1867.] the Numerical Value of Eulerh Constant. 



431 



1 + 1+ =4-49920 53383 29425 05756 04717 92964 76909 19706 



01823 96745 38296 58902 43217 68318 06557 86735 

 78157 82663 88434 12900 97472 82033 55398 82942 

 63084 20093 94581 03200 90115 13091 15572 24477 

 64889 95794 59834 14243 62248 23530 45299 19591 

 + (circulating period consists of 1^275,120 decimal places). 



l + i+ ylo = 5-18737 75176 39620 26080 51176 75658 25315 79089 



72126 70845 16531 76533 95658 72195 57532 55049 

 66056 87768 92312 04135 49921 06986 97779 79182 

 73403 18617 00828 94825 42444 49096 57618 56974 

 16326 13467 07313 21114 47132 49733 09103 51089 

 + (circulating period consists of 39^419^059^680 decimal 

 places). 



l + i+ 2lo = '^-87803 09481 21444 47605 73863 97130 86163 68374 



00246 53027 30844 64971 94472 28783 30029 84018 

 15499 64301 86679 89238 37326 83211 85439 05911 

 76542 77855 27568 86559 30203 06049 25715 75389 

 22254 75748 47845 75246 64079 54805 61627 08837 

 + (circulating period consists of 



2,498,236,128,143,832,017,541,600 decimal places). 



The following value of Euler's constant has been found from the re- 

 spective sums given above, of the 10, 20, 50, 100, and 200 first terms of 

 the Harmonic Progression : — 



E or Eul. const. = -57721 56649 01532 86060 6 (last term employed is - ^j^^J- 

 E= -57721 56649 01532 86060 65120 900 (last term is -24^4). 



E= -57721 56649 01532 86060 65120 90082 40243 1042 (last 

 term is+ ^ 



E=-57721 56649 01532 86060 65120 90082 40243 10421 



69335 9 (last term is- 

 E= -57721 56649 01532 86060 65120 90082 40243 10421 59335 



93995 35989 (last term is+ J^^- \. 



Certainly 50 decimals are correct, and probably 55, in the value last 

 given. 



March 2, 1867. 



Supplementary Paper to that of March 2, 1867, "On the Calculation of 

 the Numerical Value of Euler's Constant." By William Shanks, 

 Esq., Houghton-le-Spring, Durham. Received April 9, 1867. 

 When 71=500, we have 



1 + i+i yio =6-79282 34299 90524 60298 92871 45367 97369 48198 



13814 39680 91166 43088 89685 43566 23790 55049 

 24576 49403 73586 56039+ 



