10 



Tables for Statisticians and Biometricians 

 TABLE II. (continued). 



Note. We believe that x and z may be taken as correct to the figures tabled. 

 They were worked of course to more figures than are shown. The possibility of 

 error in the ratio \ (1 + a x )/z is greater, and may amount to five units in the tenth 

 decimal. It seemed better to leave the last two figures standing with this warning 

 rather than destroy the symmetry of the table by cutting them out. We feel com- 

 pelled however to show only twelve figures in the last three entries of this ratio. 



A more extended system of symbols than heretofore has been adopted in this 

 table to indicate the nature of the last figure. 5+ and 5~ signify as usual that the 

 real number exceeds 5 and falls short of 5. The symbol 5 e denotes that the number 

 is exactly 5 to the extent of the calculations, i.e. -63719, 16745 6 denotes that x for 

 |(1 + a x ) = -738 was found to be -63719,16745,00. It does not necessarily indicate 

 that the value terminated at the tenth or twelfth decimal. Another innovation has 

 been made. Consider -60075,97742 s ; the usual interpretation of this would be that 

 the number as actually worked was terminated by 5, 50 or 500 as the case might be, 

 and the computer was unable to settle whether to enter it as -60075,97742 or 

 60075,97743. In the present table there may be doubt as to the correctness of the 

 twelfth figure and the affixed 5 has been used when the final figures are 48, 49, 

 50, 51 or 52. Thus -60075,97742,48 or -60075,97742,51 would not be printed as usual 

 60075,97742 and -60075,97743, but as -60075,97742 s , precisely as -60075,97742,50 

 is written -60075,97742 s . This seems safer when we cannot be sure of one or two 

 units in the twelfth decimal place, and is more accurate when the 5 is actually put 

 on the machine in computing. 



We have to thank most heartily Dr W. F. Sheppard for the original loan to the 

 Laboratory of his twelve figure tables of \ (1 + a x ) to argument x, and more recently 

 for extracts (x = 2-1 to 3-1) from his sixteen figure table of log e | (1 a x ) to argu- 

 ment x by intervals of -1. We have also to thank Mr Frank Bobbins for determining 

 a large number of the values of x. 



