JoHs. Schmidt 63 



The first value under each symbol is the average of the observed 

 numbers of vertebrae in the offspring, the second (in italics) the mean 

 of the parental numbers of vertebrae. 



A comparison of the two values shows that in some cases the 

 averages of the offspring and of the parents coincide closely or rather 

 closely (e.g. xb and zd), while in other cases they differ very much 

 (e.g. xa). In other words, there does not appear to be a simple rule 

 connecting the number of vertebrae in the offspring with that in the 

 parents. A closer examination of the values makes it probable that 

 a rule nevertheless exists. 



By my previous investigations it has been proved that offspring of 

 the same parents developed under unequal environmental conditions 

 may differ in the number of organs, such as fin-rays, vertebrae, etc. 

 From this it follows that it is necessary to distinguish between the 

 realized, purely personal value of a given individual trout — this value 

 would have been a different one, if the individual in question were 

 developed in different environments — and the generative value of the 

 same individual, and that is the value which it imparts to its offspring. 



It is thus beyond doubt that an individual may have a generative 

 value different from the personal value, and it is possible, nay probable, 

 that in this point we find the cause of the apparent discrepancy above 

 mentioned between the average of the parents and that of the offspring. 



At any rate we shall start from the assumption that the average for 

 a number of offspring-individuals closely coincides with the average of 

 the generative values of the parents and inquire whetlier this supposi- 

 tion does agree with the values arrived at in the experiment. Ex- 

 pressed by formulae our assumption is then that 



— ^- =6114, ^—^ — = bl'do, — ^ = 60*o5, 



where x, y, z, a, etc, indicate the generative value of the individual in 

 question. 



By summation of the equations containing x (corresponding to the 

 first horizontal line of Table I) we find 



2a- + |(a + 6 + c + c^) = 237-52. 



In the same way we find, by summation of the equations containing 

 y and z respectively, 



2y+\{a-^h-\-c-{-d) = 238-44, 

 and 2z + ^ (a + 6 + c + fZ) = 235-58, etc. 



