NavList:

Jonathan Ho, you wrote:
"I found it much harder to keep the sextant steady at the larger 70 degree angle while trying to keep both bodies in view. I was getting quite tired arms from trying to hold the sextant"

Yes, fatigue can be a problem. And some sextant orientations are painful! One thing I realized rather quickly shooting lunars: if it hurts, don't do it. Wait for a better geometry that's not uncomfortable. Historically navigators had this option, too, because lunars --strange as it may seem-- are not time-critical sights. Though lunars historically were "all about time" (designed to determine Greenwich time), there was no immediate urgency about the process. If you've been sailing for a week without a time check, it doesn't much matter if you shoot your lunar at 10am local time, when the geometry might be uncomfortable, or you shoot at 1pm when it's easier. Don't shoot lunars if it hurts!

Also, as a practical matter, you should learn to hold your manipulate your sextant a bit differently --differently compare to the standard technique in celestial navigation. With standard altitude sights, we need one hand on the sextant's handle and one hand on the micrometer, actively adjusting the micrometer "live" because altitudes change so rapidly. Lunars change slowly, typically thirty times more slowly than altitudes. So pick a starting angle and set the sextant to that. Then grab the instrument with both hands, one on the handle, the other on the frame directly opposite, for a more stable platform. Then look through and make a visual estimate: one minute of arc gap? five minutes of arc gap? Or is it two minutes of arc overlap? With that estimate, relax, lower the sextant, and adjust the sextant away from your eye by the exact amount of your estimate. Repeat. Gap now smaller? Maybe 0.3 minutes of arc? Again, relax, and lower the sextant from your eye. Give the micrometer a little tweak, and try again. Don't adjust "live". Use both hands for stability.

And you suggested:
"I was using the standard 3.5x40 scope that came with Francis' Astra sextant. I suppose a 6-7x scope would give a better view, but I don't have nearly £300 to spend on one and have read that it makes lunar sights at sea more difficult with the boat's movement."

Agreed on price. Keep an eye out for a second-hand scope. They occasionally turn up on ebay and sell for half that price or less. Where did you read that a 7x scope makes sights more difficult at sea? Naturally there are circumstances where vessel motion would make lunars nearly impossible even with a low-power scope, but that's not really relevant. We have to deal with difficult conditions by waiting them out. After all, overcast skies make lunars more difficult, too! If physical conditions, like weather or sea state, limit your ability to shoot lunars, then you wait for better conditions. But let's suppose you're never able to shoot lunars with a higher power scope. Your budget never permits one! Does that mean you're doing it wrong? Are you, therefore, an "also ran", not a real lunarian? No, of course not. It merely changes your expectations for the quality of your best sights by a factor of two, which is not terrible. You should be looking for consistent quality, not absolute quality on some subset of sights. With a 7-power scope, you can expect individual sights with a variability of +/-0.25 minutes of arc (in a standard deviation sense, so roughly two-thirds would be better than 0.25' absolute error). If you use a 3.5-power scope instead, then you sould expect variability of +/-0.5 minutes of arc. Note that this is for individual sights. You can do significantly better by averaging sets. Four sights in a row averaged will, all other issues set aside, reduce random error --random noise in your observations-- by a factor of two. In the general case, multiple sights averaged reduce random noise in proportion to the square root of the number of individual sights. But after four sights, you'll probably hit other limits in the quality of your sights, so there's not usually much point going beyond that number.

You wrote:
"I may have been aiming for tangency of Jupiter with the moon's near limb, instead of bisecting the centre of the planet's disk. I didn't even think of using shades for Jupiter (though of course did for the moon). So perhaps this contributed to the error (if I had gone for the centre, this would have increased the lunar distance slightly, which would work to correct my error...I think?)."

Right. For Jupiter you want to place the center of that little dot on the limb. At 3.5x magnification, you may not be able to consciously "see" that tiny disk, but nonetheless if you "aim" to place the center of the planet on the limb, you should see a small improvement in results. And yes, a low-density shade may help with Jupiter sights. You want to see the planet clearly, distinctly, with visible contrast against the Moon's limb, but it should never seem "dazzling" bright.

And you wrote:
"The final possible error that I found to be quite difficult, and made me question the accuracy of my sights, was sweeping the arc to find the maximum distance. It felt like I needed a combination of yawing, rolling and translating the sextant in order to have the arc in plane with a great circle, which I found very difficult to achieve while still keeping both bodies in view! It probably just takes practice. But I was reasonably skeptical that I had achieved a proper "kissing" of the two bodies each time, however it was getting late and cold enough that I was ok to leave it as it was."

This you should experiment with to convince yourself that, in fact, it's not really the issue that you may be imagining. When you bring two nearly point-like targets into contact in your sextant, you are, necessarily, measuring the great circle angle (measuring, as you say, 'in the plane of the great circle'). The sextant can't do anything else. The only exception to this is when the two bodies are not more or less centered in the field of view. Try to make the final contact with both objects within less than 1 to 1.5° of the center of the field of view (which you can judge by the diameter of the Moon, so call it two to three "moon diameters"). There is a small error that results from being away from the center of the field of view, and this is actually identical to a telescope "collimation" error. Since you may possibly have some collimation error, too, you can experiment by searching for the spot in your field of view where the contact distance is minimized. Maybe it's not dead-center... Maybe it's a degree to the left. But don't chase something that isn't there. If you can't actively see any change when you shift the contact location to one side in your sextant, then you have nothing to worry about. If you don't see any effect from being a little off-center, then don't worry about it. If you don't see it, you can't measure it.

You wondered:
"On a side note, while looking back through archives I noticed that Frank considers Bruce Stark's tables to be a historical oddity, and not as simple or transparent as, say, Thompson's tables. What is your preferred manual/tabular method for clearing lunars?"

There are plenty of methods from the historical era that are fast and relatively easy, but I would say that everyone who is exposed to Thompson's tables, especially in a cleaned-up modern form, such as we us in my workshops, finds them irresistible. Thompson's tables are highly efficient, and they were widely used, though somewhat late in the period when lunars were regularly practiced at sea (thanks in part to being adopted into Bowditch's Navigator). In my lunars workshops, I teach Thompson's method for "practical" use and cover other methods mostly for theoretical background (to satisfy that "market demand" from some lunarian enthusiasts, though not everyone is interested in theory).

Stark's tables are indeed a historical oddity. I suspect that if Bruce Stark had had access to the vastly greater historical resources we have had available since 2005-2010 (when online historical book archives, especially Google Books, exploded), he never would have chosen to publish such idiosyncratic tables. From the end of the practical era in lunars c.1850 and even before, lunarian enthusiasts and amateur mathematical engineers have frequently worked under the (largely mistaken) notion that lunars were too difficult mathematically for common navigational use and that this was a problem that needed to be fixed. But it just isn't true. All that said, I should add that the Stark tables are well-designed, carefully organized, and competent in every way. There's nothing wrong with using them if you don't mind that they are a paper method created in the 1990s. They are unhistorical. And if we're interested in modern application of lunars in some "practical" side of navigation (and yes, there are good arguments for practical application here), then we have vast electronic computation resources available so a paper method is an anachronism unless it has some relevance to history. That's my take on it anyway.

Finally, one more bit of advice: index error is everything. I can't repeat this enough. You'll get good results from lunars, whether for historical experience determining GMT or for modern application testing your skill and your sextant, only to the extent that your index error is properly measured and applied to your sights. Find a good technique for assessing index error. Get really, really good at measuring index error. Good lunars follow... :)

Frank Reed
Clockwork Mapping / ReedNavigation.com
Conanicut Island USA