JoHS. Schmidt 181 



1 12*28 which are respectively 097 above, and 092 below the average 

 of the population which is 113*1963. The values of Table III are 

 especially interesting when compared with the corresponding figures 

 for individuals coming from the same population, but developed under 

 different external conditions (see Section IV, p. 182). 



III. Comparison of Mothers and their Offspring. 

 Significance of Internal Factors. 



This part of the investigation is directed to the question whether the 

 character examined, viz. the number of vertebrae, is hereditary, i.e. due 

 to internal factors. As the father in each single case is unknown it is 

 only possible to compare the offspring with the mother. As the material 

 is so large we can however assume that the paternal number of vertebrae 

 is on an average equal to the average of the population, i.e. about 113'20. 

 If the number of vertebrae is a hereditary character our investigation 

 should show that mothers with a great number have offspring with a 

 great number. To test this we arrange the material given in Tables I- 

 III so that for each number of vertebrae occurring in mothers we indi- 

 cate the frequency of it and the average number of vertebrae in the 

 offspring derived from these mothers. 



From Table IV, representing a very considerable material, namely 

 no less than 857 mothers and 8570 individuals- of their offspring, it 

 clearly appears that the average number of vertebrae in the offspring 

 depends upon the number of vertebrae of the mothers, since the values 

 of the offspring continuously increase as the maternal numbers of 

 vertebrae increase from 107 to 119. Such a conformity could not 

 appear if the number of vertebrae in an individual were alone deter- 

 mined by the environmental conditions during the development. 



The investigations with Zoarces thus show that there are differences 

 of hereditary nature between the various individuals, and they confirm 

 the results of R. C. Punnett, arrived at by investigation of the vivi- 

 parous shark Spinax niger^, as well as those obtained from my experi- 

 ments with Lebistes and the common trout (this Journal, Vol. viii. No. 3, 

 1919 and Vol. ix, No. 1, 1919). 



The Table thus shows that the number of vertebrae in Zoarces is 

 a hereditary character. We must, however, not expect that the mothers 



1 R. C. Punnett: " Merism and Sex in Spinax niger" (Biometrika, Vol. m, Part iv, 

 1904). 



13—2 



