Great book. It was an amazing problem: "time" that is. They have an awesome display of clocks at the British museum in London. Some of the clocks related to this issue are there. My friend and I dead reckoned across the Atlantic once in a cessna 172. We hit the Azores with about 15 miles of error. We came back using a handheld aerial sextant and a clock and were dead on at the Azores and Canada.
We didn't have a GPS (they werent available yet to mortals) or SATNAV. We could have used Loran I suppose but we figured if mariners could use a sextant, then we could. It was very interesting to generate the calculations and fix the positions. We had an opportunity to do that again with a GPS and the only real issue was being fast enough with the calculations to have a valid fix. We found that it took about 8 minutes to do the work (we weren't professional sextant users obviously) and we were moving at twice the speed as we were in the cessna 172 so we had 20 mile errors just because of our rate of speed (at least based on the GPS data).
It was an interesting process. The same guy I made those trips with later sailed his 40 ft sailboat from California to Australia via Bikini Atoll using sextant only navigation. He had two handheld GPS' on board but they were both locked in a safe and he would have had to call me on a sat phone to get the code for the safe to get it out. He never did. I thought that was pretty cool. He had a beautiful, antique sextant that he used for that trip.