A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Frank Reed
Date: 2019 Sep 30, 16:29 -0700
Chris Mitchell, you wrote:
"I realize now that there is more than one “version” of a time sight, this method that I have been asking about relies on table XXV in the older versions of Bowditch. The method that I am familiar with uses the formula: cosP = (cosZD – sinLat * sin Dec) / (cos Lat * cos Dec). In the end, both methods accomplish the same thing, I was just wondering if this newer formula method would have superseded the older Bowditch method, however the Bowditch method with its tables would definately be easier if you never had a scientific calculator to comput the formula."
Yes. That's it. It's just a question of computational convenience. The old time sight algorithm was finely tuned for logarithm tables. The standard "law of cosines" equation, which you quote above, is 100% identical to the math in the older navigation manuals differing only by trigonometric identities. Since we don'y use logarithms anymore, we gain nothing by using the old approach except, of course, a taste of history. As you say, with a calculator in hand, there's no issue, no problem. But these things are mathematically identical. If you carry enough digits in the traditional method using Table XXV in an old Bowditch, you'll get exactly the same result as you would using a calculator and the familiar law of cosines. They're only superficially different.
"Are there any other "versions" of time sights besides the two mentioned perviously (Bowditch tables & formula)?"
Oh sure. There are always endless variants that we can build by throwing trigonometric identities at the problem. But they don't solve any significant problem. There was a period of experimentation in methodologies during the transition from the "Old Navigation" (traditional time sight calculations, among other things) and the "New Navigation (the intercept method at its core but with a number of other "new" features in addition). The transitional period lasted decades, at least thirty years, and if we really stretch it half a century. In the early 20th century, various hybrid methods were developed that bridged the gap between the Old and the New. Some flew. Some didn't. Methods involving haversines were especially popular in this period, at least in British and American navigation.
You also wrote:
"Also, with the implementation of time zones I assume that keeping local apparent time became a thing of the past on ships. The only time I hear it mentioned onboard now is when referencing local apparent noon for a noon sight."
I see what you were getting at now. It's not as if they "kept" local apparent time with any accuracy. But they necessarily calculated it as part of the process of navigation. Local apparent time is identical to Hour Angle (a modern navigator would keep HA in degrees, not hours, but obviously that's just a conversion factor). At least some of those navigators understood that they were "correcting" their watches when they took a sight. You might take a sight at 3:05pm by your pocket watch, and then work it up to discover by computation that the local apparent time is 3:08:35. But there was no incentive to change the time on the watch manually at this point. They referred to this process as "regulating the watch". What we know as a time sight today would have been called a sight "for the true time" or a sight to "regulate the watch" or maybe combining the two "regulate the watch to true time".
Work time (changing of the shifts/watches, etc.) before the late 19th century/early 20th century was based on local noon but the time they kept was mean time starting from the call out of local noon. Further the call of noon was typically inaccurate by a few minutes. It wasn't the precise time that mattered. It was just the ritual, systematic work shift rollover time. And if the vessel was sailing generally east, you might get a short day. The last shift before noon might be shorter by five minutes when the next noon was called. Lucky you if you had the last, short shift. Note that if they tried to keep local apparent time steadily throughout the day, then there would never be any gaps like this. Hours would run a little slower or a little faster from one noon to the next. Instead they used mean time (mechanical time, the time kept by watches from one local noon to the next).
Earlier in the 19th century, they even had "sea days" or "nautical days" where one turned the page on the calendar, jumped from Monday to Tuesday, at noon. This was confusing, and it was obsolete by 1850. Astronomers, too, had "astronomical days" which began at noon, but just to make sure things were as messy as possible, the astronomers changed the date at the previous noon. Thus the master of a vessel at sea, an astronomer in an observatory, and a clerk in port could agree on the date for only twelve hours during any one day.
This business of keeping mean time from a traditional event of apparent time, like noon at sea, is quite similar to the modern version of various traditional religious time-keeping systems, including Jewish and Islamic time and also Eastern Orthodox time kept, e.g., in the enclave of Mt. Athos, Greece. We're in the middle of Rosh Hashanah, the Jewish New Year right now, and it began at sunset yesterday. It ends tomorrow at sunset. A new begins immediately after sunset tomorrow. In any of these modernized traditional time-keeping systems, the clock typically starts at sunset and then runs on mean time --normal modern-duration hours and minutes-- until the next sunset.
Hope that's relevant to what you were thinking about! If not or if so, we can branch off in many directions from here.