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This table is adapted to leapyear, particularly 1808. In order to make it serve for other years, the time of transit must be taken for the day following that given in the months of January and February. For the first year after leapyear, one minute is to be added to the time of transit given in the table ; two minutes for the second, and three minutes for the third after leapyear.
Again, to reduce this table to a different meridian than that to which it is adaqted, viz. Greenwich ; if the longitude is between 45° E, and 45° W, there is no correction to be applied. If the longitude is between 450 and 135° E, one minute is to be added : but if it is between 45° and 135° W, one minute is to be subtracted. If the longitude is between 135° E, and 180°, two minutes are to be added, but subtracted if the given longitude is between 135° W, and 180°.
This table is useful to find the time when the altitude of the polestar ought to be observed, to find the latitude by its meridian altitude ; it is also useful in finding the variation of the compass by the polestar.
Difference of Altitude of the Polestar and the Pole, at different distances of the Star from the Meridian.
As the polestar is generally known, that no opportunity, therefore, may be lost for determining the latitude, this table is inserted, the use of which is as follows:– . Find the interval between the time of observation of the altitude of the polestar, and that of its passing the meridian, and take out the corresponding equation from the table ; which added to, or subtracted from the true altitude of the polestar, will give the latitude of the place of observation.
I. Let the corrected altitude of the polestar be 46° 10' N. observed 8h. 30′ before its passage over the meridian. Required the latitude 2
True altitude of the polestar - - - 26° 10' N.
Latitude - - - - - - - 47 15 N.
II. At 1h. 10' after the passage of the polestar over the meridian, its altitude corrected was 58° 51' N. Required the latitude 7
True altitude of the polestar - - - 58° 51° N.
Latitude - - - - - - - 57 9 N.
Argument. Distance of the Star from the Meridian, in Sidereal Time.
The Declination of the Sun is an arch of a meridian contained between its centre and the equinoctial, which arch is reckoned in degrees, minutes, &c.
In the first quadrant of the ecliptic, from about the 21st of March, to the 21st of June, the Sun's declination is North, and increasing; and in the third quadrant, between the 22d of September and 21st of December, the Sun's declination is South, and increasing. In the second quadrant of the ecliptic, from about the 21st of June to the 22d of September, the Sun's declination is North, and decreasing; and in the fourth quadrant, between the 21st of December and the 21st of March, the Sun's declination is South, and decreasing; which will be readily perceived by inspecting the table.
In this table, the Sun's declination is given, from the year 1808 to 1823 inclusive, calculated for the instant of noon, each day, at