LII LIV] /iifi'in/m-tion ccxhii 



We now proceed in the same way with Table LII***. 

 Our difference scheme is now : 



u Au Au A*a A 



400 -825,4397, 



200 -822,7588, - -002,6809, 



100 -817,3308, --005,4220, --002,7411, 



50 -806,2600, -'011,0768, -'005,6548, --002,9137, 



25 -783,2410, -'023,0190, --011,9422, -'006,2874, -'003,3737. 



'344,6484 as before, so that our coefficients of the differences remain the 

 same and we have: 



u = '825,4397 - -344,6484 x -002,6809 + -112,9329 x -002,7411 

 - -062,3146 x -002,9137 + -041,3668 x -003,3737 

 = -825,4397 - -000,9240 + -000,3096 - '000,1816 + '000,1396. 

 Thus 72 Hes between -824,7833 and '824,6437. 



Taking as before the mean of these values we have : 



72 =-824,7135. 

 Hence by equation (ii) : 



*# = 3j$ x ${$ x -824,7135 - (-898,9183) a , 



= -000,97566, 

 or O-B = -03124. 



These values for R 2 and <?& agree to the above five decimal places exactly 

 with those calculated from the hypergeometrical series (iii) and (iv). These results 

 are interesting as showing how by aid of a logarithmic interpolation it is possible 

 to cover by five values alone the range from 25 to 400 with sufficient accuracy for 

 most statistical purposes. 



TABLE LIII. 



This is a reproduction of Glaisher's Table of the Inverse Factorials. It has been 

 found of service in calculations by the arithmometer, especially in the work of com- 

 puting new tables. It facilitates much calculation which has otherwise to be done 

 by more laborious logarithmic work. 



TABLE LIV. 



Tables of reciprocals of integer numbers to seven decimals are common, but 

 these frequently prove inadequate for the needs of computers, especially when 

 preparing new tables. The present Table was computed for use in calculating 

 certain constants of the Incomplete B-function Tables and possibly deser\.> 

 preservation. 



