216 Mr. W. Steadman Aldis. 



19. As an example, suppose the value of X Q is taken as 7 "4. Table 

 II gives 



u_ t = 0-000 424 795 741 

 u _ s = o-OOO 381 739 385 

 tt_ 2 = 0-000 343 079 156 

 w_ 1 = 0-000 308 362 213 

 ^ = 0-000 249 177 616 

 u 2 = 0-000 224 020 677 

 u s = 0-000 201 420 050 

 M 4 = 0-000 181 113 953 



whence, remembering that h = -j, it easily follows that, a minus sign 

 being understood before all the numbers, 



- 0-000 295 922 985 

 ft = 0-000 297 646 197 



7 = 0-000 300 532 225 



8 = 0-000 304 602 235 

 whence 



j8- = 0-000001 723212 

 y - p = 0-000 002 886 028 

 8-y = 0-000004070010 



Hence, using the formula (18), 



a = 0-000 295 922 985 



iV (y-P) = ' 000 00 288 603 



0-000 296 211 588 

 -a) = 0-000000861 606 



0-000 295 349 982 



The value in the table for Kj (7-4) is O'OOO 295 349 978. 

 If we apply the correction (20), the above values give 



Jfr(j8-a) - 000000 172 321 

 i (8- y ) = 116 286 



288 607 

 288603 



Correction = 000 000 000 004 



This has to be subtracted from the former value, and the result 

 agrees exactly with the value of ^(7*4) in Table II. 



The agreement is not in all cases quite so exact as in this example, as 

 may be expected from the necessary existence of more or less of error 

 in the last figures taken into account. 



