LONGITUDE AND LATITUDE, METHODS OF FINDING. We shall classify the various modes of determining geographical lati tude and longitude, partly by the instrumental means of the observer and partly by the nature of the phenomena. The problems are of course the same whatever instrument is employed, for the latitude of a place is the altitude of the pole of the heavens at that place, and the longitude is the difference between the time on the first meridian (we shall always suppose Greenwich to be the first meridian) and the time at the place, at the same physical instant.
Determination of the Latitude at Fixed Observatories and Inde pendently.-1. In determining the latitude at fixed observatories which are furnished with accurate circles, mural, transit, or altitude and azimuth circles [Cnict.el, the altitudes or zenith distances of circum polar stars are observed above and below the pole. When these are properly reduced, the place of the pole (which hes between the places of upper and lower culmination of each star) is known, and hence the latitude is found. The first object of all astronomers is to fix the latitude of their place of observation, and the details of this operation will be found in the beginning of most of the published series of observations. The account of the latitude of Greenwich in the Green wich Observations for 1836, p. lviii., of Cambridge in the Observations of 1933-4-5, and of Edinburgh, 1834-5, may be consulted by those who wish to know what the process is, with the most perfect means which we at present possess.
2. Again, if the altitudes or zenith distances of the sun he observed several days before and after the summer and winter solstices, the altitude or zenith distance of the middle point, that is, of the equator, may be deduced. Since the tables of refraction have been perfected by Besse], these observations give a satisfactory latitude. Both methods may be considered to be indopendeut, as they do not draw their data from other observatories, and no great accuracy is required in the solar tables to reduce the observations of the sun to the solstice. (Pond's :Lat., Greenwich Observations,' part v.) In the observatories of Europe, and generally where the visible pole of the heavens is tolerably high, the latitude is best determined by circumpolar stars ; near the equator an independent latitude must be deduced from circumsolatitial observations.
3. Before the introduction of circles, the latitude in fixed observa tories was derived from combining two instruments, the mural QuADRANT and the ZENITH SECTOR. The zenith distances of stars near the zenith, and to the north or south of it, were observed by the zenith sector, and also the distances of the same stars from the pole or the equator by the quadrants; hence the arc between the pole and zenith (the co latitude), or between the zenith and equator (the latitude), was deduced. The place of the pole was found on the north quadrant from circum polar stars, and the place of the equator on the south quadrant, from observations of the sun near the solstices, as we have described above. \Then the present zenith tube was erected at Greenwich, one of its intended uses was to perform the same office for the mural circle as the original zenith sector did for the quadrants.
Determination of the Latitude Diferentially.-1. The ZENITH SECTOR, when of the proper size and construction, is perhaps the most accurate instrument for determining latitudes that is, assuming data which are either known or can be obtained from fixed observa tories. With this instrument, the meridian zenith distances of several stars which pass near the zenith may be observed with great certainty; and as the polar distances of those stars are or may be determined at first-rate observatories, the polar distance of the zenith, or the co latitude, is known. The latitudes for the trigonometrical survey of Great Britain are thus deduced by comparison with Greenwich, the instrument employed being a very fine 8-feet zenith sector by Rantsden. With a better knowledge of the proper motion of the stars, the sector might be used at two places, and the arc between those places obtained from observations of the same stars at two epochs, without reference to any other observations; but at present it is safer, when practicable, to refer directly to corresponding observations made at a fixed observatory.