7H Schnildt'^ Dlallel Crosshiys with Trout 



where x, y, z, a, h, c, d are now understood to refer to the generative 

 values of the parents. These are written in the form of equations but 

 he indicates of course that exact equality is not expected, differences 

 between the two sides being allowed in the degree permitted by the 

 variation of the measurements in the samples. He therefore combines 

 them into seven equations, which are in fact the seven equations yielded 

 by applying the method of least squares. Unfortunately these seven 

 equations are not independent. They are equivalent to but six indepen- 

 dent equations and thus could be satisfied in an indefinite number of ways. 

 To obtain another equation Professor Schmidt assumed that the gene- 

 rative value of one of the parents {y) coincided with its personal value 

 (60). This is the arbitrary assumption referred to above. I surmount 

 the difficulty as follows. Seven equations which are all independent and 

 therefore do not require recourse to any arbitrary assumption can be 

 obtained if in writing down the original relationships, account be taken 

 not only of the relation of the offspring average measurements to the 

 average parental generative values, but of the parental individual 

 measurements to the parental generative values. In other words we 

 have simply to set out to find such values of x, y, z, a, b, c, d as will 

 satisfy the twelve offspring equations 



*^ = «-14, 2^" = 61-35,etc. 



and the seven parental equations 



x = 59, y = 60, etc., 

 such differences being allowed as are permitted by the degree of varia- 

 tion of the measurements. Since the sample is 50 in the case of the 

 offspring-averages, and but unity in the case of the parent measure- 

 ments, a greater divergence is permitted between the two sides of the 

 parent equations. 



The equations duly weighted by VSO, prepared for the application 

 of the method of least squares are : 



X = 59 



