ccxxxiv Tables for Statisticians and Bio metricians [XL VII XLVIII 



by this method. We first compute the ordinates at intervals of h = '004 from 

 & = '12 down towards the origin, arranging the work as in the table on p. ccxxxiii. 



We have T/ O + y z + y + . . . + yu. = '2054,8915, 



yj + 2/3 + 2/5 + . .. + 2/21 = 1849,6951, 

 2/ 2 + 2/4 + 2fo + . + 2/22 = "1260,8297, 



A = -004, 

 and using the approximation (xviii), 



a?(l -x) 80 dx = -1507,7036 x 10~ 24 . 



L 



'0 



From E. S. Pearson's Tables of the Complete F-Function*, the value of 



log ;- log r (102) - log r (21) - log r (si) 



is found to be 22-7334,7268,91, and 



- = 5-41 34,3204 x 10 22 . 



'o 



Thus /-i 2 (21, 81) = 10- 2 x -1507,7036 x 5-4134,3204 



= -0081,6185. 



Had we taken ordinates at intervals of '008, instead of '004, we should have 

 obtained the result 



7. 12 (21, 81) = -0081,617. 



This method is not really very laborious. 



(ii) Another method of determining the value of the Incomplete B-function Ratio, 

 namely, 



x,- B( . - ,1 



{P>(1) xv^(l-x) 

 Jo 



has been provided by J. H. Miillerj"; it consists in converting the Ratio into a 

 continued fraction, and evaluating its convergents. 



Let t=^ - , k = p + q 1, u s = - - . Then 

 1-a? p + s 



whore o-.> a- 



* Tracts for Computers, No. vni. Cambridge University Press. 

 t See Biometrika, Vol. xxii. pp. 284297. 



