ccxlviii Tables for Statisticians and Biometriciam [LV LVI 



TABLE LV. 



In the early editions of Barlow's Tables a table of the higher powers of numbers 

 was provided, which was omitted in later editions. This table had been found of 

 much service, and a copy was made of it for lithographic reproduction in the pre- 

 sent work. Since this was done an excellent new edition of Barlow by Dr Comrie 

 has appeared which supersedes the more recent editions ; it contains this table of 

 the higher powers. As Table LV had already been prepared and supplements 

 that on pp. 38 39 of Part I of this work, I have still thought it worth while 

 to include it in the present issue. It has the advantage of providing all the 

 powers together. 



TABLE LVI. 



This list of constants to a large number of figures has proved valuable to 

 computers in the Biometric Laboratory, and other workers may find it so also, as 

 search for the loci where such quantities have been published can be protracted. 



APPENDIX. 



On certain Interpolation Formulae enabling one to interchange ordinates 



or rearrange areas. 



(i) Given z s -z, z s -i> 2 s> 2 s+i> 2 s+z, Zs&> to find z s+ - 5 and for use near the boundaries 

 of a curve or table z s -i- & , z s -- 5 , z s+rb , 



By a Lagrangian formula for interpolation, we have : 



z s+ . 5 - 



(ii) Given the areas w s _ 2 . 5 , n s _ r5 , ?? s _. 5 , n s+ . 5> n s+l . 5 , n s+z - 5 , where the subscript 

 indicates the mid-ordinate of the corresponding area, to find the areas ?? s _ 2 , w s _i, 

 n s , n s+ i, n s + 2 , n s+3 , defined by the subscript mid-ordinates, all the ris being on unit 



