732 Fluctuations 



quiry into the phenomenon of regression, or of 

 relation of tlie degree of deviation of the prog- 

 eny to that of their parents, and the selection of 

 extreme instances for multiplication are obvi- 

 ously independent of mathematical considera- 

 tions. On the other hand an important inquiry 

 lies in the statistical treatment of these phe- 

 nomena, and such treatment requires the use of 

 mathematical methods. 



Statistics however, are not included in the 

 object of these lectures, and therefore I shall 

 refrain from an explanation of the method of 

 their preparation and limit myself to a general 

 comparison of the observed lines with the law 

 of chance. Before going into the details, it 

 should be repeated once more that the empirical 

 result is quite the same for individual, and for 

 partial fluctuations. As a rule, the latter occur 

 in far greater number, and are thus more easily 

 investigated, but individual or personal aver- 

 ages have also been studied. 



Newton discovered that the law of chance can 

 be expressed by very simple mathematical cal- 

 culations. Without going into details, we may 

 at once state that these calculations are based 

 upon his binomium. If the form (a + b)° is cal- 

 culated for some value of the exponent, and if 

 the values of the coefficients after develop- 

 ment are alone considered, they yield the basis 



