4o8 



THE GRAMMAR OF SCIENCE 



due to selection ? It is clear we cannot without an 

 artificial environment separate an adult population and 

 measure all its living members at the beginning and end 

 of a certain period. But what we can do is to measure, 

 say a sample looo adult members of a population at 

 one time and a second sample lOOO at a later time. 

 We take these two groups as fair samples of the adult 

 population at the two epochs. We must, of course, 

 choose our type of life and its locality with reasonable 

 precautions against migration of any kind, or against 

 rapid change of environment during the period under 

 consideration. 



Let the following, for example,^ be the frequency per 

 lOOO of some character in an adult population at two 

 epochs, the scale of measurement denoting some quite 

 arbitrary system of units : — 



Here the modes at the two epochs are 7 and 9, 

 the means 7.78 and 8.38, and the standard deviations 

 2.58 and 2,04. Thus both the type and variability have 

 changed between the series of observations, i.e. selection 

 has taken place. It will be seen at once that deviations 

 in excess of the mode are in one case larger and in the 

 other smaller than those with equal frequency in defect ; 

 the mean is in one case greater, in the other less, than the 

 mode ; such distributions are termed skew. It is found 

 convenient to measure this skewness by the ratio of the 

 distance between mode and mean to the standard 

 deviation," and accordingly the skewness at the two 

 epochs is given by .302 and —.303 respectively. Thus 



^ The illustration is purely imaginary. 



^ The actual positions of the mode are determined more precisely in real 

 working than when we take as above 7 and 9 for their values ; but these suffice 

 to indicate the general nature of the processes. 



