the " mean man " of Quetelet, or of 
Edgeworth's defence of that "mean man's" actuality? The uniqueness of the mode in most 
multiple frequency surfaces is a well-established fact, and if Professor Lloyd will strive to 
see what follows a differential fertility correlated with a non-modal somatic character, he 
will quickly discover how few generations suffice to make that somatic character the modal 
value. 
Professor Lloyd asserted on the basis of his rats that there was no relation of fertility to 
weight, he now says that I agree with him that there was no relation of modal weight to 
fertility. I regret that I do nothing of the kind. Knowing that age is related to weight and 
to size of litter I am quite unable to assert that his data prove or disprove anything at all with 
regard to fertility. I am only in a position to say that I have not, hitherto, been able to find 
a marked inheritance of fertility within the race, and begin to doubt its existence*. Professor 
Lloyd now turns round and leaves the question of fertility within the race which he had been 
discussing and to which his data applied, and says that in two races, which he himself 
differentiates by the number of teats with which they are provided, one has a greater fertility 
than the other. That is to say he passes from an intraracial to an interracial problem and 
from weight of rat to number of teats without apparently noticing the jump. Fertility pure 
and simple may be correlated with many things. Net fertility in man is correlated with the 
size of the pelvis, but because the pelvis is a character transmitted by heredity, it does not 
follow that fertility pure and simple is an hereditary character. The slight intensity of the 
inheritance of fertility such as we find intraracially in man and other mammals is quite 
compatible with its being only indirectly transferred because it is correlated with directly 
inherited characters. If Professor Lloyd wishes to meet my point, he should correlate fertility 
intraracially with the number of teats and then investigate whether this correlation is zero, or 
whether the modal number of teats is associated with the maximum fertility. If neither of 
these things be true, then I am quite sure that he will discover that his race is unstable and 
rapidly changing its type as far as teats are concerned. But a simple statement that two races 
of rats have different type fertilities does not seem to me to have any application to what he calls 
my "principle" — the less so when he tells us that their modal number of teats differ signi- 
ficantly. The appearance of additional teats may be the character, or one of the characters, 
which may lead to increased size of litter, but this has nothing to do with the intraracial 
inheritance of fertility pure and simple. It surely confirms my point that instability follows 
association of fertility with a non-modal character. 
* Many investigations have shown some inheritance of fertility: see for example my own paper 
with Alice Lee and Bramley Moore of 1899 (Phil. Trans., Vol. 192, pp. 257—330) on fertility in man 
and in the thoroughbred race horse. But later work by others on man, mice, swine, poultry, etc. 
seems to me to indicate that fertility is not directly inherited, but only to a secondary degree as being 
correlated with inherited physical characters. The sort of values one finds for the heredity of fertility 
range from -05 to -15. I think that in 1899 I laid too much stress on the possibility of the direct 
inheritance of fertility, but this was an inference formed before I had determined the high parental 
correlation of 0'5 for physical characters. I thought then that disturbing factors might possibly 
reduce Galton's value of I for the parental correlation to the low values we had found in the case 
of man and horse. I do not think they could reduce -J to those values. 
Biometrika vm 
32 
