Like Longitude, this is another book on historical science. This time, we're measuring the size of the solar system.
It turns out that a lot of calculations involving the size of the solar system produce ratios (e.g. the orbit of Venus is x times smaller than the orbit of the Earth, etc.) but that it's difficult to get an absolute distance for the radius of the orbit of any planet.
Every 100 years or so, Venus wanders across the Sun twice; at eight year intervals. Mind-numbing geometric analysis reveals that if you can time the Venus transition from various points on the Earth, you can figure out the radius of Earth's orbit and hence, the size of the Solar System. It's nice that transitions occur twice every 100 years because that lets you try the measurement during the first transition and examine what went wrong. You have 8 years until the second transition to try it again with the lessons learned.
Venus just crossed the Sun in June of 2012, which is what I think brought this book to my attention. This book covers what happened during the transitions of 1761 and 1769. So, it's several stories of journeys to different points on the Earth; carrying heavy, delicate and precise measuring equipment. You then spend several months figuring out exactly where you are and what time it is at your location relative to London. None of these problems were easy in the world of the mid-1700s.
Finally, the big day comes and you have several hours to make a measurement that won't be possible for another 100 years. You hope it won't be cloudy.