ccxxx Tables for Statisticians ami Biometricians [XLVII XLV1II 



Substituting, we have 

 I x l (l-x) m dx 



u 



(m+ 1)120 



x (2747/o - 6007/j + 600?/2 - 400?/3 + 150y 4 - 24 y 5 



(225y - 770 yi + 1070y 2 - 780?/ 3 



o - 3557A + 5907/2 - 4907/ 3 + 205y 4 - 35y 6 ) 



y (157/o - 70 yi + 130r/ 2 - 120y 8 + 55y 4 - 10y B ) 



(10^)5 



"I 



~ 2/5) 



+6 v 



Here the six series of T/'S in round brackets are functions of m only, and tables 

 of these six functions for the argument m would render the labour of computing 

 formula (xvi) relatively easy. This formula, however, is of little service when both 

 I and m are large. It does not therefore provide solutions for the gap between 

 Wishart's formulae, which we desire to fill. 



We have already seen that fair approximations can be made for the interval 

 x x> l'5cr and < 3<r by Camp's method*, which is by no means so laborious as 

 the expansions already referred to. 



In order to test the degree of approximation of Wishart's formulae (at least 

 in a single case) the table opposite has been kindly computed for this work by 

 E. C. Fieller. 



Notes on the Table. 



rx 



If the incomplete B-function B x (l+l,m+l) be expressed by I x l (\ x) m dx, 



Jo 



then we have seen that u = (x )/\/- , where n = I + m. The expression 



V nil V n 3 



A/ 3 , when I and m are considerable, approximates to the standard deviation of 



the curve y = y Q x l (\ x) m . Thus u is approximately the deviation from the mode 

 of the bounding abscissa of the integral measured in terms of the standard de- 

 viation. If x < - . i.e. to the left of the mode, u is negative ; it is positive if x> -, 

 n n 



i.e. to right of the mode, the positive direction of the axis of x being from left to 



* See pp. xxx xl, above. 



