Correlation and Application of Statistics to Problems of Heredity 13 



The most noteworthy point, however, is this, that Galton having the 

 correlation table before him of the statures of 928 offspring and of their mid- 

 parents proceeded after smoothing the frequencies to determine the contour 

 lines and found them to be: 



(i) a system of concentric and similar ellipses about the common mean of 

 the filial and midparental statures. 



Further: 



(ii) the regression straight lines were conjugate diameters to the two axes 

 of stature. 



He also determined from his contours the ratio of the axes of this ellipse 

 system, and the inclination of the major axis to the horizontal. The ellipse, 

 which served as type, is given in the accompanying diagram (see Fig. 4, 

 p. 14), and the observed values on this ellipse and the values computed from 

 Mr Dickson's Formulae are* : 



Galton from Contours From Dickson's Formulae 



Regression Slope 1 in 3 6 in 17 '5 



Major to Minor Axis 10 to 5-1 4l to ^2 or 10 to 5-35 



Inclination of Major Axis 25° 26° 36' 



It is needless to say that Galton was delighted with this accordance. 

 He wrote f as follows with regard to it: 



"I may be permitted to say that I never felt such a glow of loyalty and respect towards 

 the sovereignty and magnificent sway of mathematical analysis as when his [Mr Dickson's] 

 answer reached me confirming, by purely mathematical reasoning, my various and laborious 

 statistical conclusions with far more minuteness than I had dared to hope, for the original data 

 ran somewhat roughly, and I had to smooth them with tender caution }." 



We ought on no account to overlook the fact that the theory of linear 

 regression and the associated homoscedasticity were evolved by Galton from 

 his sweet-pea experiments, confirmed by his stature measurements, and 

 resulted practically in the form of the normal surface for two variates with its 

 elliptic contours, before the mathematical theory of correlated errors was 

 known to him. \ It is one of the most striking lessons in what may be achieved 

 by a patient analysis of even crude observations. Yet without being dis- 

 couraged in our own attempts at similar discoveries, we do well to remember 

 that only an exceptional mind has the insight to discriminate between the 

 essential and the non-essential in a mass of statistical data, and to select those 

 two principles which illuminate the manner in which a population reproduces 

 itself stably by aid of heredity — and what is more in so doing to pave the 

 way to the solution of many other problems of a wholly different character. 

 Fig. 5, p. 16, shows the regression line of offspring on midparent for the case of 

 stature; it is, I think, the second regression fine ever drawn, and Galton 

 indicates by the line at 45° exactly how much the offspring fall behind the 

 stature of their individual midparent. He added to this regression diagram, 

 a picture of his "Forecaster of Stature" — which might equally well be used to 



* Journal of the Anthropological Institute, Vol. xv, p. 263. 

 t Ibid. p. 255. I Ibid. p. 255. 



