I also finished Seeing Further: The Story of Science, Discovery, and the Genius of the Royal Society yesterday. I found this a mixed back. When I bought it I thought it was a Bill Bryson book—I like those—but if I had checked the description just a little bit I would have seen that it is only edited by Bryson.
The book contains a bunch of chapters, each with different authors. They are all somewhat related to the Royal Society; some involves the history of the Society and others just touch about it in passing.
Some of the chapters are very good, others are boring. It is worth a read, but not a book you would return to for a second read.