# William Spottiswoode

### Born: 11 January 1825 in London, England

Died: 27 June 1883 in London, England

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**William Spottiswoode**'s father was Andrew Spottiswoode, a member of the printing firm of Eyre and Spottiswoode, the Queen's printers, and he was related to John Spottiswoode who was archbishop of St Andrews. A year after William was born Andrew Spottiswoode became member of parliament for Saltash and four years later member of parliament for Colchester. William's mother, Mary Longman, was the daughter of the publisher Thomas Longman. William attended school in Laleham, then went to Eton College, one of the most prestigious schools in England situated on the Thames near London. However [1]:-

From Eton he went to Harrow School, another prestigious school in Greater London. Certainly this episode proved an advantage to Spottiswoode, who received better teaching in his favourite subject of mathematics in Harrow. From Harrow, Spottiswoode was awarded a Lyon Scholarship to attend Balliol College, Oxford, which he entered in 1842. Three years later he graduated with a First Class degree in mathematics. He later wrote:-... he was expelled for letting off fireworks in the town, thus offending against a decree by the headmaster.

[While at Oxford he rowed for the university in the annual Oxford-Cambridge boat race in both 1845 and 1846. In 1846 and 1847 he was awarded mathematics scholarships at Balliol College where he became a lecturer in mathematics.M]y interest in mathematics began at Oxford, and was due mainly to the energy and encouragement of my tutor Dr Temple(Bishop of Exeter).

In 1846 his father had financial problems and Spottiswoode took over the firm of Eyre and Spottiswoode so becoming Queen's Printer. The firm prospered under his leadership and he created a model company with the interests of his employees at heart. In the following year his first mathematical publication appeared;

*Meditationes Analyticae*. Herbert Rix, writing in [3], describes Spottiswoode's mathematical contributions:-

The importance of his textbookHis mathematical work was described as 'the incarnation of symmetry'. Besides supplying new proofs by elegant methods of known theorems, he did abundance of important original work. His series of memoirs on the contact of curves and surfaces, contributed to the 'Philosophical Transactions' of1862and subsequent years, mainly gave him his high rank as a mathematician. He was also the author in1851of the first elementary treatise on determinants, and to his treatise much of the rapid development of that subject is attributable.

*Elementary Theorems Relating to Determinants*(1851), referred to in this quote, can be seen from the fact that he was asked by

*Crelle's Journal*to submit a paper to the journal developing his approach to determinants further; this he did in 1856. On 2 June 1853 Spottiswoode was elected a fellow of the Royal Society. He was appointed president of the mathematical section of the British Association in 1865 and was treasurer of the Association from 1861 to 1874. He also served on the council of the Royal geographical Society from 1962 to 1864.

Spottiswoode married Eliza Taylor Arbuthnot on 27 April 1861. Eliza was the eldest daughter of William Urquhart Arbuthnot, a member of the Council for India, and she had been born in Madras, India [1]:-

Their son, William Spottiswoode, was born in 1864. He became a partner, and later a director, of his father's publishing firm of Eyre and Spottiswoode.Their at-homes in Grosvenor Place, held at the height of the London season, attracted the cream of Victorian science and cabinet ministers alike. During these events the latest news in science would invariably be demonstrated in the laboratory which occupied part of the house.

Certainly Spottiswoode was always a keen traveller and he visited a number of countries which were certainly somewhat unusual for the period. In 1856 he visited eastern Russia and took the opportunity to use his literary skills by publishing in 1857 a fascinating account in

*A Tarantasse Journey through Eastern Russia in the Autumn of 1856*. In 1860 he visited Croatia and Hungary. In 1861, the year of his marriage, Spottiswoode published

*On typical mountain ranges: an application of the calculus of probabilities to physical geography*, which attempted to use statistical methods to determine whether the mountain ranges of Asia had been formed by one or several causes. Francis Galton said that this paper had been his inspiration to apply statistics to the social sciences.

Around 1870 there were major changes to the direction of Spottiswoode's research. This was a time when he received high office in a number of societies, being president of the London Mathematical Society from 1870 to 1872 and, from 1871 to 1878, being treasurer of the Royal Society. He was also treasurer of the Royal Institution from 1865 to 1873. In 1878 Spottiswoode was elected president of the Royal Society and remained president until his death in 1883. Also in the year 1878 he was president of the British Association for its Dublin meeting. At the Dublin meeting he gave his presidential address on the growth of mechanised invention applied to mathematics.

We mentioned the change in direction of Spottiswoode's research which turned to physical topics. From 1871 he studied the polarisation of light and later he studied electrical discharge in rarefied gases. Spottiswoode published over 100 papers and several books including, in addition to the one on determinants mentioned above:

*The Polarisation of Light*(1874),

*Polarised Light*(1879), and

*A Lecture on the Electrical Discharge, its Form and Functions*(1881). The papers [2]:-

His interests however were not confined to mathematics and physics since he was also a leading expert on European languages and on oriental languages. He combined these different skills by undertaking research on the history of mathematics and astronomy in India. He was able to read the original Indian sources and his important contributions were published by the Royal Asiatic Society. His article in... were published principally in the Philosophical Transactions, Proceedings of the Royal Society, Quarterly Journal of Mathematics, Proceedings of the London Mathematical Society and Crelle, 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[4].

*Journal of the Royal Asiatic Society of Great Britain and Ireland*(1860) discussed the fact that that most of the principles of the differential calculus were known in ancient Indian mathematics before the period of Bhaskara II in the 12

^{th}century.

Kempe, in [2], summarises his mathematical contributions:-

It is remarkable that Spottiswoode was able to undertake the amount of work that he did, both scientific and administrative. However it took its toll on his health and, at least indirectly, contributed to his death [3]:-The interesting series of communications on the contact of curves and surfaces which are contained in the Philosophical Transactions of1862and subsequent years would alone account for the high rank he obtained as a mathematician. ... The mastery which he had obtained over the mathematical symbols was so complete that he never shrank from the use of 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 imbued with the love of mathematical symmetry the study of determinants had naturally every attraction.

We have mentioned above many honours which Spottiswoode received in election to learned societies and particularly to high office in these societies. We should also mention his election to the Academy of Sciences in Paris and the award of honorary degrees by the universities of Cambridge, Dublin, Edinburgh, and Oxford.He went to Italy on a short holiday to recuperate from overwork and the after-effects of a tricycle accident but after returning home contracted typhoid, and three weeks later died, on27June1883, at his home,41Grosvenor Place. He was fifty-eight years old and his death was regarded as a national loss. In recognition of his position as president of the Royal Society and his contribution to science he was buried on5July in Westminster Abbey in the presence of civic dignitaries and the whole scientific establishment.

**Article by:** *J J O'Connor* and *E F Robertson*

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**List of References** (7 books/articles)
**A Quotation**
**Mathematicians born in the same country**

**Additional Material in MacTutor**

**Honours awarded to William Spottiswoode**

(Click the link below for those honoured in this way)

1. | Fellow of the Royal Society | 1853 | |

2. | LMS President | 1870 - 1872 | |

3. | President of the Royal Society | 1878-1883 | |

4. | Fellow of the Royal Society of Edinburgh | 1883 |

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