STANDARD OF COMPARISON. 91 



chance, but must occur because of some definite law. Since Aris- 

 totle's time, the law of probabilities has been demonstrated so many 

 times that no one any longer questions it. Vast business enterprises 

 and even gamblers depend upon the law of probabilities for their 

 profits. Any one who wishes to test the law of probabilities can 

 easily do so by throwing dice. Each die is a cube having its sides 

 marked with from one to six spots so arranged that the sum of the 

 opposite sides equals seven. If any one throws two dice he may 

 get two aces, the sum of which is two; or he may get two sixes, 

 the sum of which is twelve; but if he throws the pair ten times the 

 sum will be very near seventy, or an average of seven. In one 

 hundred throws the average would be still nearer seven, and in one 

 thousand throws the average would never vary from seven more 

 than a minute fraction. 



THE SCALE AND THE LAW OF PROBABILITIES. 



Having established a standard scale of birth-ranks and having 

 twenty-five men 4 whose births we wish to apply to this scale, it 

 follows from the law of probabilities that we should find two or 

 three births in each one of the ten classes. It also follows that if 

 we take the birth-ranks of the immediate ancestors of these twenty- 

 five men we should also find their births evenly distributed along 

 the scale. From the manner in which the scale was made and 

 its comparison with what it would have been if made from other 

 sources, it is evident that whatever deviation there is from an exactly 

 uniform distribution, that deviation should be in favor of placing 

 the larger number in the classes represented by the small letters 



(4) Four of the twenty-nine have been omitted from consideration 

 because of the impossibility of finding dates relating to their ancestors. This 

 should not affect the result, because there is no reason why unknown persons 

 should differ from known ones. 



