NavList:

Modris, you wrote:
"Lunars were the only available method for rough chronometer check during very long passages, when the ship was far away from the land (this, of course, refers to pre-radio era; more typical for slow sailing ships)."

You skipped over an era :). For perhaps six decades, between the period when lunars were common and the era when wireless became available on larger vessels, there was another means of validating chronometers: one against another. Or better yet, a whole ensemble of five or ten chronometers could serve as checks on each other.

Modris, you also wrote:
"The rate of the timepiece was calculated using 2 lunar observation sets with about 8-10day interval. Observer calculated the error of chronometer on those two dates and found the rate."

What's your source for that? Don't get me wrong: it's fine if you're just describing your own estimation of how they might have gone about it. But we should distinguish that from "history". A method like you've described here could yield crude, but probably useful, values of chronometer error. But the implied rate would have been quite poor.

You added:
"Of course, another question is the accuracy of such a rating method (even the lunar distance fan Chauvenet expected 20 seconds of time possible error even under excellent conditions)."

Right. The accuracy would have been low. As for Chauvenet? His opinions on lunars are not based on practice and are largely irrelevant. Whether he said 10 seconds or 100 seconds, he was just blowing smoke. Of course his "smoke" was highly respected in the US, and he was further sanctified by the reprints of his books in the early Space Age. But respect for his smoke doesn't make it any less "smoky"! :)

You concluded:
"And I doubt that this method was widely practiced. But the artificial horizon usage for rating in a manner discussed previously in NavList, could be practiced only on land. But these are not lunar observations."

And are we talking about getting chronometer "error", which is considerably more forgiving, or chronometer "rate"? We can test for chronometer "error" much like the lunar model that you described above. And this does not require an artificial horizon or a stable platform --only a known longitude of some landmark, like one of those little islands in the "slalom course" in the Atlantic. Hit one, get a chronometer error. Hit another some days later, get a second chronometer error. Then the rate is just the difference in errors divided by the difference in days. Easy. Back then they saw it a little differently, and there were recommendations that a navigator should try to get a real rate, like the sort that might be determined by a rating on land by a specialist. Today the difference seems trivial, but it mattered to some of their discussions in the nineteenth and early twentieth centuries.

Frank Reed