xxxvi 



expressions, however complicated, nay, the more complicated they 

 were the more he seemed to revel in them, provided they did not sin 

 against the ruling spirit of all his work — symmetry. 



To a mind imbned with the love of mathematical symmetry the 

 stndy of determinants had naturally every attraction. In 1851 Mr. 

 Spottiswoode published, in the form of a pamphlet, an account of 

 some elementary theorems on the subject. This having fallen out of 

 print, permission was sought by the editor of " Crelle " to reproduce it 

 in the pages of that journal. Mr. Spottiswoode granted the request, 

 and undertook to revise his work. " The subject had, however, been 

 so extensively developed in the interim, that it proved necessary not 

 merely to revise it, but entirely to rewrite the work," which became a 

 memoir of 116 pages. To this, the first elementary treatise on deter- 

 minants, much of the rapid development of the subject is due. The 

 effect of the study on Mr. Spottiswoode's own methods was most 

 pronounced ; there is scarcely a page of his mathematical writings 

 that does not bristle with determinants. 



Two communications made by Mr. Spottiswoode in 1860 and 1863 

 to the Royal Asiatic Society upon mathematical subjects, should be 

 specially referred to. In a brief note in the Journal of that Society 

 (vol. xvii, pp. 221 — 222) he discusses the claims of Bhoskarachary, 

 an Indian astronomer, to the discovery of the principle of the dif- 

 ferential calculus ; and in a more lengthy article in vol. xx, pp. 345 — 

 370, of the same publication, he translates into modern symbols the 

 formulae made use of by the Hindoos in calculating eclipses, contained 

 in the " Siirya Siddhanta." The acquaintance which he had with 

 this work was formed by reading it in the original tongue, for among 

 his varied acquirements he possessed a remarkable knowledge of 

 several European and Oriental languages. 



Mr. Spottiswoode was not a traveller in the usual extensive mean- 

 ing of the term, but he has left us an interesting record of a journey 

 which he made in 1856 through Eastern Russia, entitled "A Taran- 

 tasse Journey through Eastern Russia in the Autumn of 1856 ; " and 

 in 1860, in company with his brother and a sister, he accomplished an 

 expedition through Croatia and Hungary. 



In 1861 Mr. Spottiswoode was married to the eldest daughter 

 of the late William Urquhart Arbuthnot, a distinguished member of 

 the Indian Council. 



In 1871 Mr. Spottiswoode turned his attention to experimental 

 physical science. The resources at his command enabled him to 

 furnish his laboratory on a scale which rendered it in some respects 

 unique. The gain to the scientific world was not due merely to his 

 own experiments, as, with characteristic generosity, he was always 

 ready to advance the discoveries of others by the loan of the costly 

 and beautiful apparatus with which he had surrounded himself, and 



