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The marine chronometer did not become widely available until the very end of the eighteenth century. They may play a part here, but they would have been rare and expensive. –  dmckee Jul 22 '12 at 18:37
@dmckee: Thank you for that excellent link! That does suggest that perhaps the lunar distance method was used. –  dotancohen Jul 22 '12 at 18:41
Couldn't they use the precise time of high noon and longitude measurement? They know their longitude from maps, and high-noon from sundials. –  Ron Maimon Jul 23 '12 at 5:43
Actually, longitude was not well-known in the 18th century. I understand that specifically Tahiti's longitude was known, that is why Cook went there. But even measuring high-noon would not be very precise. –  dotancohen Jul 23 '12 at 5:57
Land-based longitude had its own set of problems, mainly how to transport the clocks (not a problem for Cook). Land navigation was done using Lunar methods even after the seafarers switched to clocks. –  dotancohen Jul 24 '12 at 5:46
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