He had correspondents in different parts of Scotland engaged in making researches into antiquities, which he encouraged and directed. Among such were inquiries into the whereabouts of a church said to possess holy earth brought from Rome; and a hunt for ancient cupping-vessels. The work on the Catstane of Kirkliston was elaborate, and a perfect example of his method. Probably this stone, a massive unhewn block of greenstone-trap, had been a familiar object to him in his youth, for it lay alone in a field close to the Linlithgow road. In his monograph he endeavoured to show by close reasoning, with profuse references to forgotten authorities and ancient history, that the stone was the tomb of one Vetta, the grandfather of Hengist and Horsa. His argument ran as follows: The surname Vetta, which figured on the inscription carved upon the stone, was the name of the grandfather of Hengist and Horsa, as given by the oldest genealogists, who described him as the son of Victa. The inscription ran thus: VETTA F(ilius) VICTI. Vetta was an uncommon Saxon name, and no other Vetta, son of Victa, was known in history. Two generations before Hengist and Horsa arrived in England a Saxon host was leagued with the Picts, Scots, and Attacots in fighting a Roman army, and these Saxons were probably commanded by an ancestor of Hengist and Horsa. The battlefield was situated between the two Roman walls, and consequently included the tract where the stone is now placed. The palaeographic characters of the inscription indicated that it was carved about the end of the fourth century. Latin (with a very few exceptions in Greek) was the only language known to have been used at that time by Romanised Britons and foreign conquerors for the purpose of inscriptions. The occasional erection of monuments to Saxon leaders is proved by the fact mentioned by Bede that in his time, the eighth century, there stood in Kent a monument commemorating the death of Horsa. In 1659 a writer had described this tomb of Horsa as having been destroyed by "storms and tempests under the conduct of time." In 1861 Simpson was president of the Society of Antiquaries of Scotland, and delivered an address on the past and present work of archaeology which greatly stimulated antiquarian study in his country. Amongst the honours which his antiquarian achievements brought upon him was that of being appointed Professor of Antiquities to the Royal Academy of Scotland; he was also elected a member of the Archaeological Societies of Athens, Nassau, and Copenhagen.