He was keenly interested in mathematics and astronomy and was a founder member of the Royal Society of Edinburgh,[1] (elected Fellow on 17 November 1783[2]) to whose Transactions he contributed a paper proving some theorems in geometry.
[4] He was very active in social improvements in his parish, organising (in conjunction with Robert Stewart, a surgeon) a subscription for Voluntary Dispensary, and Surgery, which eventually became Dundee Royal Infirmary.
He was called before the General Assembly to reply to charges that, when ordaining Elders, on 9 September 1798, in his Parish he asked unconventional, surprise questions, and did not require them to subscribe to the Westminster Confession of Faith.
On Thursday 29 May 1800, the Assembly voted to enjoin Dr Small to be careful hereafter, to testify, by his whole conduct, that respect for the Standards of this Church, and for the fences wisely provided by our Ecclesiastical Constitution, against dangerous innovation, which corresponds to the declaration stated in his defences, as repeatedly made by him in the Kirk-session of Dundee, that he glorified in the Confession of Faith.
[7] He was reputed to be an excellent classical scholar and an interesting preacher, well versed in natural philosophy and mathematics and was a patron of literature.
He emigrated for a time to Virginia, where he was Professor of Mathematics at the College of William & Mary and tutored Thomas Jefferson, but returned to Britain, carrying a letter of introduction from Benjamin Franklin to the industrialist Matthew Boulton.