XXXI] Introduction Iv 



We have now the desired h and k and have to interpolate d/N = '28006 between 

 2771 and "2951. There results r = "9099. 



This is in excellent agreement with the value "9105 deduced from 24 terms, or 

 from the final value '9102, which can be deduced from the 12, 18 and 24 term 

 values on the logarithmic rate of decrease hypothesis : see footnote p. liii. 



TABLE XXXI (pp. 5861) 



The r-Function. (J. H. Duffell : Biometrika, Vol. vn. pp. 4347.) 



It is well known that T(x + l) = xT'(x), and this property enables us to raise 

 or lower the argument of the T-function at will. As a rule in most statistical 

 investigations we require T(x + l)/x x e~ x . The following formula due to Pearson 

 will then be found to give r(x + l)/x x e~ x with great exactness: 



lo g ( F r^l = '0399,0899 + J log a + -080,929 sin . . .(xlii). 



\ 3j & / 3C 



For values of x+1 less than 6 and often for values less than 10, we find 

 log T(a;+ 1) or \agT(p) from Table XXXI by reduction to p between 1 and 2. 



The reader's attention must be especially drawn as to the rules, given on 

 the Table itself, as to (i) characteristic, (ii) change of third figure of mantissa 

 at a bar, and (iii) the sign of the differences on the facing pages of the tables. 

 The difference tabled under 1*144, say, is the drop from 1*144 to T145. 



Illustration (i). Find T ('2346). 



By the reduction formula T(-2346) = r(l-2346)/'2346. 



Hence log T (-2346) = log T (1-2346) -1-370,3280. 



log T (1-234) = 1-958,9685 A = - 1069, 



log T (1-235) = 1-958,8616 -6A = - [641-4]. 

 . . log F (1-2346) = 1-958,9685 - [641 ] 



= T'958,9044. 



log T (-2346)= 1-958,9044 

 -1-370,3280 



588,5764 

 Or T (-2346) = 3-87772. 



