Alexander Thomson (1744?-1817)
painting owned by Eric Papenfuse
British Justice Alexander Thomson is best known as the presiding judge in the trial of the Yorkshire Luddites and his delivery of the death sentences, although in the best known transcripts of the trial his name was misspelled 'Thompson'...The early editions spelled his name correctly. The trial was held as a special commission in 1813 in the midst of the Napoleonic and Second American War of Independence (War of 1812). The wikipedia article has a brief account of their actions: , but does not mention Thomson.
Otherwise, in his role as Baron of the Exchequer (1787-1817), he heard cases involving the public revenue, that is suits by the crown against its debtors, as well as ordinary civil actions between subject and subject. Note that 'Exchequer' is derived from the checkered cloth on the table when the King's revenue accounts were settled:
The Exchequer was named after a table used to perform calculations for taxes and goods in the medieval period. According to the Dialogue concerning the Exchequer, an early medieval work describing the practice of the Exchequer. The table was large, 10 feet by 5 feet with a raised edge or "lip" on all sides of about the height of four fingers to ensure that nothing fell off it, upon which counters were placed representing various values. The name Exchequer referred to the resemblance of the table to a chess board (French: échiquier) as it was covered by a black cloth bearing green stripes of about the breadth of a human hand, in a chequer-pattern. The spaces represented pounds, shillings and pence. The term "Exchequer" then came to refer to the twice yearly meetings held at Easter and Michaelmas, at which government financial business was transacted and an audit held of sheriffs' returns
Thomson, Sir Alexander (1744?-1817), judge, was born and educated in Wolverhampton. His parentage is unknown. He entered Lincoln's Inn on 6 November 1764 and was called on 6 November 1769. Practicing in chancery, mostly as an equity draftsman for he had no pretensions to oratory and was rather diffident, he ... Reference Entry. 544 words. Thomson, Sir Alexander (1744?-1817), judge, by Patrick Polden in the Oxford Dictionary of National Biography Published in print September 2004 | Published online September 2004 | e-ISBN: 9780198614128 | DOI: http://dx.doi.org/10.1093/ref:odnb/63081
The other Alexander Thomson from Wikipedia:  was:
Alexander Thomson (January 12, 1788 – August 2, 1848) was a member of the U.S. House of Representatives from Pennsylvania.
Alexander Thomson was born in Franklin County, Pennsylvania. He apprenticed as a sickle maker. He moved to Bedford, Pennsylvania, studied law, was admitted to the bar in 1816 and commenced practice in Chambersburg, Pennsylvania. He held several local offices and was a member of the Pennsylvania House of Representatives.
Thomson was elected to the Eighteenth Congress to fill the vacancy caused by the resignation of John Tod. He was reelected to the Nineteenth Congress and served until May 1, 1826, when he resigned. He served as mayor of Lancaster, Pennsylvania, and was president judge of the sixteenth judicial district of Pennsylvania from 1827 to 1841. He was professor in the law school of Marshall College in Lancaster. He died in Chambersburg in 1848. Interment in Falling Spring Presbyterian Cemetery.