296 



NA TURE 



\yan. 28, li 



the back of the card is passed through the hole ; when it 

 is stretched it serves as a pointer, moving in a circle 

 with the pin-hole as a centre. Five vertical lines are 

 drawn down the card at the following distances, niea- 

 siucd horizontally from the pin-hole : i inch, 2 inches, 

 3 inches, 6 inches, and 9 inches. For brevity I will call 

 these lines I., II., III., VI., and IX. respectively. This 

 completes the instrument. To use it : Hold the stretched 

 thread so that it cuts IX. at the point where the reading of 

 the horizontal lines corresponds to the stature of the 

 given group. Then the point where the string cuts \'I. 

 will show the average height of all their brothers ; where 

 it cuts III. will be the average height of the sons ; where 

 it cuts II. will be the average height of the nephews ; and 

 where it cuts I. will be the average height of the grand- 

 children. These same divisions will serve for the con- 

 verse kinships ; VI., obviously so; III., son to a parent ; 

 II., nephew to an uncle; I., grandson to a grandfather. 

 Another kinship can begot from VI., namely, that between 

 " mid-parent " and son. By " mid-parental " height I mean 

 the average of the two statures : {a) the height of the 

 father, {b) the transmuted height of the mother. This 

 process, I may say, is fully justified by the tables already 

 printed in our Journal, to which I have referred. It is a 

 rather curious fact that the kinship between a given mid- 

 parent and a son should appear from my statistics to be of 

 e.\actly the same degree of nearness as that between a 

 given man and his brother. Lastly, if we transmute the 

 stature of kinswomen to their male equivalents by multi- 

 plying them after they are reduced to inches, by I'oS, or 

 say, very roughly, by adding at the rate of i inch for every 

 foot,' the instrument will deal with them also. 



You will notice that the construction of this instrument 

 is based on the existence of what I call " regression " 

 towards the level of mediocrity (which is 5 feet 84 inches), 

 not only in the particular relationship of mid-parent to 

 son, and which was the topic of my Address at Aberdeen, 

 but in every other degree of kinship as well. For every 

 unit that the stature of any group of men of the same 

 height deviates upwards or downwards from the level of 

 mediocrity as above, their brothers will on the average 

 deviate only two-thirds of a unit, their sons one-third, 

 their nephews two-ninths, and their grandsons one-ninth. 

 In remote degrees of kinship, the deviation will become 

 zero ; in other words, the distant kinsmen of the group 

 will bear no closer likeness to them than is borne by any 

 group of the general population taken at random. 



The rationale of the regression from father to son is 

 due (as was fully explained in the Address) to the double 

 source of the child's heritage. It comes partly from a 

 remote and numerous ancestry, who are on the whole 

 like any other sample of the past population, and therefore 

 mediocre, and it comes partly only from the person of the 

 parent. Hence the parental peculiarities are transmitted 

 in a diluted form, and the child tends to resemble, not 

 his parents, but an ideal ancestor who is always more 

 mediocre than the)'. The rationale of the regression 

 from a known man to his unknown brother is due to a 

 compromise between two conflicting probabilities ; the 

 one that the unknown brother should differ little from the 

 known man, the other that he should differ little from the 

 mean of his race. The result can be mathematically 

 shown to be a ratio of regression that is constant for ail 

 statures. The results of observation accord with, and 

 are therefore confirmed by, this calculation. 



Variability above and beloiv the Mea?i Stature. — Here 

 the net result of a great deal of laborious work proves, as 

 in the previous case, to be extremely simple, and to be 

 very easily expressed by a working model. .'\ set of five 

 scales can be constructed, such as I exhibit, one appro- 

 priate to each of the lines ]., II., III., and VI., and 

 suitable for any position on these lines. They are so 

 divided that when the centres of the scales are brought 

 opposite to the points crossed by the thread, in the way 



already explained, we shall see from the divisions on the 

 scales what are the limits of stature between which suc- 

 cessive batches of the kinsmen, each batch containing 10 

 per cent, of their whole number, will be included. Smaller 

 divisions indicate the 5 per cent, limits. The extreme 

 upper and extreme lower limits are perforce left indefinite. 

 Each of the scales I give deals completely with nine- 

 tenths of the observations, but the upper and lower ; per 

 cent, of the group, or the remaining one-tenth, have only 

 their inner limits defined. 



The divisions on the movable scales that are appro- 

 priate to the several lines VI., III., II. and I., are given 

 in the table, where they are carried one long step further 

 than I care to recommend in use. 



The divisions are supposed to be drawn at the distances 

 there given, both upwards and downwards from the 

 centres of the several scales, which have to be adjusted, 

 by the help of the thread, to the average height of the 

 kinsmen indicated in the several lines. The percentage 

 of statures that will then fall between the centre of each 

 scale and the several divisions in it is given in the first 

 column of the table. Example : — In line VI. 40 per cent, 

 will fall between the centre and a point i'\ inches above 

 it, and 40 per cent, will fall between the centre and a 

 point 2'4 inches below it ; in other words So per cent, will 

 fall within a distance of 2 '4 inches from the centre. Simi- 

 larly we see that 2 x 49'S, or 99 per cent, will fall within 

 4'8 inches of the centre. 



In respect to the principle on which these scales are 

 constructed, observation has proved that every one of the 

 many series with which I have dealt in my inquiry con- 

 forms with satisfactory closeness to the " law of error." 

 I have been able to avail myself of the peculiar properties 

 of that law and of the well-known " probability integral " 

 table, in making my calculations. A very large amount 

 of cross-testing has been gone through, by comparing 

 secondary data obtained through calculation with those 

 given by direct observation, and the results have fully 

 justified this course. It is impossible for me to explain 

 what I allude to more minutely now, but much of this 

 work is given, and more is indicated, in the forthcoming 

 memoir to which I have referred.' 



I know of scarcely anything so apt to impress the 

 imagination as the wonderful form of cosmic order ex- 

 pressed by the " law of error." A savage, if he could 

 understand it, would worship it as a god. It reigns with 

 serenity in complete self-effacement amidst the wildest 

 confusion. The huger the mob and the greater the apparent 



» The following will be of help to those who desire a somewhat closer idea 

 of the reasoning than I can give in a popular Address. 



Ill — mean height of race = 68-25 inches. 



7// ± .r = height of a known individual. 



«/ -i- JI-' = the probable height of an unknown kinsman in any given 

 degree. 



- (which 1 designate by iv) = the ratio of mean regression : it is shown by 



direct observation to =5 both in the case of mid-parent to son, and of man 

 to ijrother ; it is inferred to be \ in the case of parent to son. It is upon 

 these primary kinships that the rest depend. 



The " probable " deviations (' ' errors ") from the mean values of their 

 respective systems are — 



/ = that of the general population = 1*70 inch. 



b = that of any large family of brothers = I'o inch. 



y'= that of kinsmen from the mean value of ;«±.i-'. _ 



Since a group of kinsmen in any degree may be considered as statistically 

 identical with a sample of the general population, we get a general equation 

 that connectsy with 10, namely, iirp- +/^ =/". 



The ratio of regression in respect to brothers can be shown to depend on 

 , . p- - li' „ , 



the equation «■ = -^ — = 3 nearly. 



