242 Prof. K. Pearson on certain Properties 



The last equation will divide by n — 3, or 



{^-W^-^-nK 



(31) 



Substitute this value of n 3 on the right-hand side of (29), 

 and we have 



A ( w -3K,-4) _ 3A (^-2) ! _ (1()n _ 24) 



or 



w 2 



Divide out by and we have 



J n — 1 



&(n-4)-2A(2/i-5) + 3ft(n-2) + 2(n-l)=0, 

 or 



^(A-4 y 5 2 + 3/3 1 + 2)=4y5 3 -10A + 6/3 1 + 2. 

 Thus 



4^3-10^ + 6^ + 2 



n - A-4ft + 3A + 2 (32) 



n being now known (31) gives us 



n*(n — 1) ,„„v 



* 2 -4(rc-l) + 2/3 2 (^-2)-/3 3 (rc-4) ; " ' K ° 0) 

 z 2 and n being known, we have bv (23) 



^-kW^s^ • • • ^ 



Then ra 2 and e are the roots of the quadratic 



? 2 -2i? + *2=0 (35) 



m 2 and e being known, we have 



e — m 2 — n 2 

 ™i = " (36) 



Next, « and /3 are roots of 



f2_ mi ^ +m2==0 , (37) 



and y=n + « + /3+l. . ..... (38) 



Lastly, from (2) 



r=-«, q=-fi/n i and ya ?"*" 1 , , (39) 



