218 The Law qf An central Iler&Iiti/ 



Bnt it may be shewii that if the ?-'.s sire positive, increasing tlie nuniber 

 uf relatives iiscd as a biisis of prciliction reduces the value of A. The rate 

 of reduction decreases coiisiderably as \ve increase the number of correlations, but 

 for the first increase from one on to two, three ... si.\, etc. it is very sensible. 



We therefore conclude that : 



There will he less averaf/e deviation from the probable character of an ind indual 

 when we increase the number of relatives on which the prediction is based. 



As a special case we say that : 



Prediction will be closei- when we iise the ancestry as well as the parents in 

 forming it, than when we use the parents alone. 



As soon as we accept the positive character of tlie correlatit^i eoeffioients 

 between offspring and ancestry this is an absohitely certain result. It could only 

 be invalidated if the parents defined the offspring absolutely, i.e. if A for two 

 parents was zero, or the corn-lation with parentage perfect. But this is com- 

 pletely negatived bythe fact * that the same pair of parents will produce offspring 

 with very different characters, — e.g. two bay horses may give a black horse 

 and not only a bay. Thus it seems to me that any hypothesis of inheritance 

 which neglects ancestry is foredoomed to failure in the wide ränge of vital types 

 for which we have shewn already that parentage does not define offspring 

 uniquely. Tlie Variation in offspring of the same parents is not merely confined 

 to slight differences in size of organs, but in niany Covers differences in colonr, fi>r 

 example, as great as those upon which the Mendelians have b;ised their dis- 

 crimination between dominant aiid recessive characters. 



(ii) In actual mciisurement on many series the J'a come out less than nnity 

 and there are theoretical reasons for holdiug that this must always be the case. 



Hence if the variability of the offspring generation be not much larger than 

 that of the generation of any relati\e, the probable deviation from type of any 

 individual will only receive from any relative a fraction of his observed deviation 

 from his type. 



This is Mr Galton's principle of regression, the exceptionality of P, is on the 

 average onl}' e.xhibited in part by his relative Q. This purely Statistical and 

 legitimate conclusion was seized upon as a biological law, and all life, but for 

 constant selection, was assumed to be in a State of regression to some distant 

 ancestry. The expression (i) does not Warrant this assertion at all. To begin 

 with there is no reason to suppose : 



(a) That o-, = cr^, = «j-^ = (t^ = ... or that the variability of all generations 

 is the same. In numerous and large series I have not found it so f. 



* For all tlic characters yct doalt with whrther quantitative or qualitative in inaects, animsls and 

 (ilants, there is no approach to .i = 0. 



+ The oftspring generation tsnds alinost universall.v to be more variable tliun timt of any anceatral 

 generation — parents nre a selected portion of the Community. 



