William Spence (mathematician)

Spence was the second son to Ninian Spence and his wife Sarah Townsend. Ninian Spence ran a coppersmith business, and the Spence family were a prominent family in Greenock at the time. From an early age, Spence was characterised as having a docile and reasonable nature, with him being mature for his age. At school he formed a life-long friendship with John Galt, who documented much of his life and his works posthumously. After this, Spence visited many places in England, he lived in London for a few months where, in 1809, he published his first work. In 1814, he published his second work, getting married in the same year – Spence intended to live in London, and began his journey back before becoming ill, having travelled as far as Glasgow, he died in his sleep due to illness. Spence held an interest in musical composition, and played the flute. == Published works ==

Spence published An Essay on the Theory of the Various Orders of Logarithmic Transcendents: With an Inquiry Into Their Applications to the Integral Calculus and the Summation of Series in 1809. Throughout his work, he displayed a familiarity with the work of Lagrange and Arbogast, which is notable since at the time very few were familiar with their works. :\pm x/1^n - x^2/2^n \pm x^3/3^n - ... which he denoted with L_n(1\pm x). In which he took a systematic approach to solving equations up to the fourth degree using symmetrical functions of the roots. == Legacy ==

Spence's work was noted to be remarkable at the time, with John Herschel, his acquaintance and one of Britain's leading mathematicians at the time, had referenced it in one of his later publications Consideration of various points of analysis, which prompted Herschel to edit Spence's manuscripts. Spence was held in such high regard by Galt, and later Herschel that they published a collection of his individual essays in 1819. Posthumously, his work was met with appreciation from his contemporaries, with a review in the ninety-fourth number of the Quarterly Review (reproduced in Galt's The Literary and Miscellanies of John Galt, Volume 1) that described his first work in 1809 as: " [The] first formal essay in our language on any distinct and considerable branch of the integral calculus, which has appeared since… Hellinsʼs papers on the ‘Rectification of the Conic Sections". == References ==