514 



NATURE 



{April 12, 1877 



cession of curves of increasing scales of deviation. The 

 curve in the second stage may therefore be looked upon 

 as one of these intercepts ; all that it receives in sinking 

 to the third stage being an additional dose of dispersion. 



As regards the precise scale of deviation that cha- 

 racterises each population, let us trace, in imagina- 

 tion, the history of the descendants of a single medium- 

 sized seed. In the first generation the differences are 

 merely those due to family variability ; in the second 

 generation the tendency to wider dispersion is somewhat 

 restrained by the effect of reversion ; in the third, the dis- 

 persion again increases, but is more largely restrained, 

 and the same process continues in successive generations, 

 until the step-by-step progress of dispersion has been 

 overtaken and exactly checked by the growing antago- 

 nism of reversion. Reversion acts precisely after the 

 law of an elastic spring, as was well shown by the illus- 

 tration of the india-rubber sheet. Its tendency to recoil 

 increases the more it is stretched, hence equilibrium 

 must at length ensue between reversion and family varia- 

 bility, and therefore the scale of deviation of the lower 

 heap must after many generations always become identical 

 with that of the upper one. 



We have now surmounted the greatest difficulty of our 

 problem ; what remains will be shortly disposed of. 

 This refers to sexual selection, productiveness, and na- 

 tural selection. Let us henceforth suppose the heights 

 and every other characteristic of all members of a popu- 

 lation to be reduced to a uniform adult male standard, so 

 that we may treat it as a single group. Suppose, for 

 example, a female whose height was equal to the ave- 

 rage female height -f- 3° of female deviation, the equi- 

 valent in terms of male stature is the average male 

 height -|- 3° of male deviation. Hence the female in 

 question must be registered not in the feet and inches 

 of her actual height, but in those of the equivalent male 

 stature. 



On this supposition we may take the numerical mean 

 of the stature of each couple as the equivalent of a single 

 parent, so that a male parent plant having 1° deviation 

 and a female parent plant having 2° of deviation^ would 

 together rank as a single fertilised plant of -f- i^°. 



In order that the law of sexual selection should co-ope- 

 rate with the conditions of a typical population, it is 

 necessary that selection should be nil, that is, that there 

 should not be the least tendency for tall men to marry 

 tall women rather than short ones. Each strictly typical 

 quality taken by itself must go for nothing in sexual selec- 

 tion. Under these circumstances one of the best known 

 properties of the law of deviation (technically called that 

 of " two fallible measures ") shows that the population of 

 sums of couples would conform truly to the law, and the 

 value of 1° would be that of the original population multi- 

 plied by s]2. Consequently the population of tneans of 

 couples would equally conform to the law, but in this case 

 the 1° of original deviation would have to be divided by 

 V2, the deviations of means of couples being half that of 

 sums of couples. 



The two remaining processes are productiveness and 

 survival. Physiologically they are alike, and it is reason- 

 able to expect the same general law to govern both. 

 Natural selection is measured by the percentage of sur- 

 vival among individuals born with like characteristics. 

 Productiveness is measured by the average number of 

 children from all parents who have like characteristics, 

 but it may physiologically be looked upon as the per- 

 centage of survival of a vast and unknown number of 

 possible embryos, producible by such parents. The num- 

 ber being unknown creates no difficulty if they may be 

 considered to be, on the average, the same in every class. 

 Experiment could tell me little about either natural selec- 

 tion or productiveness. What I have to say is based on 

 plain theory. I can explain this best by the process of 

 natural selection. In each species, the height, &c., the 



most favoured by natural selection, is the one in which 

 the demerits of excess or deficiency are most frequently 

 balanced. It is therefore not unreasonable to look at 

 nature as a marksman, her aim being subject to the same 

 law of deviation as that which causes the shot on a target 

 to be dispersed on either side of the point aimed at. It 

 would not be difficult, but it would be tedious, to justify 

 the analogy ; however, it is unnecessary to do so, as I 

 propose to base the analogy on the exigences of the typi- 

 cal formula, no other supposition being capable of ful- 

 filling its requirements. Suppose for a moment that nature 

 aims, as a marksman, at the medium class, on purpose 

 to destroy and not to save it. Let a block of stone (Fig. 4) 



Fig. 4. 



represent a rampart, and let a gun be directed at a vertical 

 line on its side on purpose to breach it : the shots would 

 fall with the greatest frequency in the neighbourhood of 

 the vertical line, and their marks would diminish in fre- 

 quency as the distance increased, in conformity with the 

 law of deviation. Each shot batters away a bit of stone, 

 and the shape of the breach would be such that its hori- 

 zontal outline will be the well-known curve. This would 

 be the action of nature were she to aim at the destruction 

 of medium sizes. Her action as preserver of them is the 

 exact converse, and would be represented by a cast that 

 filled the gap and exactly replaced the material that had 

 been battered away. The percentage of thickness of wall 

 that had been destroyed at each degree of deviation is 

 represented by the ordinate of the curve, therefore the 

 percentage of survival is also an ordinate of the same 

 curve of deviation. Its scale has a special value in each 

 instance, subject to the general condition in every typical 

 case, that its 0° shall correspond to the 0° of deviation of 

 height, or whatever the characteristic may be. 



In Fig. 5 the thickness of wall that has been destroyed 

 at each degree of deviation is represented by the corre- 

 sponding ordinate of the horizontal outline of the portion 

 which remains. Similarly, in the case of an original 



Fig. s. 



population, in which each class was equally numerous, 

 the amount of survivors at each degree of deviation is 

 also represented by the corresponding ordinate of this or 

 a similar curve. 



But in the original population at which we are sup- 

 posing nature to aim the representatives of each class 

 are not equally numerous, but are arranged according 

 to the law of deviation ; the middle class being most 

 numerous, while the extreme classes are but scantily 

 represented. The ordinate of the above-mentioned out- 

 line will in this case represent, not the absolute number, but 

 \h^ percentage of survivors at each degree of deviation. 

 {To be continued.) 



