ccxxii Tables for Statisticians and Biometricians [XLV XLVI 



labour of computing is not really much shortened, for p will usually be fractional, 

 and accordingly the determination of the numerical values of the inverse powers of 

 p is troublesome*, and we have five interpolations to make, four to 8 2 and one to S 4 . 



If we require IQ (p), we have the formula 



......... (xiii), 



where as before x = 2 Vp tan -= = 



<L OLIX L/ 



This involves two additional interpolations into the Table of the complete F- 

 function, or since _^ 



where c is the coefficient provided for n=p-l from 100 to 400 in Table XLV, 

 one interpolation only if p lies between 101 and 401. 



Illustration (ii). Let us first apply Table XLVI to the case given in Illustra- 

 tion (i). Here the problem was to find the probability that a single individual 

 drawn at random would have a value differing from the mean by less than ^a, 

 where the parent population was described by 



y ~ / n &\ 85-67 ' 



We found P^ a = 27 9 (169'34), 



where tan = ^, sin d = -0995,0372, cos = "9950,3719, and p = 169'34. 



For interpolation in the </>-table we need 



, /- 2 \/]"69-34 (-0049,6281) 7 



x = 2 ^ tan ^ = -0995,0372 l ^'^ 



For the <j> s (x) tables we have 



<9 = -9807, </> = -0193, %0<j> = -0031,5458 s , 

 T _0 (i + 0) (l + <) = -0003,1845. 



Hence, using the central difference formula 



0) s 2 *i} 



< />) 8 ^o + (2 + 6')^i} (xv), 



we have </> (as) = '4028,4692 + -0000,2139 + '0000,0005 



= '4028,6836. 



* Dr Wishart has provided (Table XL VIII) a table of the inverse powers of numbers 50 to 100 by 

 units for p~- 5 , p~ l -, p- 1 - 8 , p~ z -, p~, p~ for another purpose. But this does not reach far enough 

 for our present aim and involves additional interpolations. 



