NavList:

Don, you wrote:
"In early 19th century texts such as Moore, Bowditch, and MacKay, I find descriptions of finding local apparent time by equal altitudes, in which a pair of sights are taken several hours before and after noon, when the altitude of the sun is changing at a more rapid rate. The math is trivial compared to that required for a time sight, yet the method is suggested not as a method of determining longitude at sea, but as a means of checking the accuracy of the chronometer while in a harbor with a known longitude."

Yes, it is in Bowditch and the others, but my sense is that they usually mention it "for completeness". There were book reviewers even back then, and if, let's say Bowditch, had failed to mention this method "which everyone knows" he would have opened himself up to accusations that he had left out "the most basic method of finding longitude". But is it really a useful method when accuracy counts? After all, the Sun's declination changes even in a few hours. Around the equinoxes, it's around one minute of arc per hour (or a speed of one knot N/S for the subsolar point). There are ways of correcting for this. There are circumstances when it's not an issue, like near the solstices. But in the end, is there really much saving in effort? If you had an almanac but no table of logarithms, it would be a good stopgap measure. For modern introductory students, it's a nice method to learn, since it gets them up to speed quickly. But "speed" is the big problem. Unless we correct for vessel motion and (equivalently) changing Sun declination, this method can be rather inaccurate.

You wondered:
"Was the equal altitudes method used at any time in the 19th century for determining longitude?"

Well, I'm sure it was at some point. But routinely? I've never seen any cases myself. I suppose the bottom line is that time sights just aren't that difficult. If you can learn to work time sights in a class in one afternoon at a basic level (as you and many participants in my classes have), then you can become an expert in five days. Given that time sights are more flexible, it strikes me that most nineteenth century navigators would have quickly recognized that they might as well just buy some logarithm tables (or a navigation manual like Bowditch).

-FER

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