He also became known to Professors Robison and Stewart, of Edinburgh, and by their advice was sent, in his thirteenth year, to the University of St. Andrew's, to study mathematics under Professor Vilant. Here, at the end of the first session, his abilities procured him the second prize, and likewise attracted the notice of the Earl of Kinnoull, then Chancellor of the University, who undertook to defray the expenses of his education, provided that he would enter the Church. Leslie prosecuted his studies at this university during six sessions, and became about this time acquainted with Playfair and Dr. Small. In 1783-4 he quitted St. Andrews and went to Edinburgh, where, though he formally entered the Divinity Hall, he contrived to devote his first session to the sciences, particularly chemistry; in fact, Leslie seems early to have relinquished all thoughts of the Church--a resolution hastened by the death of his patron, the Earl of Kinnoull, shortly after his removal to Edinburgh. While engaged at the university, he also acted as tutor to Mr. Douglas, afterwards Lord Reston, the nephew of Dr. Adam Smith, and he thus became known to that philosopher, who treated him kindly, and occasionally favoured him with directions as to his pursuits. Leslie's first essay, 'On the Resolution of Indeterminate Problems,' was composed about this time, and read to the Royal Society of Edinburgh by Mr. Playfair, in 1788, and published in their 'Transactions' for 1790. In 1788, he became tutor to two young Americans of the name of Randolph, and accompanied them to Virginia, where he remained for about a twelvemonth, during which time he visited New York, Philadelphia, &c. In January 1790, carrying, among other letters of recommendation, one from Adam Smith, Leslie repaired to London, with the intention of delivering a course of lectures on natural philosophy; but finding, to use his own words, that "rational lectures would not succeed," he employed himself for some time in writing for the 'Monthly Review,' and in other literary occupations. In April 1790, he became tutor to the younger Wedgewoods, of Etruria, in Staffordshire, who had been his former fellow-students, and with whom he remained until the close of 1792. Leslie was likewise employed during this period in experimental investigations, and in completing a translation of Buffon's 'Natural History of Birds,' published in 1793, in nine volumes, for which he received a considerable sum,--the foundation of that pecuniary competency which his industrious and prudent habits enabled him ultimately to acquire.