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In the journal of the Essex pointed out by Don Seltzer, there are two references to expectations of a change in the weather after seeing eclipses. This is a special case of the popular myth that was prevalent back then to the effect that the weather changed (in some unspecified way) at New Moon and Full Moon. How old is this myth? And when did it die out? I'm not asking for the date when the very first human ever suggested it and the very last believer died (there are probably a few even today), but rather when was it "common knowledge" that the Moon's phases were correlated with changes in the weather.

There was an article written in 1833:
"Influence of the Moon on the Weather; Substance of a Paper read at the Natural History Society of Geneva, in October, 1833, by F. Marcet."
which begins,
"On the question whether the moon has any influence over the weather or not, there are two opposite opinions; the great mass of the people, including sailors, boatmen, and most practical farmers, entertain no doubt whatever of the influence of the moon; whether the change of weather at the lunar phases will be from fair to foul, or from foul to fair, none of them pretend to decide beforehand, but most of them think, that at the new and full moon there is generally a change of some kind. On the other hand, philosophers, astronomers, and the learned in general, attribute this opinion altogether to popular prejudice. Finding no reason, in the nature of atmospheric tides, for believing that changes should take place on one day of the lunation rather than another, they consider the popular opinion to be unsupported by any extended series of correct observation."

Of course, the author demonstrates with simple historical data that there is no such effect (but he would, wouldn't he? these skeptics... they don't believe anything!). My guess here is that the legend was on the wane by the 1830s. Farming guides no doubt included it for much longer. When did mariners stop talking about weather and the change of the Moon?

For another example, in 1824, there's an article in "The New England Farmer" which assures readers that the odds are six-to-one in favor of a change in the weather at New Moon and five-to-one in favor at full moon! And this was not just an American legend. William Bligh aboard the Bounty back in 1789 waited in the terrible stormy seas off Cape Horn a few days hoping that the change of the Moon would bring better weather.

-FER

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