MATHEMATICAL CONTRIBUTIONS TO THE THEORY OP EVOLUTION. 265 



(13.) Many like propositions may be stated with regard to the action of selection 

 on the correlation of characters. They require but little modification to state them 

 for artificial or natural selection, as they are here stated for what we have termed 

 random selection. The above will, however, suffice to indicate how every form of 

 selection of variability or correlation influences in a manner capable of quantitative 

 expression the variability and correlation of all other directly and indirectly corre- 

 lated organs. Selection cannot be of service in altering one organ only, it alters at 

 the same time the whole inter-relationship of a complex of organs. Evolution by 

 natural selection can never be the change of one organ to suit a particular environ- 

 ment ; it is the balance of advantage and disadvantage produced by the change of 

 all organs involved in the attempt to select one of them. The moment the intimate 

 correlation of organs in animal or plant life has been fully realised and this i-ealisation 

 owing to recent statistical investigations has become fairly easy then the conception 

 of natural selection as moulding any single organ to what may be fittest to its sur- 

 roundings must be discarded. The selection of the " fittest " in one organ would 

 probably mean the selection of the unfit in other organs, and a general balance of 

 fitness in the complex of organ is all that is possible.* 



IV. ON THE PROBABLE ERRORS AND THE COEFFICIENT.-; OF CORRELATION BETWEEN 

 ERRORS MADE IN THE DETERMINATION OF THE CONSTANTS IN THE CASE OF 

 SKEW VARIATION. 



(14.) The case of Skew Variation has been dealt with at length by one of the 

 present authors in the second paper of this series. He has shown that in a great 

 variety of cases it can be dealt with by a series of curves having three principal 

 algebraical types, each defined by a certain number of constants. The probable 

 errors of the determination of these constants were not then investigated, but it is 

 clearly of great importance for the practical use of these curves to know how far 

 these constants can, for any given number of observations, be depended upon to give 

 an accurate measure of the skevvness and its special features. At the same time an 

 investigation of the probable errors of these constants leads us to a number of novel 

 properties which are connected with the theory of evolution in the frequent case of 

 skew variation. 



* Take, for example, result (xxxvi.) ; as far as terms of the second order are concerned R ffli '., s = \/2 . r l2 r l3 . 

 Hence, with positive correlation between three organs, the effect of trying to get a group very stable in 

 oue organ, i.e., with a negative Ao-j, is to reduce the correlation between every other pair of organs ! In 

 other words, we have to reduce variation at the expense of correlation, increased stability of one organ 

 is gained at the expense of decreased stability in the inter-relationship of other organs. This may 

 possibly be illustrated by the long bones of the French, where the lesser variability of the male relative 

 to the female connotes also a lesser correlation. See LEK and PEARSON : " On the Relative Variation 

 and Correlation in Civilised and Uncivilised Races," ' R. S. Proc.,' vol. 61, pp. 354-350, 

 VOL. CXCI. A. 2 M 



