CHAP. XX.] PROBLEMS ON CAUSES. 341 



M+ N- I _ j. M + N-l I 



~~W~ ~p' ~~W "v ; 

 whence 



M 



fJL + V 



We find 



whence 



Cipi c n p n 



and finally, 



m +1 = ^ m + 1 M 



fJL - Cl/?l' ' /U - C n pn 



n : +l = ^ r,\ . n n + I = ~ 



Substitute these values with those of M and N in (9), and 

 we have 



(fl - Ctfi) (in - C z p z ) . . (fJL- C n p n ) fl + V-l 9 



_ v^ _ 



(v - c, (l- Pl )} {v -c z (\- p z )} . . {v - c n (1 -p n )) ~ p 



which may be reduced to the symmetrical form 



+ v - = 



/i 71 ' 1 



(v-fiQ-pQ) ..(v-c.Q^-^)} (12) 



Finally, 



Let us then assume 1 - v = u 9 we have then 



u _ (M - C ip0 0* - c 

 "- 1 



