( 323 ) 



or 



H^h'^ 



'Hh — f--T [H-hy ^ (H-hy ^ 



(10) 

 jr [_ ' 2.1 ! ' 2' 2 ! 



On comparing this expression witli (7) it is at once seen that in 

 this manner too great a number of small deviations must be found, 

 as the module of the deviation zero, computated by (10) 



'Hit 



\/ 



is always smaller than that derived from (7) ; 



The position of the four points where the two curves intersect 



are found by equating the expressions (7) and (10); if the development 



can be stopped at the third term they are given by the roots of the 



biquadratic : 



pX^ — ^X» + 5 = (11) 



^ 6 



4:(]/H—]/hy 



{H-hy 



With the help of the form. (8) for d-, it can be shown that, if a 

 series of figures follows the law (6) the computation of Jt according 

 to (2) must necessarily lead to values which are somewhat too high : 



2(ji, {H-hy f ^ H\-^ 



Putting 

 we find : 



('""fj 



»' Hh 



H-\-h = p, H-h = q, 



H of 1 o' 1 7' 



Zo^ - = 2 ^ 1 -1- - ^ + - ^ + 



_ = ^_ __ __ ;:^>^ . • . (12) 



/ I q' 1 q' \' 



4. In the following applications of these reasonings to deviations 

 taken collectively for all months, the frequencies are reduced to a 

 total number of 1000 : by exponential law is understood the simple, 

 normal law of errors (1), 



22* 



