The moon, on the contrary, is so close aboard that the angle of parallax reaches a value of nearly 1´; as a minute of altitude means a minute of latitude and in turn a mile, so with this body the error due to parallax must be carefully determined.
In the case of the sun, however, it is somewhat of a waste of time to bother with parallax, for it never exceeds 8´´ or 9´´ and such fine calculation is uncalled for in ordinary navigation where so many greater errors must be kept in sight. However, we desire to eliminate every known element of error without undue figures, so it is recommended that Table 20B, Bowditch, be used, where without extra trouble the parallax may be found conveniently combined with the refraction.
When a body is in the sensible horizon, the parallax is greatest. The angle of parallax subtended by the radius of the earth is then an acute angle of a right-angled triangle and is as large as it can possibly be with the body at the same distance. As the body obtains altitude above the horizon, the right angle of the triangle (at the observer) becomes obtuse and our acute angle of parallax becomes smaller and smaller until the body reaches an altitude of 90°—in our zenith, when the obtuse-angled triangle has resolved itself into the perpendicular line that passes through our position and the earth’s center. The angle of parallax here disappears.
When a body is in the horizon, its parallax is known as Horizontal Parallax in contra-distinction to Parallax of Altitude. The latter has become generally known among navigators merely as parallax.
Our position on the surface causes a body to appear lower than if viewed from the center of the earth, so the error of parallax is added to the observed altitude; when, however, it is combined with refraction it is subtracted in an observation of the sun, but added when the moon is used.
The parallax of the moon is excessive because the radius of the earth becomes a considerable amount when compared with the close proximity of the body, and causes a considerable angle at the body between the lines drawn from the observer and that drawn from the center of the earth. The change in parallax is so great that it becomes necessary in order to preserve accuracy to correct the observed altitude for index correction, dip and semi-diameter, to secure an approximate corrected altitude before attempting to correct for parallax. The horizontal parallax, which is the angle subtended by the earth’s radius when the moon is in the horizon, is taken from the Nautical Almanac, and with this and the approximate altitude as arguments, enter Table 18, Bowditch, and pick out, having regard for correction tables at the right, the parallax and refraction combined.
The usual corrections to the observed altitude of the sun or stars can be picked out at once from Table 46, Bowditch, where they are all combined for a quick correction.
CHAPTER VI
Latitude
Meridian Altitude