88 



Prof. J. C. Adams 



[Feb. 7, 



Table VI. — Period of Conjunction of Mercury and Jupiter. 

 (0° denoting Conjunction — 63 sets for Kew — 43 sets for Trevandrum.) 



o 



o 



Kew. 



Trerandrum. 



A 



1 OA 



and SO 



+ 633 



+ 453 



On 



SO 



/» A 



» 60 



+ 759 



+ 270 



60 



90 



+ 652 



+ 129 



A A 



90 



1 OA 



„ 120 



+ 328 



"1 t A 



—118 



120 



1 f A 



„ 150 



1 1 A 



—119 



— 384 



1 t:A 



150 



1 OA 



180 



I" A A 



— 504 



—467 



180 



„ 210 



-678 



-487 



210 



„ 240 



-677 



-407 



240 



„ 270 



-548 



-122 



270 



„ 300 



-322 



+ 223 



300 



„ 330 



- 10 



+ 415 



330 



„ 360 



+ 343 



+ 503 



I desire, in conclusion, to thank Mr. William Dodgson, who has 

 given me much assistance in the calculations and diagrams of this 

 paper. 



III. " Note on the Value of Euler's Constant ; likewise on the 

 Values of the Napierian Logarithms of 2, 3, 5, 7, and 10, 

 and of the Modulus of common Logarithms, all carried to 

 260 places of Decimals." By Professor J. C. Adams, M.A., 

 F.R.S. Received December 6, 1877. 



In the " Proceedings of the Royal Society," vol. xix, pp. 521, 522, 

 Mr. Glaisher has given the values of the logarithms of 2, 3, 5, and 10, 

 and of Euler's constant to 100 places of decimals, in correction of 

 some previous results given by Mr. Shanks. 



In vol. xx, pp. 28 and 31, Mr. Shanks gives the results of his 

 re- calculation of the above-mentioned logarithms and of the modulus 

 of common logarithms to 205 places, and of Euler's constant to 110 

 places of decimals. 



Having calculated the value of 31 Bernoulli's numbers, in addition 

 to the 31 previously known, I was induced to carry the approximation 

 to Euler's constant to a much greater extent than had been before 

 practicable. For this purpose I likewise re-calculated the values of the 

 above-mentioned logarithms, and found the sum of the reciprocals of 

 the first 500 and of the first 1000 integers, all to upwards of 260 

 places of decimals. I also found two independent relations between 

 the logarithms just mentioned and the logarithm of 7, which furnished 

 a test of the accuracy of the work. 



