January 27, 1898J 



NA TURE 



293 



LETTERS ^ TO THE EDITOR 



[ The Editor does not hold himself responsible for opinions ex- 

 pressed by his correspondents. Neither can he undertake 

 to return, or to correspond with the writers of, rejected 

 manuscripts intended for this or any other part of NATURE. 

 No notice is taken of anonytiious covimunications.'\ 



A Diagram of Heredity. 



The law of heredity which was formulated by myself 

 in a memoir entitled " The average Contribution of each 

 several Ancestor to the total Heritage of the Offspring" {Roy. 

 Soc, June 3, 1897, and Nature, July 8, 1897), and which, as 

 I am exceedingly gratified to learn, is now strongly corroborated 

 by an independent investigation, has recently been illustrated 

 by a useful diagram. This was devised by Mr. A. J. Meston, of 

 Allen Parm, Pittsburg, Mass., U.S.A., and communicated by 

 him to the Horsetnan (Chicago, December 28), the leading 

 American newspaper on horsebreeding, together with a popular 

 explanation of the law in question. Believing, as I do, and I 

 am not now alone in the opinion, that the law is a real advance 

 in hereditary science, I think that Mr. Meston's diagram deserves 

 a place in your columns, as conveying in a very intelligible 

 form the chief features of the law. 



These are that the total heritage of the offspring is derived as 

 follows. The two parents between them contribute on the 

 CEverage one half of each inherited faculty, each of them con- 

 tributing one quarter of it. The four grandparents contribute 

 between them one quarter, or each of them one sixteenth ; and 



so on, the sum of the series ^ + ^ + 1/8 + 1/16 + &c. being 

 equal to l, as it should be. It is a property of this infinite 

 series that each term is equal to the sum of all those that 

 follow : thus J = J + 1/8 + 1/16 + &c. ; J = 1/8 + 1/16 + 

 &c., and so on. The prepotencies or subpotencies of particular 

 ancestors, in any given pedigree, are eliminated by a law 

 that deals only with average contributions, and the varying 

 prepotencies of sex in respect to different qualities, are also pre- 

 sumably eliminated. Corrections for these can of course be 

 made in any particular pedigree, taking care that the corrected 

 series still amounts to i exactly. 



It should be borne in mind that the word " Heritage " has a 

 more limited meaning than " Nature," or the sum of the inborn 

 qualities. Heritage is confined to that which is inherited, 

 while Nature also includes those individual variations that are 

 due to other causes than heredity, and which act before birth. 

 Now individual variation in a race that is stable, must have a 

 destructive as often as a constructive effect. Consequently its 

 effects balance one another in average results, and disappear 

 from a law which deals only with these. 

 The area of the square diagram represents the total heritage 



NO. 1474, VOL. 57] 



of any particular form or faculty that is bequeathed to any 

 particular individual. It is divided into subsidiary squares, 

 each bearing distinctive numbers, which severally refer to dif- 

 ferent ancestors. The size of these subsidiary squares shows 

 the average proportion of the total heritage derived from the 

 corresponding ancestors. The distinctive numbers are the same 

 as those which I employed many years ago in connection with 

 the * ' Family Records " with which I was at that time engaged : 

 they were found both then and subsequently to be very con- 

 venient. The Subject of the pedigree is numbered I. Thence- 

 forward whatever be the distinctive number of an ancestor, 

 which we will call n, the number of its sire is 2«, and that of its 

 dam is 2« 4- l. All male numbers in the pedigree are therefore 

 even, and all female numbers are odd. To take an example — 

 2 is the sire of i, and 3 is the dam of I ; 6 is the sire of 3, and 

 7 is the dam of 3. Or, working backwards, 14 is a male who 

 is mated to 15 ; their offspring is 7, a female, who is mated to 

 6 ; their offspring is 3, a female, who is mated to 2, and their 

 offspring is i, the Subject. The connection of all this with the 

 binary system of notation is obvious, and need not be further 

 alluded to. [In Mr. Meston's own diagram, the number i is 

 assigned to the sire, and 2 to the dam, and so on. This detracts 

 from the simplicity of the nomenclature, and therefore I do not 

 adopt that part of his diagram.] The distinction between the 

 male and the female squares is made still more conspicuous by 

 colouring the latter ; but, yielding to the exigencies of printing, 

 I have replaced colour by printers' ink. So all male squares 

 in my version of Mr. Meston's diagram have white grounds and 

 black numerals, and all female squares have black grounds and 

 white numerals. 



The numbered squares could be continued indefinitely : in 

 this small diagram they cease with the fourth generation, which 

 contributes a i6th part of the total heritage, therefore the whole 

 of the more distant ancestry, comprised in the blank column, 

 contribute i/i6th also. Francis Galton. 



" Some Unrecognised Laws of Nature." 



Pressure of important business has prevented me from 

 writing ere this to claim space in your columns to enter a pro- 

 test against the misrepresentations, as well as the whole tone, of 

 the review— which appeared in your columns of the 9th ult. — of 

 the above work, in which I have had the privilege of assisting 

 during the past six years. Heretics have long learned not to 

 expect mercy, or even to look for justice, at the hands of the 

 orthodox. But from a reviewer who, oblivious of the proverb 

 Qui s' excuse s' accuse, warned his reatlers that he at least was 

 " not one to regard lightly the danger of summarily rejecting a 

 germ of new discovery because it happens to conflict with 

 orthodox opinions," we have a right to expect something very 

 different from the venomous outpourings and direful warnings 

 and threats that might flow quite naturally from an irate theo- 

 logian when reviewing a work which strikes a blow at the very 

 foundations of his dogmas and doxies. And this is the very 

 head and front of our offending, that, heedless of authority, we 

 regard " the whole doctrine ot 'energy,' with all its astounding 

 and contradictory corollaries," as absurd ; as the product of 

 the infantile, and necessarily anthropomorphic, imagination of 

 primitive man ; and that we have attempted to show how 

 phenomena may be accounted for without having recourse 

 to such figments of the imagination. In this we may have 

 succeeded or not ; the immediate verdict will largely, if not 

 entirely, depend on the mental attitude of the judge, and for 

 the ultimate verdict we must be content to wait. But 

 your reviewer may find some comfort in the assurance that 

 the facts of science, slowly accumulated through long ages, 

 would not be affected, nor need the human race necessarily be 

 plunged "once more into pre-Galilean ignorance," even if 

 all the assumptions, the metaphysical conceptions — of ethers, 

 "dead" matter, "animating" energy, &c. — on which current 

 explanations of these same facts are based, were summarily 

 consigned to the limbo of similar long- forgotten " working 

 hypotheses." And it is these hypotheses we assail, not the facts. 



Of his criticisms of the fundamental principles, or rather 

 principle, on which all our explanations are based, I need say 

 nothing, for I can safely leave them to the judgment of all 

 who take the trouble to read our work. I may mention, how- 

 ever, that his review is itself a strong a posteriori verification of 

 the law of persistence in its application to psychological 

 phenomena. But I must protest against the, conscious or un- 



