56 



/?£/./. SYSTEM TECHNICAL JOVRX.M. 



of the law are, themselves, inconsistent with the assunii)lioii of such 

 a law. Prof. Pearson was one of the first to point out this fact. He 

 considers among others an example originally given by Merriman ' 

 in which the obser\ed distribution is that of 1,000 shots fired at a 

 target. The thcnrctiral n'>rmal is the solid line in I-'i'j "1 and the 



HIL 



-E^b-ra*^ 



1-iff. .s 



observed frequencies arc the small circles. When represented in this 

 way there appears to be a wide divergence between theory and ex- 

 perience. Of course, some divergence may always be expected as 

 a result of variations due to sampling; and, too, we must always 

 question a judgment based entirely upon visual observation '" of a 

 graphical representation of this character. Prof. Pearson uses his 

 method — which will be discussed later — for measuring the goodness 

 of fit between the theoretical and observed distributions. He " 

 finds that a fit as bad or worse than that observed could have been 

 expected to occur on an average of only 15 to 16 times in ten million. 

 We must conclude, therefore, that these data are not consistent 

 with the assumption of a uni\'ersal normal law. 



A Priori Reasons. From the physicist's \iewpoint the origin of 

 the Gaussian law may be explained upon a moie satisfactory basis. 



'"Method of Least Squares," Eighth Edition — I'agc 14. 



"This point will he emphasized later: — first, hy showing that these data 

 al^l'car consistent with a normal law when plotted on prohability paper, and 

 second, by showing that some frequency distributions appear normal when 

 plotted even though they arc not. The other data in this table will l>e re- 

 ferred to later. 



" Reference to the original article and a quotation therefrom given in the 

 eleventh edition of the Encyclof'cdia Brilaunica on the article "Probability." 



