Sir Brooke Boothby was an amateur poet and philosopher who took an active interest in the new scientific and technical ideas which were bringing about the industrial revolution in the English Midlands at that time. He had formed a friendship with Rousseau of which he was very proud. In 1776 Boothby visited Rousseau in Paris and Rousseau, fearing prosecution by the authorities, gave him for safekeeping the manuscript of Roussean Juge de Jean-Jacques ('Rousseau judge of himself'), an important defence of himself and his ideas.
Rousseau died two years later, in 1778, and two years after that, in 1780, Boothby had the manuscript published in England. This is the book in the picture and Boothby was clearly so pleased with himself for publishing it that he commissioned the painting: it may be seen as a tribute from an English liberal thinker to the great French revolutionary philosopher.
Boothby's clothes are also interesting. It was poets and artists from about this time who seem to have established the idea that artists and 'intellectuals' should dress in an unconventional and informal way. At first glance, Boothby looks very elegant and tidy but a closer look reveals that by the standards of the time he was carelessly dressed - both his waistcoat and coat sleeves are unbuttoned and this was understood as symbolic of an intellectual and poetic personality who is above everyday trivialities such as 'correct' dress. The wide-brimmed black hat would also have indicated that Boothby had turned away from the civilised world to think deep thoughts alone in nature.
Simon Wilson, Tate Gallery: An Illustrated Companion, Tate Gallery, London, revised edition 1991, p.31