Archibald Smith 
FRS FRSE (10 August 1813, 
Greenhead, 
Glasgow – 26 December 1872, 
London) was a 
Scottish mathematician and 
lawyer.
He was the only son of James Smith FRS (1782-1867), a wealthy merchant and antiquary of 
Jordanhill, Glasgow,[1] and his wife Mary, daughter of 
Alexander Wilson, professor of astronomy in 
Glasgow University. Archibald studied at Glasgow University in 1828, and then at 
Trinity College, Cambridge, where he was 
Senior Wrangler, said to be the first Scot to achieve this position,[1] and first 
Smith's prizeman in 1836, elected a fellow of Trinity College.[2] He was one of the founders of the 
Cambridge Mathematical Journal. He entered 
Lincoln's Inn, and was called to the bar in 1841, practising as an equity draughtsman and property lawyer.
His scientific work was mainly in the field of applications of 
magnetism and the 
Earth's magnetic field. He obtained practical formulae for the correction of magnetic compass observations made on board ship, which General Sir 
Edward Sabine published in the 
Transactions of the Royal Society: Smith later made convenient tables. In 1859 he edited 
William Scoresby's Journal of a Voyage to Australia for Magnetical Research and gave an exact formula for the effect of the iron of a ship on the compass. In 1862, in conjunction with the hydrographer 
Sir Frederick John Owen Evans FRS (1815-1885), then superintendent of the compass department of the navy, he published an Admiralty Manual for ascertaining and applying the Deviations of the Compass caused by the Iron in a Ship.
He was elected a Fellow of the 
Royal Society of Edinburgh in 1837.[4] Elected a 
Fellow of the Royal Society in June 1856, he was awarded its 
Royal Medal in 1865 "for his papers in the Philosophical Transactions and elsewhere, on the magnetism of ships".[5] In 1866 Emperor 
Alexander II of Russia presented him with a gold compass, set in diamonds, and emblazoned with the Imperial Arms.
In 1853 he married Susan Emma, daughter of Sir James Parker of 
Rothley Temple, 
Leicestershire. They had six sons and two daughters, the eldest 
James Parker Smith, becoming M.P. for 
Partick, 
Lanarkshire.