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SCIENTIFIC THOUGHT. 



43. Every mathematical instrument, when applied to a 



Application 



eriw eory f nove l purpose for which it was not originally in- 

 vented, " derives as much benefit in its development 

 as it confers through being made use of." Thus Mr 

 Galton's application of the theory of error to the 

 facts of distribution and variation not only enabled 

 him to bring method and order into such questions 

 raised by the Darwinian theory l as natural selection, 



1 It is perhaps premature to 

 speak with great confidence of the 

 actual results which have been 

 gained by this novel branch of 

 scientific inquiry, or of the practical 

 importance which these results may 

 have in the future with regard to 

 some of the great social questions. 

 Still, in a history of thought it is 

 of importance to note how, through 

 Mr Galton's writings, the problem 

 of Inheritance has acquired quite 

 a new aspect. This finds expres- 

 sion in his famous so-called "law 

 of filial regression," which goes 

 against "the current belief that 

 the child tends to resemble its 

 parents " (p. 104). In fact, all 

 opinions and theories which had 

 been propounded before Gal ton, 

 either popularly or scientifically, 

 were based upon a one-sided re- 

 gard to the more visible portion 

 of the ancestry viz., the parents ; 

 whereas, if any general theory like 

 that of " pangenesis," or of " stirps," 

 or of the " differentiation of the 

 germ-plasma and the body-plasma " 

 be made the basis of discussion, the 

 whole ancestral tree must be con- 

 sidered to contribute to the for- 

 mation of the characters of any 

 individual. In fact, we have be- 

 fore us not one pair, but an endless 

 line of pairs which are, as the 

 terms of a series, connected by 

 the powers of the number two ; 

 and it is then easily seen, without 



going into refinements (which, how- 

 ever, in the further elaboration of 

 the problem, may become very 

 important), that the first term of 

 the series, which represents the 

 parents, contributes only one-half 

 of the whole, that is, each parent 

 one quarter. It is also evident, if 

 each parent only contributes on 

 the average one quarter, that an 

 exceptional bias in any direction 

 communicated by them would be 

 balanced in the long-run by the 

 opposite action of the remaining 

 ancestry, and that, contrary to 

 ordinary belief, inheritance would 

 operate in the direction of bring- 

 ing each individual back to the 

 average of the whole lineage. Mr 

 Galton first observed this law of 

 regression to the average by definite 

 countings with seeds and "a com- 

 paratively small number of ob- 

 servations of human stature"; and 

 he remarks that if it was only by 

 these experiments and observa- 

 tions that the law of regression had 

 been established, it could not have 

 been expected that the truth of 

 the apparent paradox would be 

 recognised. When, however, the 

 rule was once expressed, it was 

 "easily shown that we ought to 

 expect filial regression, . . . two 

 different reasons for its occurrence " 

 existing " the one connected with 

 our notions of stability of type, the 

 other as follows : the child inherits 



