From two altitudes of the sun together with the intermediate or elapsed time between the two observations and the estimated Greenwich time to compute the latitude of the place.
- For the proper time when the altitudes are to be taken, consult the remarks in the book of requisite tables pages 21 and 22.
- From the apparent altitudes find the true altitudes.
- Find the declination of the sun for the middle Greenwich time between the two observations.
- [This number and any text possibly associated with it are not in the notebook copy.] [p. 7:]
- Let half the elapsed time be reduced to degrees and minutes.
From the above data the latitude may be computed as in the following example.
Suppose the apparent altitude of the sun's lower limb at the time of the first observation = 43°28', time per watch 2h 41m before noon. Apparent altitude at second observation 56°21', time per watch 30m before noon. Estimated Greenwich time May 12th 1799 about 8 hours p.m. Latitude by account 50°19'N. Required the true latitude?
- Set down the supplement of the angle found in the table when A is greater than 90°. Let the cosine of C be increased or diminished by as much as a + b—10 exceeds or wants of cotangent C, the nearest arch in the table.
- Set down the supplement of the angle found in the table when I is greater than H.
- Subtract except when A is less than the co-latitude by account and when M exceeds 180° take the cotangent and secant of its excess above 180° and set down the remainder.
- Subtract unless when M is greater than 90°. Note If both altitudes when corrected be equal, the latitude may be found by Problem 1st calling half the elapsed time the true hour of the day or distance (in right ascension) of the body from the meridian. Or if the two altitudes be nearly equal, you may, without any sensible error, take the mean and work as above by Problem 1.
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