KUNGL. SV. VET. AKADEMIENS HANDLINGAR. BAND 58- N."0 3- 17 



As s may be assumed to be a great number and as /?„ happens to have the form 



J " i 



,-i G = -^ + term of order -^ 



an approximation of the order leads to the above form (C) for the .4-function. 



o 



Similar discussions of the orders of magnitude have been given by Charlier 1 

 in the case of the description of the point binomial by functions of type A. 



Owing to the importance of the subject we shall here investigate the case of 

 tvvo variates. 



The hypothesis of elementary errors assumes that there are at work s error- 

 sources, which we denote by Qi,Q 2 ,Q 3 , • . . Q s - The errors produced by, say, the 

 source Q t being denoted by x if we assume that the probability that in a certain in- 



stance a\ will fall within the limits x ± - dx is given by the function 



fi(x)dx. 

 The observed variates x and y are then given by 



X — A/j 3/| "T" K>2 *^2 ' 3 *^3 ' " " "• "*8 *^s 



y = /, x 1 + l 2 x 2 + l 3 x 3 -\ f h x s 



where k t and I t are constant coefficients characteristic of the source Q { . 



As has been shown by Charlier 2 the hypothesis generally leads to a correla- 

 tion function of type A. I f it be of type A we have 



W) F{x , v) = lf{x , y) + lA JI^É. 



Tn the course of his work Charlier 3 introduced some quantities c l $. o^, a { %, . . . 

 which are characteristics of the probability function /; (x t ) of the source Q t . Assuming 

 all the probability functions of the error souices to be of type A the nature of these 

 characteristics is defined by writing the ^4-function in the symbolical form of Edge- 

 worth, whence we have 



where 



aW a(*> oW 



fi(xi) = e B bi g ffi (xi) 



i[i\Xi) = . • e 2 



1 Chakliek: Die strenge Form des Bernoullischen Tlieorems, loc. cit. n:r 43. 

 -' Charlier: The correlation function of type A, loc. cit. n:r 58. 

 3 Loc. cit. 



K. Sv. Vet. Akad. Handl. Band 58. N:0 3. 



