OF ARTS AND SCIENCES: JUNE 4, 1872. 463 



ration he could have made for his great scientific career. And here 

 again, doubtless, he owed something to a father's example. The world 

 has been so dazzled by the brilliant results of Sir William Herschel's in- 

 comparable powers of vision, his bold scientific imagination, and his mag- 

 nificent instruments, as not to see that he had also been a musician who 

 entranced fashionable audiences in the theatre and concert-room and in 

 oratorios, and that he studied algebra and geometry in order that he 

 might master Robert Smith's " Harmonics, or the Philosophy of Musical 

 Sounds." Arago has recalled from oblivion the fact that in 1779 Her- 

 schel gave the solution to a difficult problem on the vibrations of a loaded 

 cord, which may be seen in Leybourn's edition of the " Ladies' Mathe- 

 matical Diary." The younger Herschel, in the eulogy which he pro- 

 nounced upon his worthy compeer, Francis Baily, makes this confession 

 in regard to the state of science in England at the beginning of the pres- 

 ent century : " Mathematics were at the last gasp, and astronomy nearly 

 so." The ponderous notation of fluxions, which required the giant arm 

 of a Newton to wield successfully, was retained at the English universi- 

 ties after science had outgrown it, and the finer methods of the Conti- 

 nental mathematicians were ignored. Herschel did his part, as student 

 and graduate, to inaugurate the revolution which finally culminated in 

 such mathematicians as Hamilton and MacCullagh, Sylvester and 

 Gregory, Boole and Cayley, Tait, Adams, Airy, and Thompson. The 

 president of the British Association in 1871 (a most competent 

 witness) said : " In respect to pure mathematics, Sir John Herschel did 

 more, I believe, than any other man, to introduce into England the 

 powerful methods and the valuable notation of modern analysis." 

 Herschel was one of the first to recognize the value of Hamilton's 

 quaternions, which he described as a " Cornucopia from which, turn it 

 how you will, something valuable is sure to fall." If Herschel had de- 

 voted his life to the development of the pure mathematics, as he seemed 

 at first inclined to do, he might have taken rank with the highest in that 

 field of investigation. His earliest publications were upon this subject, 

 and he frequently returned to his first love, as late even as 1850. 

 There is no occasion to regret that a mind of a high order, and 

 thoroughly imbued with the mathematical spirit, should have been 

 transplanted into the domains of geology, chemistry, physics, and astron- 

 omy, for there were fields there already white and waiting for a harvest, 

 and only a mathematician could be the reaper. All of these sciences 

 aspire to that high estate which some have already reached, when 



