Hartley, I think we are both trying hard to agree with each other on the skills and daring these mariners must have possessed in order to cross oceans in their day. It is interesting comment about the lunar method. Was it relatively more accurate because the chronometers of the time were such poor keepers of time as to make them impractical to use in a marine environment? And why was the Royal Navy offering such a big prize for the invention of a practical chronometer if they already had a better way of determining longitude?
Skills and daring indeed!!
From what I've read, it was because the chronometers of the time were such poor keepers of time in a marine environment. These were mechanical devices, remember, and very subject to vibration (ie. thumping off the back of a wave) or temperature fluctuations (ticking faster or slower). Some even had to be wound up at exactly the same time each day to compensate for the main-spring unwinding at different rates. IIRC, Cook took three
with him - just in case - and found some were better than others. In this part of the world, being out by a minute in a week or so is more than sufficient to put you on the rocks...
The huge prize you mention was to come up with something that didn't
require pages of calculations.. because, even back then, not everyone who went to sea was good at mathematics. If you look into it, taking a Noon Sight isn't rocket science, but the longitude calculations to go with it make rocket science look easy!