In 1846 he left Oxford to take his father's place in the business, in which he was engaged until his death. In 1847 Spottiswoode issued five pamphlets entitled
Meditationes Analyticae, that explored complex mathematical ideas through analytic methods, particularly focusing on functions and calculus. These pamphlets, among other things, exhibited advanced mathematical analytics and solutions to complex equations that examined the behavior of mathematical functions more deeply and precisely. These were his first publications of original mathematical work. From then on, he published new research almost every year. In 1856 Spottiswoode travelled in eastern
Russia, and in 1860 in
Croatia and
Hungary; of the former expedition he has left a record,
A Tarantasse Journey through Eastern Russia in the Autumn of 1856 (London, 1857). In 1870 he was elected president of the
London Mathematical Society. In 1871 he began to turn his attention to experimental physics, his earlier researches bearing upon the light
polarization and his later work upon the electrical discharge in rarefied gases. He wrote a popular treatise on the former subject for the
Nature Series in 1874. In 1878 he was elected president of the
British Association and in the same year president of the
Royal Society, of which he had been a fellow since 1853. He died in London of
typhoid fever on 27 June 1883 and was buried in the south transept of
Westminster Abbey. As a mathematician, he occupied himself with many branches of his favorite science, more especially with higher algebra, including the theory of
determinants, with the general calculus of symbols, and with the application of analysis to geometry and mechanics. The following brief review of his mathematical work is quoted from the obituary notice which appeared in the
Proceedings of the Royal Society (xxxviii. 34): His papers, numbering over 100, were published principally in the
Philosophical Transactions,
Proceedings of the Royal Society,
Quarterly Journal of Mathematics,
Proceedings of the London Mathematical Society and ''Crelle's Journal
, and one or two in the Comptes Rendus of the Paris Academy; a list of them, arranged according to the several journals in which they originally appeared, with short notes upon the less familiar memoirs, is given in Nature'', xxvii, 599. == Publications ==