" Correlation of Averages" for Four Variables. 375 



£l4. 



A 



(P2i Pm Pm) = — '0640. 



f=-(P34P4iPi 2 )=--2483. 



^~ = +(pzi P4 2 Pia)= -(-'1081)= + -1081. 



|f = - (pa P12 P23) = --1045. 



Treating the Plymouth values of the p's in the same way, 

 we obtain the second set of proportionate coefficients. The 

 following Table exhibits all the results : — 





Pi 

 A' 



P2 

 A 



Pz 

 A* 



Pi 

 a" 



?12 



A ' 



?13 



A ' 



?14 



A ' 



?23 



A ' 



?24 



A ' 



A • 



Naples . . . 



•2013 



•3991 



•3844 



•2642 



-•1436 



•1886 



-•0640 



-•2483 



-•1081 



-•1045 



Plymouth. 



•1486 



•4172 



•3680 



•2342 



-•1220 



•1458 



-•0355 



-•2673 



-•1195 



-0701 



Next to find -r- we may use the method of Professor 



Edgeworth's last paper*, which is less laborious than the 

 other method. Accordingly 



Pu P12 P13 Pu 



P21 P22 P23 P24 



£>31 PS2 PS3 P34 



Pil P<L2 ^43 Pii 



=!.&+».& 



9l3 



9u 



^ +Pl2~£ +Pl3~£ +PH ^ 



= •2013 

 -•1023 

 = •099 = *10 correct to two places of decimals f. 



* Ante, p. 350. 



t It should be noticed that these results, like all the others, can be 

 relied on to two places of decimals only, since this is the number given in 

 the original data, i. e. the values of the p's. 



