280 On a Criterion for Testing Theories of Inheritance. [Mar. 4, 



(13.) The present paper has, I think, brought out the following 

 points : — 



(i) A variability criterion between contending theories of inheritance 

 is possible, and is easily applied. 



(ii) Variability plotted to parental character will give (a) a horizontal 

 straight line on the Theory of Ancestral Heredity, (b) a parabola with 

 axis along the axis of parental character on Mendelian Principles, (c) a, 

 hyperbola with its real axis perpendicular to the axis of parental 

 character on the Theory of Alternate Inheritance which is summed up 

 in the idea of parentally differentiated groups within the family. 



(iii) As far as my own measurements on stature, span, forearm, and 

 cephalic index in man go, there is nothing to support the view that 

 the variation curve of (ii) is effectively represented by either a parabola 

 or a hyperbola. Within the limits of the probable errors of random- 

 sampling it appears to be a horizontal straight line. 



Further applications of the criterion will no doubt be soon forth- 

 coming, but it is essential they should be made with a full under- 

 standing of what the various theories amount to, and how they must 

 be applied to observations. In particular it is very needful that we 

 should distinguish between the mean of an individual family as deter- 

 mined from all its ancestry, and the mean of an array of offspring of 

 given parentage-type — but with all varieties of earlier ancestry — 

 determined from that parentage only. 



