William Spence

William Spence (1777 to 1815) was a Scottish mathematician born in Greenock, the second son of a coppersmith. He never attended university: he learned the skills of a manufacturer in Glasgow, returned to Greenock, and helped found a small literary society with his school friend John Galt, who later wrote his biography. In 1809 he published An Essay on the Theory of the Various Orders of Logarithmic Transcendents, which studied the series now called polylogarithms and gave the first table of the dilogarithm, to nine decimal places for whole values up to 100; the dilogarithm is often called Spence's function. His last work, published in 1814, treated algebraical equations up to the fourth degree through symmetrical functions of their roots. He died in Glasgow in 1815, and John Herschel edited his Mathematical Essays, which appeared in 1819.