clxxviii Tables for Statisticians and Biometricians [XXXP *, LI" 



Somewhere between these two the value p we are seeking must lie. For want of 

 better information take x = |(/3 + p) = "40 nearly, as a jumping off point for our 

 first approximation. Then 



^2 = ^ = 15, Po 2 = r^ = -20, 

 as a first approximation. 



Equation (lii), with E n+ i = E n E' , becomes 



24A" 2 - 9-8A" - 24 = 0, 

 which gives E' = 1-224,7959. 



We have now to substitute this value in (li). That equation becomes, since 



1 

 111 ~ oT ' 



21E'- 375 



4-166,6667 + 9-4A" - 5'25A" 2 

 -117,792,86 _ 



Hence p z r = -J 84,9063, and & = '369,813. 



We now start to find a second approximation 

 We have Po 2 = rp 2 ='l 84,9063, 



and p 4 = '034,1903, 1 - pf = "905,8097, 



The equation for E' becomes now 



24-1 45,2425 E' 2 - 9-060,4087^' - 24 = 0, 

 whence E' = 1-202,1116. 



This value of E' must now be substituted in the new equation (li). We have 



215.8097A"- -310,4583 



e = 



4-381,6832 + 7'820,8 1 1 1 #' - 5*395,2425 tf' 2 



Thus p 3 r = p Q 2 + e' = 176,3822, 



and accordingly p 3 = -352,764. 



We will now make a last approximation. 



Here P *= -176,3822, 



and we have Po 4 = -031,1107, 1 - ro 4 = '968,8893. 



The equation for E' becomes 



24'222,2325' 2 - 8-642,7278 E' - 24 = 0, 

 giving #'=1-189,668, 



