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sensible horizon (on shore an artificial horizon is always used). A larger angle is evidently always observed; and this correction, which can be taken from the 11th table, is always subtractive. The correction for the index error has already been explained.
On March 15, 1838, the observed double altitude of the sun's upper limb, taken with a sextant, was 42° 37′ 15′′, the thermometer at the time standing at 42°,* and the barometer at 29.98 inches. Required the altitude, corrected for semidiameter, refraction, and parallax.
Reading on the arc
Arc of excess
Correction for refraction and parallax.
* In rough altitudes, such as those taken at sea for latitude, no correction is made on ac
count of the state of the thermometer or barometer.
On April 6, 1838, at 9 P.M., Greenwich time, in latitude 51° 30', the double altitude of the moon's lower limb was observed 97° 21′ 50′′. Index error of sextant, 50".
Barometer, 30.1 inc. Required the corrected altitude.
* This might have been obtained at once by inspection, by using the tables of Parallax.
In these examples no allowance has been made for the dip of the horizon, as the observations were made with an artificial horizon: with the fixed stars no correction is required for semidiameter or parallax.
TO DETERMINE THE LATITUDE.
Method 1st.-By observations of a circumpolar star at the time of its upper and lower culminations.
This method is independent of the declination of the star observed: the altitudes are observed with any instrument fixed in the plane of the meridian, or (not so accurately, of course) with a sextant or other reflecting instrument, at the moments of both the upper and lower transits of the star; or a number of altitudes may be taken immediately before and after its culminations, and reduced to the meridian, as will be explained. In either case, let Z denote the observed or reduced meridional zenith distance of the star at its lower culmination, and r its refraction at that point; also let Z' and ' denote the zenith distance and refraction at its upper culmination. Then the correct zenith distance of the pole, or the co-latitude of the place, will be = (Z + Z') + 1⁄2 (v + r′). According to Baily, a difference of about half a second may result from using different tables of refraction.
Method 2nd.-By means of the meridional zenith distance (or co-altitude) of the sun, or a star whose declination is known.
The altitude of the sun or star being determined at the moment of its superior transit, as before explained, and corrected for refraction, and also for parallax and semidiameter when necessary, the latitude required will be—
Z+D, if the observation is to the south of the zenith.
D-Z, if to the north above the pole.
180-(Z + D) to the north below the pole.
Z being put to denote the meridional zenith distance, and D the declination (when south).
This is evident from the figure below, ES, ES', and QS" being the respective declinations of the objects S, S', and S"; and PO or ZE the latitude of the place of observation, which is
Perhaps the rule given by Professor Young for the two first cases is more simply expressed thus:-Call the zenith distance. north or south, according as the zenith is north or south of the object. If it is of the same name with the declination, their sum will be the latitude; if of different names, their difference; the latitude being of the same name as the greater.
On April 25, 1838, longitude 2m 30s east, the meridional double altitude of the sun's upper limb was observed with a sextant 104° 3′ 57′′; index error 1' 52"; thermometer 56°; barometer 29-04. Required the latitude of the place of observation.
On March 31, 1838, at 5h 12m 57s by chronometer, the meridian altitude of the moon's upper limb was observed 67° 1′ 5′′; the index error of instrument being 1' 0"; barometer 30.1 inc.; thermometer 51°; the approximate north latitude was estimated 52°, and longitude 2m 21′ 5′′ E. Required the latitude*.
* The number of corrections required, and the necessary dependence upon Lunar tables, render an altitude of the moon less calculated for determining the latitude than one either of the sun or a star.