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While we're at it, measuring the angular diameter of the Sun or Moon with a sextant is the flip side of the coin from measuring index error using the Sun or Moon. Bring the Sun's reflected and direct images together with the reflected image above, limbs perfectly touching. Note this on-arc angle. It should be around half a degree. Let's suppose it's 32.1' for a specific example; call that D₁. Then reverse the images so that the reflected image is below the direct image, again with the limbs in perfect contact. Record this off-arc angle. Let's suppose it's 30.8' for a specific; call that D₂. The angular diameter of the Sun or Moon is then just the average of the two values:
  DIA = (D₁+D₂)/2
while the index error is half the difference:
  IE = (D₁-D₂)/2.
In the specific numerical example, I have given here, the diameter is then 31.45' while the IE is 0.65' (implying that the index correction is -0.65' and you could either round up or down). Normally the diameter is thrown out, but if you divide it by two and compare with some known value for the SD from a Nautical Almanac or some other source (making sure you account for the augmentation), then you have a nice check on your observations and work. Half the diameter in this case rounds to 15.7', and if that's what your source says for the augmented SD, you can have good confidence in your IE value as well.

You can detect the changes in the Moon's size directly and easily using this method, corresponding to changes in distance of just a few hundred miles. Note that with the Moon, you have to make sure you make the measurement along the line of the Moons horns, which is nearly pole-to-pole. 

Frank Reed