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I quote below the key passage on "lunars" from Jean Lee Latham's "Carry On, Mr. Bowditch". The character "Nat" is Nathaniel Bowditch. The action begins after 'Nat' reads a note from his captain (Capt. Prince) telling him to 'Carry on, Mr. Bowditch' in his search for error's in Moore's Practical Navigator...

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   "Nat grinned and went topside again with his sextant. Tonight ought to be a good one for a lunar. The moon was due to pass over a star that was bright enough to see in spite of its nearness to the moon. But the same thing happened that happened so many times. Just when the moon neared the bright star, a cloud got in the way. Nat shrugged and sighed. There ought to be a better way to work a lunar! He studied the glittering heavens. Was there another star bright enough tonight -- that the moon would pass over? Of course not. He knew that.

   That one... the moon would pass below it... that one... the moon would pass above it... that one...

   The idea hit Nat so suddenly that he gasped. He raced below and for the second time that night crashed into Prince's cabin without knocking.

   Prince was asleep, but he was on his feet in an instant. "What was it?"

   "A new way to work lunars! Come on deck! As fast as you can!" He dashed out the door and up the companionway. He was on deck again before he remembered he hadn't said 'sir'. When Prince joined him, Nat's words tumbled over themselves as he explained. "This business of waiting for the moon to occult a star --it's a nuisance. But what if we take the position of the moon in relation to three stars? For instance, right now, we can get the angle between --"

   Captain Prince said, "Wait!" He sent for his sextant. "Mr. Collins, swing into the wind, back sail and hold steady!"

   Soon they were checking lunars the new way. When they had taken several sights, they went below. Nat checked the stars in the almanac and made his computations. His method worked!

   Nat glowed. "See? That's mathematics! It should give you the right answer!"

   Prince sighed. "Yes, Mr. Bowditch. And now -- please -- no more discoveries tonight!"

   "Aye, aye, sir!" Nat laughed and went topside again. He was too excited to sleep.

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I thought this section would be worth quoting in full since "Carry On, Mr. Bowditch" has become a very popular book for young people in the fifty years since it was first published. It's recommended to many home-schoolers in the US. And it is a terrific read, a fine fictionalization of life in the late 18th/early 19th centuries. It's hard to put down, even for adult readers. It's just such a shame that this one detail, the single thing for which Bowditch originally won fame, could get so mixed up in the explanation. Of course, lunars had been in active use for decades before Nathaniel Bowditch even heard of them, and of course all that stuff about occulations is nonsense historically. Nathaniel Bowditch's contribution, on the mathematical side, was to streamline a few calculations in lunar observations which had already been thoroughly analyzed by the best nautical astronomers and mathematicians of Europe. His real contribution, along with his publisher Edmund Blunt, was pedagogy and marketing -- he persuaded practicing navigators that they could easily use lunars, and that they had to buy his book to do it. But it sure wasn't as exciting as the book version above!

 

By the way, Latham discusses celestial navigation matters at various other points in the book and usually gets it right.