1886.] 



Family Likeness in Stature. 



63 



sible problems are evidently very various and complicated, I do not 

 propose to speak further about them now. It is some consolation to 

 know that in the commoner questions of hereditary interest, the 

 genealogy is fully known for two generations, and that the average 

 influence of the preceding ones is small. 



In conclusion, it must be borne in mind that 1 have spoken through- 

 out of heredity in respect to a quality that blends freely in inheri- 

 tance. I reserve for a future inquiry (as yet incomplete) the 

 inheritance of a quality that refuses to blend freely, namely, the 

 colour of the eyes. These may be looked upon as extreme cases, 

 between which all ordinary phenomena of heredity lie. 



Appendix. By J. D. Hamilton Dickson. 



Problem 1. 



A point P is capable of moving along a straight line P'OP, making 

 an angle tan _1 |- with the axis of y, which is drawn through the 

 mean position of P ; the probable error of the projection of P on Oy 

 is 1*22 inch : another point p, whose mean position at any time is P, 

 is capable of moving from P parallel to the axis of % (rectangular 

 co-ordinates) with a probable error of 1'50 inch. To discuss the 

 " surface of frequency " of p. 



1. Expressing the " surface of frequency " by an equation in x, y f z, 

 the exponent, with its sign changed, of the exponential which appears 

 in the value of z in the equation of the surface is, save as to a factor, 



? ' 2 '-JgM. . . (i) 



(1-22)3 ■ 9(1-50)2 



hence all sections of the " surface of frequency " by planes parallel to 

 the plane of xy are ellrpses, whose equations may be written in the 

 form, 



(iw + w= c ' a— • • • • m 



2. Tangents to these ellipses parallel to the axis of y are found, by 

 differentiating (2) and putting the coefficient of dy equal to zero, to 

 meet the ellipses on the line, 



y p 3fl-2# _a 



(1-22)2 *9(i-50)* ' 



_6_ y . . . . . (:?) 



that is i= 9 ( 1 ' 5Q ) 3 = _A_ 



x _JL_ 4 17-6 



(l-22) 2_h 9(l-50) 3 



or, approximately, on the line y=z\x. Let this be the line OM. 



