212 Prof. F. Y. Edgeworth on the 



If the units of the variables be taken so that k l9 Jc 2 , k 3 , &c. 

 each = J, then l 12 , l ls , &c. will he replaced by ^p 12 , ^p^, &c, 

 the coefficients of correlation which have been discussed in a 

 former paper *■ 



To obtain a second approximation to the compound law of 

 error by this method : beginning with the case of two varia- 

 bles, put as before 



&=?%$$ £ifd#dy> 



principal axes being employed. Also put 



n — %^^dxdy, 



P = « 6«V » 

 9 = » S*V » 

 ?^ 8 11 





"We have then, for z the law of the compound, the following 

 system of equations : — 



dz 



lie 



dz_ 

 dm 



dz 



dn ' 



dz 

 dp 



dz 

 dq 



dz_ 



dr ' 



1 d 2 z m 



2 dx 2 l 



ld& 



2dy 2 ; 



1 d 3 z 

 ~6d^ 



1 d* 



2 da?dy' 



1 d z z 

 2d^ay ; 



1 d&_ 



6 ^ 3; ' 



, dz ~i dz , o dz t ~ dz , dz A 

 ^ + ^^-+2^-77 +372^ +2/? j-+^^- =0, 



. dz dz t Q dz dz dz 



* Phil. Mag. 1892, xxxiv. p. 194 et seqq. 



(i) 



(2) 

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(4) 

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 (?) 

 (8) 



