( 322 ) 



the resulting probability of a deviation being situated between x and 

 cc -f- civ is then : 



H 



da; r 



z e-^'^' d 



{H- 



and the equation of the frequency curve: 



y = 



-h"'x^ fi—H'X^~\ 



2{H-h)\/jT\_ w' 



Developing this expression we may put : 



^ 2''.3! ^ 2S5! J 



y — 



H-\-h 

 2[/jr 

 If we put: 



(6) 



(7) 



00 



(In = 2 I A-"?/ d: 

 



Ave find with the help of: 



CO 



2 I T« 6-^' dT= r 



m 



and 



00 



ƒ 



e—P^ — e—9^ q 



dz =z log — , 



z p 



for the moments of different order with respect to the maximum 

 ordinate : 



Fo = 1 ' M2 = ^^^ — 



2Hh 



Mi = ^ = 



log 



H 



1 H-\-h 



. . (8) 



{H-h)]/:T ^ h ' ^' 2(/jr hVi^ 

 From a series of deviations following the law (6) the two character- 

 istic constants H and h can be derived by computing the moments of 

 the second and third order. They are found to be equal to the roots 

 of the quadratic : 



P 



(ly^r 



q = 



(9) 



2{A^^ 2|Ltj 



If we had put a similar series to the test of the normal law (1) 

 we should have found for the equation of the frequency curve; 



