ccxxxvi Tables for Statisticians and Biometricians [XL VII XLIX 



Thus G =-00429,21 346. 



The actual value as found by quadrature is '00816,185; thus the 9th or 10th 

 convergent would suffice for seven-figure accuracy, and for many purposes the 6th 

 or 7th would be close enough. The llth and 12th convergents give the value most 

 probably correct to the 9th figure, i.e. '0081,61854. As we have noted the great 

 advantage of the method is that the true value always lies between those given by 

 the (2s l)th and the 2sth convergents. Its application is not really very laborious, 

 certainly less so than Methods A and B just discussed, and far more exact. They 

 fail in the region of 1*5 to 3'0 times the standard deviation from the mode. The 

 above integral is taken within this region and the 7th or 8th convergent gives the 

 result correct to at least 1 in the 7th decimal place. 



The method of equation (xiii) provides the answer '008,1583, being in error 

 by '000,0036 while the method of equation (xii) gives '008,2511, or is in error by 

 000,0892, i.e. in the fourth decimal place or the second significant figure. The 

 reduction of the Incomplete B-function to a continued fraction seems likely there- 

 fore to supply the gap between the two methods discussed above and even to 

 cover advantageously a good deal of the ground where they function adequately, 

 since it involves no laborious interpolations*. 



TABLE XLIX. 



Values of the Differences of the Powers of Zero. Table of 

 q (p, s) = &PQP+*/r (p + s + 1), 



from p = 1 to 20 and s = to 20. (K. Pearson and Ethel M. Elderton, Biometrika, 

 Vol. xvii. p. 200 ; Ethel M. Elderton and Margaret Moid, ibid. Vol. xxn. pp. 306 

 308.) 



These differences of the powers of zero are of service in a number of problems, 

 and are required for the calculation of several formulae in the theory of probability. 



* The continued fraction method is illustrated on numerous examples by Dr Miiller (loc. cit.), but 

 the Incomplete B-function covers such a wide range of curves of varying forms that it is not at present 

 possible to assert that the continued fraction method will be found equally applicable to all cases. 



