19.3 Horizontal, noon Do. midnight Difference in 12 hours. Proportion for 5h 12m. 57, and 2m. 21.5. long. 25.9 Corrected for 5h. 12m. 57s. and 2m 21.5' E. longitude. 56 27.9 Correction for latitude (see 4th Lunar Table, Pearson) 0 07.1 An observer not furnished with a mural circle, or other instrument fixed in the plane of the meridian with which to measure meridional altitudes, can obtain his latitude more correctly than by observing a single approximate meridional altitude, with a sextant, or other reflecting instrument, by taking a number of altitudes of the sun or a star on each side of the meridian, and from thence determining the correct altitude of the object at the time of its culmination. This method, termed the" reduction to the meridian," is susceptible of great accuracy; and the repeating circle described in page 128, is peculiarly adapted for these observations, on account of the rapidity with which they can be taken. The distance of the sun or star from the meridian (in time) is noted at the moment of each observation, by a chronometer, when the former is the object, and by a sidereal clock (if there is one) when the latter, to save the conversion of one denomination of time into the other. The formula given by Mr Baily freed from the second part of the equation, which it is seldom necessary to notice, is x = A+ cos L. cos D sin Z where I represents the latitude (known approximately). D the declination. Z the meridional zenith distance, also known approximately. A a quantity depending upon the horizontal angle of the object, and given in the 13th table, page 193, under the head of" Reduction to the meridian.", the required correction, in seconds. When the sun is the object observed, a further correction must be made on account of the change in declination during the time occupied by the observation, which is expressed by S-being the change of declination in one minute of time, minus when decreasing. E the sum of the horary angles observed to the east, expressed in minutes of time, and considered as integers. W their sum to the west, and n the number of these observations. When a star is the object observed, and the time is noted by a chronometer, regulated to mean time, the value of A must be multiplied by 1.0054762 Also, if the clock does not keep its rate either of sidereal or mean time accurately, a further correction is imperative; and A must be multiplied by 1 + .0002315 r, where r denotes the daily rate of the clock in seconds, minus when gaining, and plus when losing. EXAMPLE. On March 8th, 1837, the following observations were taken, with a six-inch sextant, the chronometer being + 9m. 16., index 1'20"; barometer, 29.54; thermometer, 50°. Method 3rd.-By the altitude of the pole star, at any time. If the altitude of the pole star can be taken when on the meridian, its polar distance, either added to, or subtracted from, the altitude, gives at once the latitude; and when observed out of the meridian, as at the point S or S' in the figure, the latitude can be easily obtained, as follows: Let Z PO represent the meridian, Z the zenith, P the pole, and aSa the circle described by the polar star S, at its polar |