1878.] on the Value of Enters Constant. 91 



This mode of finding S 500 and S 1000 is attended with the advantage 

 that if an error were made in the calculation of the former of these 

 quantities, it would not affect the latter. 



The logarithms required have been found in the following manner : — 



T * 1 10 1 25 J. 1 81 1 50 A A 1 126 



Letlogy=a, log 24=&, lo ggQ=c, log-^=d, and hg^=e. 

 Then we have 



log 2 = la - 2b + 3c, log 3 = 1 la - 3b + 5c, log 5 = 1 6a - 46 -f 7c. 



Also log 7=| (39a-10& + l7c-d) ; 



or again, log 7=19&— 4& + 8c-fe, 



and we have the equation of condition, 



a— 2b + c=d + 2e, . 



which supplies a sufficient test of the accuracy of the calculations by 

 which a, b, c, d, and e have been found. 



Since log y= -log 



log |= -log (l-jl) 

 log|= log(l + gg) 

 log |= -log (1-4) 



logg= fcS^ + i^o) 



If we have settled beforehand on the number of decimal places which 

 we wish to retain, and have already formed the decimal values of the 

 reciprocals of the successive integers to the extent required, then the 

 formation of the values of a, b, c, d, and e, will only involve operations 

 which, though numerous, are of extreme simplicity. 

 In this way have been found the following results : — 



Log 10-f 9= '10536 05156 57826 30122 75009 80839 31279 83061 20372 98327 

 40725 63939 23369 25840 23240 13454 64887 65695 46213 41207 

 66027 72591 03705 17148 67351 70132 21767 11456 06836 27564 

 22686 82765 81669 95879 19464 85052 49713 75112 78720 90836 

 46753 73554 69033 76623 27864 87959 35883 39553 19538 32230 

 68063 73738 05700 33668 65 



Log 25-7-24= -04082 19945 20255 12955 45770 65155 31987 01772 11747 63352 

 02297 28561 42083 06828 16287 62241 55690 62020 38337 10701 

 85958 13391 57612 02856 02344 55254 44440 90711 64191 09254 

 90615 87090 13793 32587 08185 56690 89768 86470 69797 42768 

 97243 12354 16791 64980 33118 36535 36811 73829 09383 64151 

 16223 48133 67972 69296 



