Kinds of Variation 159 



measure the length of hair in the wool of sheep, or the length 

 of fibre in cotton, or the thickness of hide in cattle. Physical 

 measurements can be combined to give us proportions, as the 

 relative length and width of the head, the ratio of sitting 

 height to standing height, or of girth to length. 



In all of such measurable characters we find individuals 

 differ, and they differ in a mathematically constant manner. 

 In a given population the individuals may vary as much as 

 ten or twelve inches in height, although there is in every 

 population a tendency for the various statures to cluster 

 around a central point. The number of individuals of a 

 given stature constantly diminishes as this stature departs 

 from the mean. This was first worked out by a Belgian 

 mathematician, Quetelet, in 1845. One does not need to be 

 a mathematician, however, to follow the argument. These 

 measurements and calculations merely present in a more pre- 

 cise form what every person of ordinary intelligence already 

 knows, namely, that there are more people of about the so- 

 called average height than there are very tall or very short 

 people. It is exactly what we mean when we say that a 

 person is exceptionally tall or exceptionally short. We mean 

 by exceptional relatively rare, not common or frequent. 

 The mathematical formula shows us, however, that the dis- 

 tribution of such measurements follows a regular course, so 

 that while it is impossible to tell in advance how tall a par- 

 ticular person is going to be, we can tell with a remarkable 

 degree of accuracy what proportions of individuals we will 

 find for any given stature (Fig. 38). It is this principle 

 that enables the quartermaster or the manufacturer to stock 

 up shirts or shoes without danger of running short on some 

 sizes and of having a surplus of others. 



The distribution of variations according to this so-called 

 chance curve, or the law of probability, is found to hold for 

 many different kinds of measurable qualities. If we adopt 

 an arbitrary scale for measuring degrees of pigmentation in 

 the hair, we shall find variation in hair color to follow the 

 same distribution. If we count parts that are variable in 



