xliv BIOGRAPHICAL NOTICE. 



field of mathematics, clearly indicate the bent of his mind and his favourite subjects 

 of study: they are also noticeable for a high degree of finish, which is very unusual 

 in examination questions. 



Like Euler and Gauss, he took very great pleasure in the numerical calculation 

 of exact mathematical constants. We owe to him the calculation of thirty-one 

 Bernoullian numbers, in addition to the first thirty-one which were previously known. 

 The first fifteen were calculated by Euler, and the next sixteen by Rothe, the whole 

 thirty-one being given in vol. xx. of Crelles Journal. Making use of Staudt's very 

 curious theorem with respect to the fractional part of a Bernoullian number, Adams 

 calculated all the numbers from B& to 62 . The results were communicated to the 

 British Association at the Plymouth meeting in 1877, and were also published in 

 vol. Ixxxv. of Crelles Journal. A much fuller account of the work, which was very 

 considerable in amount, appeared in an appendix to vol. xxn. of the Cambridge 

 Observations, where the process of calculation of the first, B. f ,, and of the last, B&, is 

 given in detail. Adams proved that if n be a prime number other than 2 or 3, 

 then the numerator of the wth Bernoullian number is divisible by n. This afforded 

 a good test of the accuracy of the work. 



Having thus at his command the values of sixty-two Bernoullian numbers, he 

 was tempted to apply them to the calculation of Killer's constant. For this purpose, 

 not only the Bernoullian numbers, but also the values of certain logarithms and sums 

 of reciprocals were required. He accordingly calculated the values of the logarithms 

 of 2, 3, 5, and 7 to 263 (afterwards extended to 273) decimal places, and by their 

 means obtained the value of Euler's constant to 263 places. He also calculated the 

 value of the modulus of the common logarithms to 273 places. The papers containing 

 these results appeared in the Proceedings of the Royal Society for 1878 and 1887. 

 Anyone who has had experience of calculations extending to a great many decimal 

 places is aware of the difficulty of manipulating with absolute accuracy the long lines 

 of figures ; but this was an enjoyment to Adams, and the work, as carried out with 

 consummate care and neatness, in his beautiful figures, is an interesting memorial of 

 the patience and skill that he devoted to any work upon which he was engaged. 



Some may think that the portion of his own time occupied by these calculations 

 might have been more advantageously spent : but there is a charm of its own in 

 carrying still further the determination of the historic constants of mathematics, which 

 has exercised its attraction over the greatest minds. Those who feel the least possible 

 interest in calculation for its own sake, and even dislike ordinary arithmetical com- 

 putations, have been unable to resist the fascination of doing their share towards the 

 calculation of the absolute numerical magnitudes which are so intimately connected 

 with the foundations of the sciences dealing with abstract quantity. There is a special 

 pleasure also in applying the resources of modern mathematics to obtain the values 

 of these incommensurable constants to such an incredible degree of accuracy, and in 

 verifying the distant figures by methods depending upon subtle principles and com- 

 plicated symbolic processes, of the absolute truth of which we thus obtain so striking an 

 assurance. 



Adams had the greatest possible admiration for Newton, and perhaps no one haa 

 ever devoted more careful and critical attention to Newton's mathematical writings, 



