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Fred,

This is where you are going wrong: If the disks of sun and moon were
touching each other in the sky (like at the beginning of an eclipse),
there centers would be at a certain distance. Now you reason that if they
overlap, the distance of their centers would be smaller; and if there was
a gap, this distance would be larger. Right?

But the nature of the measurement with the sextant is such that it turns
these relations around! You start out looking at the moon while the
sextant is reading zero. Then you increase the angle between the two
mirrors (and thus the reading) until the limbs of sun and moon touch each
other; now you read the distance; if you turn the micrometer so as to
increase the angle even further, you get a greater READING of the
distance while the disks will overlap. If you turn the micrometer back
until you get a gap, you get a smaller READING for the distance.

Of course, the actual distance is always the same; it's the sextant
reading that changes in that peculiar way. Thus, Arthur is right.

Not meaning to beat a dead horse, but I seem to remember that Davies
plastic sextants come with a warning to avoid back lash errorr by "making
the final adjustment of the micrometer always towards the larger angle".
At first glance this looks strange: Would not most people prefer to make
the final adjustment during an altitude observation such that the final
movement of the body is DOWN, towards the horizon, rather than UP meaning
that the body would emerge from the water? Yes, of course! But down (i.e.
closing the gap) is towards the greater angle! Same problem.

Fred Hebard wrote:

> Arthur,
>
> Regarding whether the lunar GMT being fast of the actual was due to a
> gap in contact or an overlap, I still believe it was a gap.  The
> basis for my reasoning follows: the distance between the moon and sun
> was increasing with time.  If the time reported was 4:05, for
> example, rather than 4:00, which is the situation, this would imply
> that a greater distance was recorded than actually occurred.  A
> greater distance leads to a gap.  If the distance had been decreasing
> with time, than a fast time would have been due to an overlap.  I
> almost had myself talked into the reverse thinking after reading your
> post; this is tricky.

   

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