February 2, 191 1] 



NATURE 



44, 



represent grapnically, and to his delight and surprise 

 ihe rough contour lines, which he drew on the table 

 itself, had the appearance of a family of similar and 

 ^.imilarly situated ellipses. The line which joined the 

 ineans of the organs of the offspring for a given organ 

 in the parent was seen to be straight, and to be the 

 locus of the points of contact of a system of parallel 

 tangents to the ellipses. Gallon had reached from his 

 ^raph the fundamental idea of the simplest type of 

 correlation surface — the generalised Gaussian with 

 linear "regression," and he was not slow to realise its 

 great importance and its wide application to the inter- 

 relationship of contemporaneously varying or asso- 

 ciated phenomena. He summoned mathematical aid, 

 and with the help of Mr. Dickson determined the form 

 of the Gaussian frequency surface. Years afterwards 

 it was discovered that the mathematics of that surface 

 had been worked out by Bravais, in considering the 

 distribution of shots over a target. Nowadays we 

 know that there are frequency surfaces which are not 

 Gaussian. Wherein then does the transcendant im- 

 portance of Gallon's work lie? Why, in the fact that 

 he was not considering shots at a target, but that he 

 was seeking for a key to open a door for exact quan- 

 titative methods into the whole wide range of vital 

 phenomena. From Bravais' mathematical treatment 

 of the Gaussian surface nothing followed, until Galton 

 independently rediscovered it with no idea of shots at 

 a target in his mind, but with the idea of investigating 

 problems in genetics, in evolution, and in sociology^. 



His work first pointed out to us how the whole field 

 of nature lay open to exact numerical treatment, if 

 we dropped the category of causation and adopted 

 that of correlation.^ Not from Bravais' mathematics, 

 but from the suggestion and inspiration of Gallon's 

 contour lines on his table of observations, has sprung 

 the whole body of modern statistical theor\-. The 

 problem of evolution, and the study of heredity, were 

 for Galton actuarial problems. Needless to say, he 

 did not place on one side the study of individuals, he 

 was ever in sympathy with individual observation and 

 experiment. But, as the late Prof. Weldon expressed 

 it in a sentence which had Gallon's hearty assent, " the 

 actuarial method must be an essential part of the 

 equipment of any man who would make and under- 

 stand such experiments." It was in this very sense 

 that Galton initiated the Royal Society ''Committee 

 for conducting Statistical Inquiries into the Measur- 

 able Characteristics of Plants and Animals." And for 

 a long time he had in mind the eventual foundation 

 and endowment of an experimental station for varia- 

 tion, heredity, and selection, treated by statistical 

 methods. If his gift to posterity be now found to 

 have taken another form from his original idea, the 

 change is not unassociated with his views on the 

 need for adequate statistical treatment, or with the 

 change of purpose and method which led to his with- 

 drawal from the Evolution Committee. 



If we turn from the inspiration and suggestion pro- 

 vided bv Galton in many varied forms of inquin.' to 

 his actual contributions to our knowledge, two will 

 occur to the minds of most readers, not necessarily 



^ " The conclusions .... depend on ideas that must_ first be well com- 

 prehended, and which are now novel to the large majority of readers and 

 unfamiliar to all. But those who care to brace themselves 'or a sustained 

 effort, need not feel much regret that the road to be travelled over is indirect 

 and does not admit of being mapped beforehand in a way they cau clearly 

 understand. It is full of interest of its own. It familiarizes us with the 

 measurement of \-ariabilitv and with curious laws of chance that apply to a 

 vast diversity of social subjects. This part of the inquiry may be said to 

 Tun along a road on a high level, that affords wide views in unexpected 

 direciions, and from which easy descents may be made to totally different 

 -goals to those we have now to reach. I have a great subject to write upon, 

 but I feel keenly my literary incapacity to make it easily intelligible without 

 sacrificing accuracy and thoroughness." — (Francis Galton. " Natural In- 

 heritance,"' rSSg, p. 2). It is those "easy descents" to "totally different 

 goals " which have proved very arduous, not because they were not obvious 

 and easy so soon as tbe "high level road" had been made, but because 

 they turned out to lead into strictly preserved but brgely unlilled '' strays." 



NO. 2153, VOL'. 85] 



because tney are the most important, but beciuse some 

 statement of them has crept into elementary text- 

 books and popular works on science. The first of 

 tnese is the oft-quoted " Law of Regressicm " ; it was 

 not originally a theoretical deduction but deduced by 

 Galton trom his own measurements and observations 

 on individuals. It amounts to the statement that if 

 in a stable population — i.e. one in which no selection 

 is taking place, and which is mating at random — a 

 group ot all the parents be selected which have a 

 character of a given intensity, then the average of the 

 same character in their offspring will be nearer to the 

 mean of the whole population than the parental value. 

 .As Galton stated this statistical result, it has been 

 over and over again verified by mass-investigations. 

 But it has been singularly often misinterpreted by 

 commentators. One group of them extended it into 

 a general law that all populations tend to regress to 

 mediocrity, if we suspend natural selection ; they quite 

 overlooked Gallon's statement that the population was 

 stable. No such general regression to mediocrit}' was 

 involved in Gallon's law of regression; it was a statis- 

 tical law of distribution of offspring resulting from 

 the stability of the population. Another group of 

 critics selected certain special parents, overlooking 

 Gallon's word "all," and endeavoured to show that 

 the law did not apply to their offspring, and must 

 therefore be erroneous. The fact is that the ver\' law 

 itself, when applied to the offspring of somatically 

 selected ancestry and not to all parents of the class, 

 shows the cessation of regression, and it is upon this 

 verj' cessation of regression for selected sub-classes 

 that the general stability of the Gallonian population 

 depends. 



The second contribution to the theory of heredity 

 with which Gallon's name has been generally asso- 

 ciated is that termed the "Ancestral Law of Heredit\-." 

 The conception Galton had in mind was the following 

 one : in a population mating at random and stable in 

 character, what would be the average relation of each 

 class of individuals in the new generation to each 

 grade of their ancestry? Naturally, he measured the 

 relation by his new method of correlation, practically 

 bv aid of the steepness of his regression lines. The 

 degree of resemblance to successive grades of the 

 ancestry was found to diminish in a geometrical pro- 

 gression. The exact numbers reached by Gallon from 

 his data (J, ^, ^-, &c.) have not been verified by 

 further observation. But the fundamental features of 

 his method, the idea of applying multiple regression 

 and the diminution of the degree of resemblance in a 

 geometric series, have been found correct. Indeed, we 

 now realise that almost any delerminantal theory — 

 including that of Mendel — leads directly to Gallon's 

 Law of Ancestral Heredity as slated abov'e. No direct 

 test of adequate ^ character has yet been made on 

 Gallon's Law, as it is commonly cited — a form which 

 he originally stated himself with great hesitation 

 (" Natural Inheritance." p. 136), and which does not 

 appear wholly in accord with other parts of his obser- 

 vational or theoretical treatment. Strange as it may 

 seem, no one has yet worked out the relationship corre- 

 sponding to the usually stated form of Gallon's Law 

 for a simple Mendelian population breeding at 

 random ; the theoretical investigation of it is beset 

 with many analytical difficulties and not a few logical 

 pitfalls. All the criticisms of this law have turned 

 on results deduced from selected gametic ancestors. 



It has been asserted with some plausibility,' that 

 Gallon's deductions would cease to be of any value 



1 Certain investigations have been made, but in every case they will be 

 found not to fiilQl the conditions as to average relitions, wh'ch Galton laid 

 down. Gallon's own material for "Basset Honrds"is really inadtnissible, 

 for there is scarcely any doubt about the fictitious character of many of the 

 putative sires. 



