386 



Prof. Karl Pearson. 



" Mathematical Contributions to the Theory ot Evolution. On 

 the Law of Ancestral Heredity." By Karl Pearson, 

 M.A., F.R.S., University College, London. Received 

 January 12, — Read January 27, 1898. 



(A ~New Year's Greeting to Francis Gralton, January 1, 1898.) 



(1) Introductory. — In Mr. Galton's * Natural Inheritance ' we find a 

 theory of regression based npon the " mid-parent." This formed the 

 starting point of my own theory of biparental inheritance.* At 

 the time Mr. Galton published his theory I venture to think that he 

 had not clearly in view some of the laws of multiple correlation with 

 which we are now more familiar. This certainly was my own con- 

 dition when writing my memoir on heredity in 1895, and although 

 in that memoir I pretty fully developed the theory of multiple 

 correlation as applied to heredity, it had not then become such a 

 familiar tool as two years' pretty constant occupation with it has since 

 made it. Accordingly I misinterpreted a second principle of heredity 

 propounded by Mr. Galton, and reached the paradoxical conclusion! 

 that "a knowledge of the ancestry beyond the parents in no way 

 alters our judgment as to the size of organ or degree of characteristic 

 probable in the offspring." I assumed Mr. Galton to meanj that 

 the coefficients of correlation between offspring and parent, grand- 

 parent, great-grandparent, &c, were to be taken r, r 2 , r 3 , &e. The 

 conclusions I drew from this result were, had the result been true, 

 perfectly sound. The recent publication of Mr. Galton's paper on 

 Basset hounds has led me back to the subject, because that paper 

 contains facts in obvious contradiction with the principle above 

 cited from my memoir of 1895. At first, I must confess, I was 

 inclined to lay less stress on Mr. Galton's general law than it 

 deserved, and attributed our divergence to the admitted roughness 

 of colour data. After some correspondence with Mr. Galton and an 

 endeavour on my part to represent his views in my own language, 1 

 have come to the conclusion that what I shall in future term Galton's 

 Laic of Ancestral Heredity, if properly interpreted, reconciles the 

 discrepancies in ' Natural Inheritance ' and between it and my memoir 

 of 1895. It indeed enables us to predict a priori the values of all the 

 correlation coefficients of heredity, and forms, I venture to think, 

 the fundamental principle of heredity from which all the numerical 

 data of inheritance can in future be deduced, at any rate, to a first 

 approximation. 



* 1 Phil. Trans.,' A, vol. 187, pp. 253—318. 

 f Ibid., p. 306. 



X I still think that this is the meaning to be extracted from pp. 132-5 of 

 ' Natural Inheritance.' 



