Although Maclaurin died nearly forty years before the founding of the Royal Society of Edinburgh he played a very important part. The Society for the Improvement of Medical Knowledge was founded in Edinburgh in 1731 and Maclaurin became one of its members. Not happy with such restricted topics, he worked to expand the Medical Society of Edinburgh into a wider society to include other branches of learning. Perhaps he already had in mind a society broadly similar to the Royal Society of London of which he had been a Fellow since 1719.
In 1737 the broader Society was formed with the full title "Edinburgh Society for Improving Arts and Sciences and particularly Natural Knowledge". As one might expect this was far too long a title for people to use, and the Society was known as the Philosophical Society of Edinburgh. Maclaurin himself acted as one of the two secretaries of this expanded Society and at the monthly meetings he often read a paper of his own or a letter from a foreign scientist on the latest developments in some topic of current interest.
The Philosophical Society of Edinburgh was not the only Edinburgh Society of which Maclaurin was a member. He also belonged to the Rankenian Club which met in Ranken's Inn in Edinburgh. This Club was founded in 1716 nearly ten years before Maclaurin was appointed to the University of Edinburgh, and it was a Club which suited Maclaurin with its mixture of congenial fellowship and the aim of its members in pursuing knowledge. It is generally accepted that the Philosophical Society of Edinburgh was the major player in the move towards the establishment of the Royal Society of Edinburgh, but undoubtedly the Rankenian Club played its part.
Shapin describes the events which led to the founding of the Royal Society of Edinburgh in , see also his paper . The year 1782 was crucial in its foundation. That was in the year in which the Society of Antiquaries of Scotland, at this time quite a new Society, decided to seek a Royal Charter. The Society had fairly broad aims which it stated as:-
... the cultivation of both antiquities and many aspects of general knowledge.
Both the University of Edinburgh and the Faculty of Advocates worried about this proposal by the Society of Antiquaries for they saw an expanded Society with a Royal Charter as a competitor to them in certain of its functions. In a move to counter this proposal the Professor of History at the University of Edinburgh, John Walker, proposed that the University of Edinburgh, the Faculty of Advocates, the Philosophical Society of Edinburgh, and the Society of Antiquaries of Scotland should seek a Royal Charter to establish the Royal Society of Edinburgh. The proposal drawn up by Walker was entitled:-
Proposal for establishing at Edinburgh, a Society for the advancement of Learning and Useful Knowledge.
The Society of Antiquaries of Scotland of course realised that this was an attempt to head off their proposal and they strongly objected to Walker's document. There were meetings which were designed to smooth the way forward and overcome the objections which were now put up by the Society of Antiquaries. Unable to agree, a meeting between the Rev Robertson, Principal of the University of Edinburgh, and Buchan, the leader of the Society of Antiquaries, was suggested. This meeting between the two men took place but broke up in total disarray with considerable anger on behalf of Buchan.
This left two separate parties who now both aimed to set up a Royal Society in Edinburgh. The Philosophical Society of Edinburgh proposed to the University of Edinburgh that they go it alone in setting up the Society. The Faculty of Advocates and a Member of Parliament for Edinburgh made preliminary enquiries in London and advised the University of Edinburgh to proceed. The authors of  write:-
The Senatus [of the University of Edinburgh] met on 30 November 1782, a petition was submitted to the King, and on 29 March 1783 the King's signature was obtained. On 6 May 1783, the Royal Charter and that of the Society of Antiquaries were extended under the Great Seal in Edinburgh.
The first meeting of the new Royal Society of Edinburgh took place in the Old Library of Edinburgh University on Monday 23 June 1783. It was decided that all members of the Philosophical Society of Edinburgh should automatically become Fellows of the Royal Society of Edinburgh. All accepted except, as one might have anticipated, Buchan. Others including professors from the other Scottish universities, were invited to the Fellowship. From its beginnings the Society set itself up as a Scottish wide Society, based in Edinburgh.
The beginning of the Royal Society of Edinburgh was described in the first volume of the Transactions of the Royal Society of Edinburgh published in 1788. It is factually correct but omits any of the drama involved in the setting up of the Society which we have described above:-
About the end of the year 1782 in a meeting of the Professors of the University of Edinburgh, many of whom were likewise members of the Philosophical Society and warmly attached to its interests, a scheme was proposed by the Rev. Dr Robertson, Principal of the University, for the establishment of a Society on a more extended plan, and after the model of some foreign academies, which have for their object the cultivation of every branch of science, erudition, and taste.
It is worth noting that Alexander Wilson was one of the founding members of the Society and John Playfair was a member who:-
... for the first two decades of the Society was the life and soul of the institution.
The Royal Society met in the library of Edinburgh University in its early years. In 1810 the Society purchased 42 George Street, and it occupied this building until 1826 when the Royal Institution Building on Princes Street was completed. For about 80 years it occupied part of the Royal Institution Building. The story of how the Society was ejected from the Royal Institution and their subsequent fight for a new home is recounted in our article William Thomson , later Baron Kelvin of Largs, was President from 1873 to 1878 and again from 1886 to 1890. From 1890 to 1895 Thomson was President of the Royal Society of London, then, this time as Lord Kelvin, he was President of the Royal Society of Edinburgh for a third time from 1895 until his death in 1907. Two others from our archive held the office of President: D'Arcy Thompson from 1934 to 1939, followed by Edmund Whittaker from 1939 to 1945.
Three mathematicians from our archive served the Royal Society of Edinburgh as General Secretaries: Playfair from 1798 to 1819, Tait from 1879 to 1901, and Chrystal from 1901 to 1912. It was during Chrystal 's time as General Secretary that the Society was forced out of its rooms in the Royal Institution and the story of this is told in the separate article Tait was twice a winner of the Keith Prize (a feat few have equalled) and Joseph Wedderburn was elected a Fellow in 1903 when he was 21 years of age making him one of the youngest Fellows ever elected. Some years later Herbert Turnbull won both the Keith Medal and Gunning Victoria Jubilee Prize.
There is a link below to some of the mathematicians in this archive who have been elected Fellows of the Royal Society of Edinburgh:
Fellows of the Royal Society Of Edinburgh (Alphabetical list)
Fellows of the Royal Society Of Edinburgh (Chronological list)
The Royal Society Of Edinburgh and the purchase of 22-24 George Street
Other Web site:
The RSE home page
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