BIOGRAPHICAL NOTICE. xliii 



improvements in the processes and mode of representing the subject, or of attaining 

 to an even more accurate result. A striking instance of this innate craving for per- 

 fection is afforded, even as early as 1845, by his calculation of the second orbit of 

 the new planet. No able mathematician who is engaged upon a fruitful research can 

 continually defer publication with impunity : the subject opens before him ; his views 

 expand ; the earlier results, so interesting at the moment of discovery, lose their charm 

 in comparison with the problems still unsolved and the novel vistas of thought opened 

 out by them ; and the rearrangement and rewriting of the old work always an irksome 

 task become intolerable when later and still unfinished developments on the same 

 subject are exciting the mind. In Adams's case the difficulty of satisfying himself, 

 and reaching his own standard of completeness, also contributed to his apparent 

 reluctance to publish his work. Those who knew him will remember his words when 

 pressed, "I have still some finishing touches to put to it." It was well known that 

 he made important researches upon the motion of Jupiter's satellites, and their pub- 

 lication was anxiously awaited. It does not appear that he ever made any serious 

 attempt to put his longer investigations in order for the press, though occasionally, as 

 his manuscripts on the different subjects increased in bulk, the feeling would come over 

 him strongly that it was time for him to do so. Although there is no similarity 

 between the simple and easy style of Adams's writings and the cold severity of 

 Gauss's, there is a certain resemblance in their mode of work. Each had the same 

 dislike to early or incomplete publication, and " Pauca sed matura " might have been 

 the motto of both. In beginning a new research, Adams rarely put pen to paper 

 until he had carefully thought out the subject, and when he proceeded to write out 

 the investigation he developed it rapidly and without interruption. His accuracy and 

 power of mind enabled him to map out the course of the work beforehand in his 

 head, and his mathematical instinct, combined with perfect familiarity with astronomical 

 ideas and methods, guided him with ease and safety through the intricacies and dangers 

 of the analytical treatment 1 . He scarcely ever destroyed anything he wrote, or per- 

 formed rough calculations ; and the manuscripts which he has left are written so 

 carefully and clearly that it is difficult to believe that they are not finished work 

 which has been copied out fairly. The sheets are generally dated, and during many 

 years he kept a diary of the work he had done each day. 



His contributions to pure mathematics show the same power and excellence, and, 

 as the subject affords greater opportunities for the display of elegance and style, they 

 indicate even more plainly the attention he bestowed upon the form of his results, 

 as well as upon the substance. A paper communicated to the Royal Society in 1878 

 may be specially noticed, in which an expression is given for the product of two 

 Legendrian coefficients, and for the integral of the product of three. The extent of 

 his mathematical interests is perhaps best seen by looking over the series of papers 

 which he set in the Smith Prize Examination. These questions, which cover a wide 



1 This method of working characterised him from the wrote out rapidly the problems he had already solved ' in 



first, for in his Tripos Examination it was noticed that his head'." It may be mentioned here that in this exami- 



" in the problem papers, when everyone was writing hard, nation he received more than double the marks of the 



Adams spent the first hour in looking over the questions, Second Wrangler. This affords striking evidence of 



scarcely putting pen to paper the while. After that he Adams's mental powers, for he was not a rapid writer. 



