Applying the Corrections to the Angle Lewis Measured
Creator:
Bob Bergantino; Ginette Abdo
Description:
The angle that Lewis measured during this noon shot is not the altitude of the sun's center but: 180° minus 2x the altitude of the sun's lower limb. The angle he measured also includes angles caused by mirror misalignment (index error), refraction (see Step D), parallax (see Step E), sun's semidiameter (the angle between the sun's lower limb and its center (see Step F) and the sun's declination (angular distance north or south of the equator (see Step G). All these angles have to be eliminated in order to derive the true altitude of the sun's center with respect to the earth's center. The first step in making corrections to the observed angle usually is to subtract the index error (or in some manuals, apply index correction) but . . .A) Lewis first divides the angle he measured by 2. Because Lewis had to measure the angle between the ray reflected from the index mirror and that from the artificial horizon, the observed angle is twice that from a natural horizon alone. B) Then he subtracts the result of Step A from 90°. Since Lewis already has divided the observed angle by 2 in Step A, he must subtract that result from 90°, not 180°. C) Next Lewis adds half the OCTANT°S INDEX ERROR. Lewis, in his journal for July 22, 1804, recorded that the octant's index error in the 'back-method' was +2°11'40.3". The octant's index error actually was +4°23'20.6"; that is, it read too high by that amount. Lewis, however, began his corrections by dividing his measured angle by 2 and, thus needed to apply only half the index error (though still calling it 'index error'). Because Lewis's octant read high, the index error should be subtracted, but owing to the sequence Lewis used to make his corrections, he needs to add 2°11'40.3" to the result of Step B.
