Correlation and Application of Statistics to Problems of Heredity 3 



causation in a sense different from that of Cuvier; he would mei"ely think in 

 terras of associations with differing grades of intensity. Be this as it may, 

 Galton's second idea of measuring the degree of relationship arose from the 

 fact that he had recognised that two characters measured on a human heing 

 are not independent, they vary with each other. The femur of man has its 

 characters associated with those of the humerus. 



Galton did not realise immediately that his two problems admitted of 

 the same solution. His first actual attempts at solution of the inheritance 

 problem were based on the weight of the seeds of mother and daughter 

 plants. In the first place he used, about 1875, some seed like that of cress (see 

 Vol. ir, p. 392), and he started by endeavouring to correlate grades or ranks. 

 This could not be very successful because the regression curve and the 

 "isograms" (see Vol. II, p. 391) are not linear, but extremely complicated 

 curves. Later in 1875 (ibid. p. 187) we find him experimenting with 

 Darwin's assistance on the weight and diameter of sweet-pea seeds, and here 

 he reached his first "regression line." I reproduce (p. 4) from Galton's data 

 in a note-book the first "regression line " which I suppose ever to have been 

 computed. I have recalculated the constants and redrawn the line. It is 

 for sweet-pea diameters in mother and daughter plants. The correlation 

 coefficient is - 33, almost exactly 1/3. Two points must here be noticed. 

 First the parental mean is considerably higher than the offspring mean. If 

 the offspring mean denotes that of the general population, this would 

 indicate that Galton's parental population was not a random sample of the 

 original general population. Secondly the means of the diameters of the 

 daughter plant peas for each size of mother plant pea, give a series of points of 

 rather irregular distribution, which conforms as well to a sloping straight line 

 as to any other form of curve. Here we have the origin of Galton's "regression 

 straight line." We see that as size of mother pea increases, so does size of 

 daughter pea, but whether in excess or defect of mean the daughter pea 

 does not reach the deviation of the mother's diameter from the mean value, 

 the offspring is less a giant or a dwarf than the mother pea. This is Galton's 

 phenomenon of regression. In this case the variabilities of mother and 

 daughter peas were approximately equal, and Galton reached the idea that 

 the slope of the regression line would measure the intensity of resemblance 

 between mother and daughter. If there were no slope the diameter of 

 daughter pea would be the same for all diameters of mother pea. If it 

 sloped at 45°, i.e. a slope of unity, the daughter pea's diameter would be 

 exactly that of the mother pea's, supposing their means were the same ; if 

 they were not, the deviations from their respective means would still be 

 equal. 



It is strange that both Galton and Mendel should have started from peas, 

 the former from sweet and the latter from edible peas. Galton tells us dis- 

 tinctly why he chose the former, namely because he would not be troubled 

 to the same extent by variation in size of peas within the same pod. We 

 must leave it to the future to judge whether the correlational calculus, which 

 has sprung from Galton's peas, is or is not likely to be of equal service with 



1—2 



