506 Prof. K. Pearson. Generalised Tlimrii [Sept. 11, 



the character to be fixed in some way by the number of protogenic or 

 allogenic couplets in the constitution of the individual zygote. It would 

 have been equally easy to fix it by the heterogenic couplets. My 

 object is to discover the chief features of heredity in a population 

 breeding at random under a generalised system of pure gametes, and 

 to determine how far the results are in accordance with the biometric 

 experience of what happens in such populations. 



I am quite aware that my theory, although far more general than 

 Mendel's, is not the most general which might be propounded. A 

 whole crop of Mendelian formulae have been proposed for isolated 

 special cases by various writers. But I venture to think that this 

 has been done with a certain want of scientific responsibility. Their 

 authors do not seem to have realised that every such formula involves 

 absolutely rigid laws for inheritance within a population mating at 

 random, and that before such formulae are propounded, a research 

 ought to be made as to what general laws of heredity flow from them 

 and whether such laws are in accordance with existing experience. 

 The present memoir will indicate that to follow up one such general 

 Mendelian theory requires a great deal of mathematical labour, 

 and that in future the onus of testing the generality of a Mendelian 

 formula propounded to account for some single hybridisation result 

 ought to fall on its propounder. 



What the present investigation does demonstrate is this, that the 

 most general theory of the pure gamete hitherto developed leads to 

 broad features of inheritance, which are in perfect accord with the 

 biometric theory of inheritance in populations. Nor, if this theory of 

 the pure gamete were correct, is there anything to be surprised at in 

 the result. The biometric theory is purely a statistical description 

 based upon experience and is not dependent upon any physiological 

 hypothesis. On the other hand, any physiological hypothesis applied 

 to heredity must fall if it does not accord with the results obtained 

 by observations on such populations. 



(2). Developing the theory described above we find : 

 (a). That segregation occurs when the hybrids cross. 

 (b). That when the members of this segregating generation cross at 

 random the population accurately reproduces itself, and supposing no 

 artificial, natural or reproductive selection to take place, a stable popu- 

 lation or " race " is created, which is permanent and shows a permanent 

 proportional frequency for each sub-class of the population. There is 

 no room for further segregation or for "mutations" a,s long as this 

 state of affairs is maintained. Any selection, however, would at once 

 produce a progressive change in the population. 



(c). The regression of the offspring on any ancestor whatever is 

 linear. 



(d). The ancestral correlations form a geometrical series. The 



