The origins of the Royal Society lie in an 'invisible college' of natural philosophers who began meeting in the mid-1640s to discuss the new philosophy of promoting knowledge of the natural world through observation and experiment, which we now call science.
Its official foundation date is 28 November 1660, when a group of 12 met at Gresham College after a lecture by Christopher Wren, then the Gresham Professor of Astronomy, and decided to found 'a Colledge for the Promoting of Physico-Mathematicall Experimentall Learning'. This group included Wren himself, Robert Boyle, John Wilkins, Sir Robert Moray, and William, Viscount Brouncker.
The Society was to meet weekly to witness experiments and discuss what we would now call scientific topics. The first Curator of Experiments was Robert Hooke. It was Moray who first told the King, Charles II, of this venture and secured his approval and encouragement. At first apparently nameless, the name The Royal Society first appears in print in 1661, and in the second Royal Charter of 1663 the Society is referred to as 'The Royal Society of London for Improving Natural Knowledge'.
The Society found accommodation at Gresham College and rapidly began to acquire a library (the first book was presented in 1661) and a repository or museum of specimens of scientific interest. After the Fire of 1666 it moved for some years to Arundel House, London home of the Dukes of Norfolk. It was not until 1710, under the Presidency of Isaac Newton, that the Society acquired its own home, two houses in Crane Court, off the Strand.
From the beginning, Fellows of the Society had to be elected, although the criteria for election were vague and the vast majority of the Fellowship were not professional scientists. In 1731 a new rule established that each candidate for election had to be proposed in writing and this written certificate signed by those who supported his candidature. These certificates survive and give a glimpse of both the reasons why Fellows were elected and the contacts between Fellows.
You gain reputation with the BRS by running missions in Port Royal, Rosseau and Point-a-Pitre and by sinking Fairfax Pirates for reputation. Fairfax pirates are often found lurking around St. Johns.
Once you are esteemed (2500 points) the missions in Riding rocks are unlocked and you can pick up special items including a pistol as you work you way to Celebrated.
In-game, the BRS is competing against the French Academie Nationale.