always observed; and this correction, which can be taken from the 11th table, must be always subtractive.

The correction for the index error has already been explained in page 132.

EXAMPLE I.

On March 15th, 1838, the observed double altitude of Ō, taken with a six inch sextant, was 42° 37′ 15′′, the thermometer at the time standing at 42o, and barometer 29.98 inches. Required the altitude corrected for semidiameter refraction and parallax.

EXAMPLE II.

On April 6th, 1838, at 9 P. M., Greenwich time, in latitude 51° 30', the double altitude of D was observed 97° 21′ 50′′. Index Thermometer, 54°. Barometer, 30.1.

error of sextant, 50".

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, the only correction required is for refraction.

PROBLEM III.

TO DETERMINE THE LATITUDE.

Method 1st.-By observations of a circumpolar star at the time of its upper and lower culminations, and 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, 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 deduced meridional zenith distance of the star at its lower culmination, and r its refraction at that point; also let Z` and r' 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 = 1⁄2 (Z + Z') + } (r + r).

According to Mr. 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.

DZ, 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, or ES' and QS" being the respective declinations of the objects S, S,' and S"; and PO or ZE, the latitude

of the place of observa

tion, which is equal to (ZS + ES) in the case of the star being to the south of the zenith Z; or ES'-ZS-when to the north above the pole P; and 180-(QS" + ZS") when to the north below the pole.

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.

EXAMPLES.

On April 25th, 1838, in longitude 2m 30s east, the meridional double altitude of Ō was observed with a sextant 104° 3′ 57′′, index error 1' 52", thermometer 56°, barometer 29.04. Required the

On March 31st, 1838, at 5h 12m. 57. by chronometer, the meridian altitude of was observed 67° 1' 5"; the index error of instrument being 1' 0", barometer 30 1.; thermometer 51°; the approximate latitude was estimated 52°, and longitude 2m. 21′ 5′′. 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.