120 DOCTRINE OF EVOLUTION 



stration by the naturalists who have employed the 

 laborious methods of statistical analysis that the laws 

 according to which differences occur are the same where- 

 ever the facts have been examined. A single illustra- 

 tion will suffice to indicate the general nature of this 

 result. If the men of a large assemblage should group 

 themselves according to their different heights in inches, 

 we would find that perhaps one half of them would 

 agree in being between five feet eight inches and five 

 feet nine inches tall. The next largest groups would 

 be those just below and above this average class, 

 namely, the classes of five feet seven to eight inches 

 and five feet nine to ten inches. Fewer individuals 

 would be in the groups of five feet five to six inches and 

 five feet ten to eleven inches, and still smaller numbers 

 would constitute the more extreme groups on opposite 

 sides of these. If the whole assemblage comprised a 

 sufficient number of men, it would be found that a 

 class with a given deviation from the average in one 

 direction would contain about the same number of 

 individuals as the class at the same distance from the 

 average in the opposite direction. Taking into account 

 the relative numbers in the several classes and the 

 various degrees to which they depart from the average, 

 the mathematician describes the whole phenomenon 

 of variation in human stature by a concise formula 

 which outhnes the so-called ^' curve of error." From 

 his study of a thousand men, he can tell how many 

 there would be in the various classes if he had 

 the measurements of ten thousand individuals, and 

 how many there would be in the still more ex- 

 treme classes of very short and very tall men 



