In 1763 Smith resigned his professorship and became the tutor for the duke of   Buccleuch. This was an interesting story.  The Chancellor of the Exchequer Charles Townshend, who became famous by imposing high tax on tea imported to English colonies in America, and so causing the Boston "Tea Party" and eventually the American revolution, this Charles Townshend married in 1754 the  Countess of Dalkeith, the  very rich widow of the Duke of Buccleuch.
In 1763 Townshend wanted to educate his stepson the young Duke of Buccleuch by  sending him for several years to Europe. He needed a tutor to accompany the young Duke. Townshend wanted Smith for this job and offered him the salary almost twice as high as the one Smith was  getting at the university and, of course,    also coverage of all the travel cost. After returning from the trip Smith would be  getting the same amount as a pension for the rest of his life.
Smith accepted, he was searching for such a job for many years. Tutoring children of powerful nobility was at that time quite common and respectable job of intellectuals. In the years 1464 - 1766 Smith traveled with young Duke of Buccleuch mostly in France. This gave him opportunity to meet there some famous philosophers, economists and scientists. Among them it were Voltaire, Russeau, Quesnay, Turgot, D'Alambert and Helvetius.