KUNGL. SV. VET. AKADEMIENS HANDLINGAR. BAND 58 NCO 3. 21 



a {i> 1 

 5 be great or small. Then the y p l) +q = ~j+q\ are independent of s. As oj, 



must, however, be small of the order - the a$+ a for p>-\-q>2 must necessarily be of 



s 



a still smaller order of magnitude. Then the coefficients o pq must be of the order 

 of unity only in case p + q = 2; when p + q>2 they must (due regard being had to 

 their higher dimensions) be of a smaller order. If the y l *\ 3 are on the whole of the 

 same order for any assigned value of p+q vve should expect y pg to differ only by 

 a constant factor from their mean. Then y pq is also independent of s and we 

 should find 



.hen p + q 



3 



fi pq of the 



order 77= 



Vs 



V 7 " 



= 4 



fivt ■ 



1 



— 



S 



p + q = 



-6 



fi P9 » >' 



1 



» 



S 



and when p + q=^5 or greater t han 6, fi pq of a smaller order than 3| - 



In order to obtain an approximation of the order - we should ha ve to include 



also the terms multiplied by (i p for p+q = G. We need not, however, use the whole 

 of these terms. Indeed we only have to put 



(31) 



Jo 





Jio 



2 



) 







A. 





A« 



fi» 



■> 





Al 





Ao 



fi» 



+ 



2 Ptt ' 



fi 31 





fis<J 



^0 3 



-f 



fin fi»> 



A« 



= 



fioa 



fin 



+ 



1 r 



fi» 



= 



> 

 Pos 



fin 



> 





fhe 



= 



fila 

 2 









Hence, even in this case we need take into account only the first four orders 

 of moments. 



In (B) therefore we have to make i + j = 3, 4, 6, and for the fi ti for i + j=Q to 

 insert the values (31). 



To decide whether we sball have recourse to the one or to the other kind of 

 approximation we propose to use the following rule, which really is only provisional 



