182 Racial Studies in Fishes 



with for instance 119 vertebrae have offspring with on an average 

 119 vertebrae. As will be seen from the table that is not the case, the 

 average being only 116"3. In the jfirst place the paternal number is not 

 119, but about 113'2 (the average of the population), a circumstance 

 that causes the offspring to "regress" towards the average value of the 

 population. Further " regression " is due to the fact that the maternal 

 numbers of vertebrae, for example, 119, are personal values, while their 

 generative values in all probability will deviate less from the average of 

 the population than do the personal values \ Provided the material be 

 sufficiently large, the following relation must presumably hold : 



^(Average $ ? 119 4- 113-2) = Average Offspring of $ ? 119, 



where "Average $ $ 119" is the average of the generative values of 

 mothers with 119 vertebrae and "Average Offspring of $ $ 119 " is the 

 average of the offspring originating from those mothers. 



I am not going to discuss the results of Table IV more closely here. 

 As the present large material, however, seems to deserve a more 

 thorough statistical treatment than I am prepared to give it I have 

 asked the statistician Miss Kirstine Smith, D.Sc. to deal with it and 

 I hope the results will before long be ready for publication in the 

 Comptes Rendus du Laboratoire Carlsberg. 



IV. Comparison of Two Different Populations developed under 

 THE SAME Environment. Significance of Internal Factors, 

 continued. 



The two populations in question differ essentially in the average 

 number of vertebrae, which for the first of them, the population dealt 

 with above, from the mouth of the fjord (Station 31) is about 113'2, and 

 for the other population, from the innermost part of the fjord (Station 34, 

 see Fig. 1, p. 186) about lOS'O. The experiment was carried out thus. 

 In June 1916, i.e. at a time of year when the sexual products oi Zoarces 

 are not yet ripe, about 300 specimens of each population were caught. 

 They were removed to an embanked area in the neighbourhood of 

 Station 31 and put into big perforated wooden boxes, placed on the 



1 About the concepts " personal " and " generative " value see Johs. Schmidt : "Racial 

 Studies in Fishes," III (this Journal, Vol. ix, p. 63, 1919) and "La valeur de I'individu a 

 titre de g^n^rateur, appreci^e suivant la m^thode du Croisement diall^le " (G. R. Labora- 

 toire Carlsberg, Vol. xiv. No. 6, Copenhagen, 1919) . 



I take the occasion to correct a slip in the footnote p. 67 of the first paper. In the 

 third line from the bottom instead of accuracy read probable error. 



