NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Sextant accuracy & lunars (re: venus)
From: Frank Reed CT
Date: 2004 Oct 9, 19:40 EDT
From: Frank Reed CT
Date: 2004 Oct 9, 19:40 EDT
Alex E wrote:
"But few days earlier, in the discussion on this list,
the general agreement was that you cannot do better with a modern
sextant:-)
(I am accumulating evidence that they could do better in early
XIX century when Lunars were indeed important for practical
navigators)."
Nah. You should take a look at some of the posts I've made in the past ten months regarding lunars in actual practice as seen in the logbooks at Mystic Seaport. Lunars were what they were: a technique of moderate accuracy (roughly +/- 15' in longitude) applied once a week or so as a check on the dead reckoning. Later when chronometers were common, lunars were used with declining frequency as a rough check on the longitude by chronometer.
But there are always exceptions! There were extraordinary cases of extremely expensive, astronomical-quality sextants in the hand of bona fide nautical astronomers yielding results two or three times better than any other lunars observers. These exceptions stand out precisely because they were so extraordinary. They are remembered because they were not normal. This is similar to a phenomenon in historical research. You'll sometimes hear that "everyone knows" that craftsmen built things better a hundred years ago (or 200, or 300, etc.) because we see chairs and artifacts from that era (take your pick of era) in museums and they are so wonderfully made. This common knowledge is a fallacy. Extraordinary objects demonstrating fine craftsmanship are the objects that are preserved and treasured for generations. The "creaky chair" with the bad joints ended up as kindling for the fire. The work of art was stored away and eventually given to a museum. It's a "sampling effect". By analogy, some lunars observations have become famous for their quality because they were evidence of such extraordinary skill. They are remembered because they were uncommon. The lunars on Cook's first voyage come to mind... Not everyone can afford to bring along a professional astronomer from the Greenwich Observatory with one of the world's best sextants, but the accuracy of the lunars on that trip (apart from errors in the almanac itself) are exceptional.
I didn't have time to participate in the sextant accuracy discussion you've had recently. But consider this: what is the angular resolution of the unaided human eye (corrected for faults)? Would you agree that it is about 1 to 2 minutes of arc? Assuming that the angular resolution of the unaided eye is indeed close to 1.5 minutes of arc, it is then a simple matter to place a limit on individual sextant observations. If your sextant's telescope has a 4 power magnification, your resolution is 0.38 minutes of arc at best. If your sextant's telescope is 7 power, your resolution is 0.21 minutes of arc at best [see PS]. This ignores all other errors. Of course, as Chauvenet noted in his "advice" article which George H recently made available to the list (online at HistoricalAtlas.com/lunars/chauvenet), the various simple errors cannot reasonably hope to reduce the observational error below 10 seconds of arc. And this analysis was not coming from someone who disliked lunars. Chauvenet was a true lunarian! He was a lunars booster, a shore-bound optimist who hoped (and this was in 1868) that lunars might yet stage a comeback at sea.
Frank R
[ ] Mystic, Connecticut
[X] Chicago, Illinois
PS: Most anyone who has studied a little optics knows that the the resolution of an optical system actually is limited by aperture and not magnification. But that is the best theoretical resolution. The practical apparent resolution is determined by the magnification and the limiting resolution of the human eye unless that value is smaller than the theoretical. In binoculars and small telescopes with fixed oculars, the magnification is chosen to match the theoretical resolution as well as possible. So 7x35 binoculars (and sextant monoculars) are 7 power because that's just about the right amount to match the theoretical resolution limit of a 35mm aperture.
"But few days earlier, in the discussion on this list,
the general agreement was that you cannot do better with a modern
sextant:-)
(I am accumulating evidence that they could do better in early
XIX century when Lunars were indeed important for practical
navigators)."
Nah. You should take a look at some of the posts I've made in the past ten months regarding lunars in actual practice as seen in the logbooks at Mystic Seaport. Lunars were what they were: a technique of moderate accuracy (roughly +/- 15' in longitude) applied once a week or so as a check on the dead reckoning. Later when chronometers were common, lunars were used with declining frequency as a rough check on the longitude by chronometer.
But there are always exceptions! There were extraordinary cases of extremely expensive, astronomical-quality sextants in the hand of bona fide nautical astronomers yielding results two or three times better than any other lunars observers. These exceptions stand out precisely because they were so extraordinary. They are remembered because they were not normal. This is similar to a phenomenon in historical research. You'll sometimes hear that "everyone knows" that craftsmen built things better a hundred years ago (or 200, or 300, etc.) because we see chairs and artifacts from that era (take your pick of era) in museums and they are so wonderfully made. This common knowledge is a fallacy. Extraordinary objects demonstrating fine craftsmanship are the objects that are preserved and treasured for generations. The "creaky chair" with the bad joints ended up as kindling for the fire. The work of art was stored away and eventually given to a museum. It's a "sampling effect". By analogy, some lunars observations have become famous for their quality because they were evidence of such extraordinary skill. They are remembered because they were uncommon. The lunars on Cook's first voyage come to mind... Not everyone can afford to bring along a professional astronomer from the Greenwich Observatory with one of the world's best sextants, but the accuracy of the lunars on that trip (apart from errors in the almanac itself) are exceptional.
I didn't have time to participate in the sextant accuracy discussion you've had recently. But consider this: what is the angular resolution of the unaided human eye (corrected for faults)? Would you agree that it is about 1 to 2 minutes of arc? Assuming that the angular resolution of the unaided eye is indeed close to 1.5 minutes of arc, it is then a simple matter to place a limit on individual sextant observations. If your sextant's telescope has a 4 power magnification, your resolution is 0.38 minutes of arc at best. If your sextant's telescope is 7 power, your resolution is 0.21 minutes of arc at best [see PS]. This ignores all other errors. Of course, as Chauvenet noted in his "advice" article which George H recently made available to the list (online at HistoricalAtlas.com/lunars/chauvenet), the various simple errors cannot reasonably hope to reduce the observational error below 10 seconds of arc. And this analysis was not coming from someone who disliked lunars. Chauvenet was a true lunarian! He was a lunars booster, a shore-bound optimist who hoped (and this was in 1868) that lunars might yet stage a comeback at sea.
Frank R
[ ] Mystic, Connecticut
[X] Chicago, Illinois
PS: Most anyone who has studied a little optics knows that the the resolution of an optical system actually is limited by aperture and not magnification. But that is the best theoretical resolution. The practical apparent resolution is determined by the magnification and the limiting resolution of the human eye unless that value is smaller than the theoretical. In binoculars and small telescopes with fixed oculars, the magnification is chosen to match the theoretical resolution as well as possible. So 7x35 binoculars (and sextant monoculars) are 7 power because that's just about the right amount to match the theoretical resolution limit of a 35mm aperture.
