Two stars for the first half of the book, four stars for the 2nd, so that leaves me at 3 stars for the whole thing.
Several of the early essays of this collection focus on the early history of the Royal Society and the philosophy of science. They're very academic, hard to read, and full of RS-related name dropping. I'm sure they're valuable in their fields, but it took me a few weeks to get through them... kept falling asleep or reading other things.
But hang in there! Or just skip those! The essays in the 2nd half of the book are more science than history, more what fans of Bill Bryson are probably looking for. My favorite just might be Ian Stewart's summary of where math shows up in everyday life. But Oliver Morton's on cycles in the world, or Gregory Benford's on the flow of time are really excellent, too.
Mostly I want to say that there are some real gems here. Some of them are mostly there to fulfill the commemoration of a very specific event (350 years of the RS) that most of us don't care all that much about. So skip around. But this book is definitely worth reading.