The History of the Royal Society of London
Full Title: The history of the Royal Society of London for improving of natural knowledge from its first rise, in which the most considerable of those papers communicated to the Society, which have hitherto not been published, are inserted as a supplement to the Philosophical Transactions
This is less a history and more a transcription and fleshing out of Robert Hooke's minutes of the meeting of the Society taken from his notes, recently recovered and how available at Hooke's Folio Online. Birch's text is an often-frustrating summary, flat words concealing strong emotions.
Volume I - 1756 (Google Books)
Volume II - 1756 (pdf) from January 4, 1664/5 to December 21, 1671
Volume III - 1757 (pdf) from January 11, 1671/2 to December 18, 1679
Volume IV - 1757 (pdf) from January 8, 1679/80 to December 14, 1687
Thomas Birch (1705-1766 ) in 1741