102 DARWINISM AND HUMAN LIFE 



weigh. In 1871 Mr. J. A. Allen measured numerous 

 individual representatives of some common species 

 of American birds, and found that, as regards 

 important points, e.g. length of bill and length 

 of wing, birds of the same sex and season, caught 

 at the same place, on the same day, showed 

 numerous variations, often large in amount. " The 

 facts of the case," Mr. Allen says, " show that 

 variation of from 15 to 20 per cent, in general 

 size, and an equal degree of variation in the relative 

 size of different parts, may be ordinarily expected 

 among specimens of the same species and sex 

 taken at the same locality, while in some cases 

 the variation is even greater than this." 



(2) Proportion between Frequency and Amount 

 of Variations. Another fact has been made clear 

 in regard to variations : there is a proportion 

 between the frequency of a particular change 

 and the amount of its departure from the mean 

 of the character in question. In other words, 

 the variations, when plotted out, show what is 

 called the Curve of Frequency of Error. 1 In 



1 Quetelet (1846) showed that variation followed the law of 

 frequency of error, the mathematical expression of which was 

 discovered by Gauss. Sir John Herschel, in illustrating this, took 

 the case of a rifleman aiming at a target. " It was pointed out 

 that, irrespective of the skill of the rifleman, the shots, after a 

 large number of trials, would be aggregated most thickly about 

 the centre of the target, and would be more and more thinly scat- 

 tered the farther the distance became from the centre of the target. 

 The only difTerence between the targets of a good and of a bad 

 rifleman is that in the former case the total area which contains 

 all the shots would be smaller than in the latter case. But in 

 each case the centre of the area would coincide with the centre 

 of the target, and the distribution of shots within the area would 

 be similar. The explanation of this result rests upon the cir- 

 cumstance that, each time the rifleman takes aim, a number of 

 factors come into operation, tending to disturb the correctness 



