1878.] 



on the Value of Eulers Constant. 



93 



M = '43429 44819 03251 82765 11289 

 65661 14453 78316 58646 49208 

 18706 10674 47663 03733 64167 

 81226 58521 27086 56867 03295 

 77384 90514 28443 48666 76864 

 43543 43573 17247 48049 05993 



18916 60508 22943 97005 80366 

 87077 47292 24949 33843 17483 

 92871 58963 90656 92210 64662 

 93370 86965 88266 88331 16360 

 65860 85135 56148 21234 87653 

 55353 05 



where M denotes the modulus of common logarithms. 



50 



In these calculations the value of log has been determined with 



less accuracy than that of log and therefore the value of log 7 



found by means of the latter quantity has been preferred. 



If now in the formula which gives Euler's constant we take 

 oi = 500, we find the following results : — 



K 50 o= '00000 03333 33200 00025 39671 87309 34479 09501 49853 06920 

 81561 41982 03143 98353 10049 47690 35814 25947 82825 73530 

 80967 33251 23444 83365 27221 32891 79715 39888 78668 70158 

 11997 43277 84264 18919 84678 56672 58294 26067 37401 94207 

 08483 64907 04495 03811 66583 11699 18899 16275 81704 82573 

 08004 99446 91635 



S 500 = 6-79282 34299 90524 60298 92871 45367 97369 48198 13814 39677 

 91166 43088 89685 43566 23790 55049 24576 49403 73586 56039 

 17565 98584 37506 59282 23134 68847 97117 15030 24984 83148 

 07266 84437 10123 70203 14772 22094 00570 47964 42959 21001 

 09719 01932 14586 27077 01576 02007 28842 06850 09735 01135 

 74118 52998 6631 



Loge 500= 6 -21460 80984 22191 74263 67422 42594 91605 47278 04331 52606 

 36739 79303 69340 93242 07062 36272 51021 28288 27237 62074 

 83901 87110 62880 60166 54305 61594 90289 71296 61913 55661 

 26910 65179 94054 14829 26073 41092 64585 48079 22114 05716 

 58115 31635 24264 74180 14925 98528 81625 94504 71489 68628 

 97329 77937 00975 



E= "57721 56649 01532 86060 65120 90082 40243 10421 59335 93992 

 35988 05767 23488 48677 26777 66467 09369 47063 29174 67495 

 14631 44724 98070 82480 96050 40144 86542 83622 41739 97644 

 92353 62535 00333 74293 73377 37673 94279 25952 58247 09491 

 60087 35203 94816 56708 53233 15177 66115 28621 19950 15079 

 84793 74508 5697 



Again, if in the same formula we take n = 1000, we find the fol- 

 lowing : — 



^-=0-0005 



R 10 oo= -00000 00833 33325 00000 39682 49801 59487 73237 84632 11743 

 88611 32124 18782 98862 06644 51967 06850 04241 14869 65631 

 43736 78499 44114 24665 37423 82138 50259 70190 89962 61572 

 33894 07843 88131 36054 55889 69002 08034 44545 27898 47738 

 31546 74821 27649 54293 18527 10448 88349 55931 43201 82238 

 86978 52223 81562 



