DARWINISM ATTACKED. 61 



favourable and 5 unfavourable ; and no less than 184,756 times by 

 10 favourable and 10 unfavourable. Let us consider that the organ- 

 isms acted on by 20 favourable and o unfavourable agencies have 

 their size increased 20 per cent.; those acted on by 15 favourable 

 and 5 unfavourable by 15 5 = 10 per cent. ; and so on. If now 

 these percentage increments and decrements be plotted out at equal 

 distances on a base line, and ordinates corresponding to the theo- 

 retical frequencies erected from each, then by joining these ordinates 

 we shall obtain a curve which is practically identical in form with 

 the probability curve of the law of frequency of error. Thus, by a 

 simple arithmetical method, we obtain a series approximating more 

 and more closely to the probability curve, the greater the number 

 of times the expression ( l / 2 -}- ^) is expanded. Expanded 20 

 times, the average error is less than .5 per cent., and for a greater 

 number of times it becomes rapidly smaller and smaller." 



This discovery and formulation of the law of individual varia- 

 tion namely, that such variation occurs according to the law of 

 probabilities was first made by the Belgian anthro- 



discofere^ofvari- pologist ' Q uetelet ("Lettres sur la theorie des Proba- 

 ation according bilites." Brussels, 1846), on a basis of the examina- 

 to the law of tion of the height and chest measurements of soldiers, 

 chance, j t was i a t er elaborately confirmed by Francis Galton 



(numerous papers and the book, "Natural Inheritance," 1870-1890), 

 by quantitative determinations of the height, weight, span of arms, 

 breathing capacity, strength of pull, strength of squeeze, swiftness 

 of blow, and keenness of sight in men and women. It has been 

 most illnminatingly discussed by Karl Pearson in "The Chances of 

 Death, and other Studies in Evolution," 2 vols., 1897. Since then 

 the recognised necessity of a more thorough study and understand- 

 ing of variation, as the indispensable foundation of species-forming 

 has led to a large development of the statistical and mathematical 

 study of variation, under the name of biometry, a study largely due 

 to the initiative and genius of the English mathematician and natural 

 philosopher, Karl Pearson (numerous papers from 1894 to present). 

 Most of the methods and formulae for determining precise mathe- 

 matical expression of variation conditions have been devised by him. 

 These methods and formulae permit of an actual mathematical com- 

 parison of variation among various parts in one species (immensely 

 enlarging our definite knowledge of structural correlations), or 

 among similar or wholly different parts in various species. With 

 the statistical facts or data of variation thus put into precise mathe- 

 matical expression, these expressions may be submitted to a deal 

 of independent mathematical treatment ; rather bewildering, it must 

 be confessed, to most biologists, but presented by the biometricians 



