å4 O. v. L. Charlier. 



where and are certain constants and and 9^ are two normal curves, eacli 

 with its special value of the coordinates of the mean [b^ and h.^) ^^'^^ of the standard 

 deviations and a^. 



Designating now with 



(X — by 



another normal-curve, we have, according to the general theory, 

 (35) c, 'f , + c, 'f, = ^0 'f + ^3 'f'" + ^1, 'f" + • • -, 



6 and a being determined in such a manner, that and A„ shall vanish. 



The formula (26) in the »Meddelanden» N:o 27 gives us the following general 

 expression of the coefficients A, 



^" y 1 '^'^ ^'^^ 



where i?, (.r) is given through formula (28*) in the same memoir. 



Multiplying (35) successively by J?^, JR.^, li^, . . . and integrating, we 



now obtain the following equations for determining the unknown quantities c^, b^, 

 •^li fcg' '^r ^^^^ convenience we have introduced the denominations 



(36) 



1) T 







■''2 



= H -V — a^ 













= b,, 











(37) 



The equations now take the form 



y/f,r,(3,r,-2^J+ //1.^2(3^^2 

 2/f,?,(3.r2_2^/J)+ ?/i.22(3^i 





1, 



y 2^ 2 = 



0, 



■^2 y 2 '^2 



0, 



~ 2v/,) = - 









+ Gyl) = - 







*'2 ' 



to be calculated. It is to be observed that C3, and are known functions of 

 the moments of the given frequency curve. 

 We have indeed 



(3H) C. = [so'ß.,, 



where ß, (for s — 3, 4, 5, . . .) are the characteristics of the frequency curve (Com 

 pare (5*)). 



