Karl Pearson 
375 
Now these results bring out several interesting points. It is doubtful whether 
the probable error of the correlation ought to be calculated on 990 cases and not 
rather on the number of parents, 26. Further, these parents are far from a random 
sample; the S.D. as compai'ed with that of the offspring shows that the parents 
have been selected with markedly high and low numbers of tentacles. The 
regression has thus more meaning than the correlation*. We see then that 
tentacles in Hydra are really inherited, but with a value "138, only about a third 
to a fourth of the intensity of heredity in many other characters in other species — 
compare Warren's values in the case of Daphnia and Hyalopterus. Let us see 
exactly what this means : it signifies that if we were to take a species in which 
heredity was as marked as in most characters in man, or as marked as in Daphnia, 
we should have to mix it with two to three times as many pairs in which there 
was no resemblance between the character in order to weaken down the measure 
of hereditary resemblance to that manifested by Hanel's Hydra. In other words, 
a mixture in which one-third only exhibited normal hereditary values of the 
character and two-thirds characters having no hereditary significance, would 
produce the same intensity of heredity as is manifested in this material f. What 
chance, we may ask, has any selection of two or three individuals at most out of 
each family of 20 to 40, got of exhibiting continuous selective influence ? 
To test the generality of the above results a Table was now formed (Table II) 
giving the correlation between all available parents and their offspring. We find : 
Parents (224) Offspring (6436) Correlation Regression 
Mean 7-234 7-275 f -182 -135 
Standard Deviation 1-225 -908 (±-008 ±'006 
Thus we clearly see when we pass from the 26 foundation stock to the available 
224 parents, that the material has not been so markedly selected, but parents are 
* The regression would not be changed by the selection of parents, and would represent the correlation 
in a stable population. 
t The low value of the correlation between parent and offspring is undoubtedly due in chief part to 
the variation with growth in the number of tentacles. This point has been demonstrated by Albrecht 
Hase in an interesting memoir (" Ueber die deutschen Siisswasser-Polypen Hydra," Archiv filr Ras-nen- 
und Gesellschafts-Biologie, Jg. vi. S. 721). He shows that the average number of tentacles increases 
in Hydra grisea from the first day of separation as follows : 
1st Day 20th Day 50th Day End of Culture 
6-14 6-71 8-42 9-14 
It is clear that the hereditary factor must be obscured by such growth changes. But I do not think 
Hase is correct in his conclusion that the number of tentacles has no hereditary value ; my analysis 
shows that the hereditary value is there, but much obscured. Hase holds that Hanel's experiments 
have shown complete regression in the line, because she is dealing with a character which has no 
" Erblichkeitswert," and that she has only thus obtained results in accordance with Johannsen's. I am 
entirely in agreement with him, that a first condition of any experimenting on " pure line " material, 
is to show that the character chosen has "Erblichkeitswert." This both Pearl and Jennings have 
failed to do. But Hanel's data do exhibit "Erblichkeitswert," if only in a very attenuated degree. 
But to the same degree they show, what Hanel and Jennings imagine they do not show, that regression 
does take place within the pure line, and that properly instituted selection would produce effect within 
the limits of the pure line. There is a similar attenuated "Erblichkeitswert" in Johannsen's own 
material which shows in a similar manner to Hanel a partial regression within the pure line. 
48-2 
