278 PROFESSOR K. PEARSON AND MR. L. N. G. PILON 



(i.) Any selection of the organ by size tends to alter its variability, but not its 

 skewness; this follows from (Ivi.) and (Iviii.). Further, if, as we have supposed, the 

 range be limited on the side of dwarf organs, then any increase of size means a 

 decrease of variability, and vice versd. 



(ii.) Any selection of variability is a selection of skewness; this follows from (lx.). 

 If a selection be made from a general population, which has less variability, then it 

 will tend to greater normality. In other words, it would appear that stringent 

 selection tends to generate normal distribution. Thus, if out of a skewly distributed 

 population we make a number of random selections, that with the least variability 

 will be most normal. Select at random again out of this latter selection, and the 

 least variable group will again be the most normal, and so on. 



Now take a problem of this kind involving group, and not individual, selection. 

 Let a large general population break itself up at random into groups, and let us 

 suppose these groups, not individuals among them, to carry on a struggle for 

 existence an inter-group, not an intra -group, struggle. Then, if it be an advantage 

 to a group that its members shall be among themselves close to a type, i.e., less 

 variable, then the more normal groups will survive, for variability is positively 

 correlated with skewness. Now suppose each group to be periodically subdivided at 

 random into new groups the mathematical description of some process of group 

 reproduction then we see how normal distribution may be a result of a stringent 

 inter-group selection of groups whose individuals have the closest resemblance to 

 each other intra-group resemblance. 



(iii.) Any selection of the size of an organ produces by (Ixxiv.) an alteration in 

 the distances between the mean and the mode, and between the mean and the end 

 of the range. 



A random selection which has its mean larger than that of the general population, 

 will, if the mode be on the dwarf side of the mean, tend to have its mode and mean 

 nearer together than are the mode and mean of the general population, while on 

 the other hand, to raise the mean is to raise the dwarf limit to the range. 



A considerable number of like results might be stated, but the above will be 

 sufficient to emphasize the general principle that a random and d fortiori an 

 artificial selection of the size of an organ, does, whenever its distribution is skew, 

 influence in a definite manner the variability of the organ. It is quite safe to assert 

 that it will also influence the correlation of organs. When we notice how wide-spread 

 is skew variation in nature, we may assert that the general rule is that no modifica- 

 tion can be made in any of the features mean sizes, variabilities and correlations 

 of a group of organs without at the same time modifying all the others.* 



* A paper has recently been published by Messrs. DAVENPORT and BULLARD in the ' Proceedings of the 

 American Academy of Science' (see Illustration II. below) on "The Variation and Correlation of the 

 Glands in the Legs of Swine." Unfortunately the authors have overlooked the markedly skew character 



