Which Earl of March is this?

[William Douglas]

Contessa della Rena was the wife of a Florentine wine merchant, who became mistress of various members of the English aristocracy. By 1759 she was in England under the protection of William Douglas, Earl of March, a notorious rake whose main interests were horse-racing, dancing girls and opera. In the last of these, March and his mistress would have come into contact with Giardini, whose forays into production of the Italian opera [was noted previously].

La Rena sat to Reynolds over a period of months from July 1759 to September 1761. In the resulting portrait, she is depicted holding an open folio of music, which is inscribed at the top of the page, Dal Sig. Giardini. In a letter of 1766, writing to his close friend George Selwyn, March refers to Giardini as an enthusiasm he shares with La Rena.

I understood that the Earl of March title was tied up with the Duke of Queensberry in 1759, so cannot work out who this refers to.

Does anyone know?