XXXI] Introduction Iv 



We have now the desired h and k and have to inteqjolate djN = '28066 between 

 •2771 and -2951. There results /■ = -9099. 



This is in excellent agreement with the value 9 105 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. 58—61) 



The T-Function. (J. H. Duffell : Biometrika, Vol. vii. pp. 4.3—47.) 



It is well known that F (x + l) = xr{x), and this property enables us to raise 

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

 investigations we require r(a;+ l)/ay'e~''. The following formula due to Pearson 

 will then be found to give T {x + l)/;c^e~* with great exactness : 



log (^-~5^^) = -0399,0899 + i log x + -080,929 sin 2^!^ (^^^-y 



I^or values of x+1 less than 6 and often for values less than 10, we find 

 log r {x + 1) or log r (j)) 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 1'145. 



Illustration (i). Find F (-2346). 



By the reduction formula F (-2346) = F (l-2346)/-2346. 



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



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



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

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

 = 1-958,9044. 

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

 -1-370,3280 



-588,5764 

 Or F (-2346) = 887772. 



