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Geoffrey Kolbe, you wrote:
"The essence of the method is the LOPs from a number of star fixes will cross 
neatly at a given point on the chart, but that point will in error in 
longitude due to the error in the chronometer. The longitude error in a lunar 
LOP will be slightly different due to the faster motion of the moon across 
the sky. The trick then is to adjust the time so that all LOPs - including 
the lunar LOP - cross at the same point. The amount of adjustment required 
gives the error in the chronometer.
I had not seen this described before and thought it quite neat."

I have a hunch that we are seeing the influence of John Karl's advisor on this 
book, namely Ken Gebhart. I've seen and heard Ken describe this technique in 
just those terms more than once (including between sessions at Mystic last 
June). He didn't invent it, of course. It's been around in one shape or form 
for centuries. But Ken does like to sell the method that way.

This method of getting longitude by lunar altitudes has two problems, but 
they're not necessarily more problematic than standard "lunar distance" 
sights. 

First, this method only works if the motion of the Moon on the celestial 
sphere (in SHA and Dec). is more or less vertical at the time its altitude is 
observed. Since the Moon's "horns" are nearly perpendicular to its motion 
among the stars, there is a simple observational test. If the line through 
the horns is within thirty degrees of horizontal, then you can safely use 
this method with minimal error. Even at 45 degrees tilt, the accuracy is 
reduced from 1.00 to 0.707. Since it was considered acceptable, though not 
desirable, to use stars which were as much as 45 degrees out of line for 
lunar distances, we should probably apply that same standard to longitude by 
lunar altitudes. By contrast, if the horns are nearly vertical (consider the 
Moon while it's rising, even right at due East, at the time of the "harvest 
moon" in high latitudes), then the motion from a change in GMT will not much 
affect the observed altitude.

Second, the horizon at sea probably shouldn't be trusted to more than half a 
minute of arc. This applies mostly to sights taken at different times. If we 
can observe the Moon's altitude and almost simultaneously observe altitudes 
of other bodies, the lower limit on the horizon error probably can be dropped 
to 0.25 minutes of arc. Measuring lunar distances, by contrast, does not have 
this difficulty. On land, you can measure lunar altitudes with an artificial 
horizon, and the problem of the horizon vanishes. In that case, and when the 
above geometric condition for the orientation of the Moon is satisfied, lunar 
altitudes are an excellent means of determining GMT using that method of 
adjusting the LOPs to match as described in John Karl's book. 

So we have a puzzle: why weren't lunar altitudes for longitude ever used or 
recommended in practice (historically)?

-FER




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