32 



Mr. W. Shanks on the 



[Nov. 23, 



s oooo = 9'°945° 88 5*9 8 443 6 9 6 7^ 6 "455 33393 43939 *7 82 9 8 7 8 n 30381 



14.506 16283 85209 05328 30500 87619 93914 09299 23691 97409 



31969 93538 



S io,ooo = 9'7 8 7 6 o 60360 44382 26417 84779 04851 60533 48592 62945 57769 



16183 89460 95668 16020 24943 15950 68001 25x27 29008 08825 



2S66^ 45713 



When we have S 100 we have excess of + Bernoulli terms over — 

 Bernoulli terms as follows : — 



+•00000 83332 50003 96783 73773 23792 87768 83353 90186 48901 



78976 95889 08023 27933 88599 8l 9 J 3 48032 53704 54782 29326 



45555 64243 



For S l00 the sum of the + Bernoulli terms is 



+'00000 83333 33337 30158 73773 44885 67821 37321 67823 08773 

 00082 30639 33761 49846 36254 14224 82920 15089 51978 53129 

 32622 35457 80834 33466 17877 22649 42919 19943 83311 44605 

 09910 37086 58144 47970 79756 1 381 3 15081 18650 05862 58830 

 54^5 



For S 100 the sum of the — Bernoulli terms is 



—•00000 00000 83333 33375 00000 21092 80052 53967 77636 59871 

 21105 34750 25738 21912 47654 32311 34887 61384 93958 76677 

 70933 50276 12351 60205 99358 40193 39578 24455 06318 691S0 

 82191 70839 75485 79804 74621 35198 75347 46810 82718 00710 

 6 9953 



For S 200 the sum of the + Bernoulli terms is 



+•00000 20833 33333 39533 73016 61283 59538 59711 91078 12258 

 22890 92137 92329 17052 51095 23490 89894 78957 35141 06774 

 04433 65950 49748 89147 11592 75754 43919 38271 38143 50271 

 65525 60887 11534 99567 61791 58429 85003 06150 05862 58830 

 54 26 5 



For S 200 the sum of the — Bernoulli terms is 



—•00000 00000 05208 33333 49609 37505 14960 84887 28877 09510 

 05685 64006 82170 11770 13023 01074 35246 38458 75084 75675 

 04222 29829 71026 50819 24197 13084 02015 36765 99447 44527 

 25466 44760 75767 81 146 37524 18401 87847 46810 82718 00710 

 69953 



For S 500 the sum of the + Bernoulli terms is 



+•00000 03333 33333 33358 73015 87309 34487 73462 42678 21147 

 87864 83345 53789 61875 16264 59799 20761 22352 44796 75809 

 19590 05554 



