The French Academy of Sciences (from 1699-1793, the Royal Academy of Sciences), was established in 1666 to encourage French scientific research and received a charter and statutes from Louis XIV in 1699. Together with the Royal Society of London it was in the vanguard of scientific development in Europe and pioneered the commercial and practical application of scientific discoveries.
Membership of the Academy was limited to relatively few full members whose election was influenced by royal favour, but there were some eighty corresponding members. Among them was Desaguliers. The Duke of Richmond was admitted an honorary member in 1728, one of ten at that time. And two other members of the Horn Tavern were also members of the Academy: Charles Du Fay (1698-1739), and Baron Montesquieu. Both men were also FRSs.
The painting by Henri Testelin (1667), a public domain image, is of Jean-Baptiste Colbert presenting the members of the Royal Academy to Louis XIV.