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zenith, altitude, method, star, meridian, instrument, declination, refraction and stars

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LATITUDE. The astronomical latitude of a place is the altitude of the celestial pole on the declination of the zenith. From the me chanical point of view it may be defined as the angle between the plane of the earth's equator and the observer's plumb-line or vertical. Neither of these definitions makes an assump tion as to the form of the earth and this astro nomical latitude is seldom identical with the geocentric, nor even with the geodetic latitude of a place. It is, however, the only kind of lati tude which can be directly determined from astronomical observations. There are six methods of determining latitude.

1. By most obvious method is to observe, with the meridian circle or some analogous instrument, the altitude of a circumpolar star at its upper culmination, and again, 12 hours later, at its lower. Each of the observations must be corrected for refraction and the mean of the two corrected altitudes will be the latitude. This method has the advantage of being an independent one and does not re quire any data (such as the declination of the stars used) to be accepted on the authority of previous observers. But to obtain much ac curacy it requires considerable time and a large fixed instrument. In low latitudes the refrac tion is also very troublesome.

2. By the Meridian Altitude or Zenith Dis tance of a Body of Known Declination.— If we use the meridian circle, we can always se lect stars that pass near the zenith where the refraction will be small ; moreover, we can se lect them in such a way that some will be as much north of the zenith as others are south and thus eliminate the refraction errors. But we must take our star declinations out of cata logues made by previous observers and so the method is not an independent one. At sea the latitude is usually obtained by observing with the sextant the sun's maximum altitude, which of course occurs at noon. Since at sea it is sel dom that one knows beforehand precisely the moment of local noon, the observer takes care to begin to observe the sun's altitude some 10 or 15 minutes earlier, repeating his observa tions every minute or two. At first the alti tude will keep increasing, but immediately after noon it will begin to decrease. The observer uses, therefore, the maximum altitude obtained, which, corrected for refraction, parallax, semi diameter and dip of the horizon will give him the true latitude of his ship. On account of the sun's motion in declination and the northward or southward motion of the ship itself, the sun's maximum altitude is usually attained not precisely on the meridian, but a few seconds earlier or later. This requires a slight correc tion to the deduced latitude, explained in books an navigation or practical astronomy.

3. By If the observer knows his time with reasonable ac curacy, he can obtain his latitude from ob servations made when the body is near the meridian, with practically the same precision as at the moment of meridian passage. The great

advantage of this method is that the-observer is not restricted to a single observation at each meridian-passage of the sun or of the selected -star, but can utilize the half-hours preceding and following that moment. The meridian-cir cle cannot be used, as the instrument must be such as to make extra-meridian observations possible. Usually the sextant or universal in strument is employed.

4. The Zenith Telescope method is generally known as the American, because first practically introduced by Captain Talcott of the United States engineers, in a boundary survey in 1845. Its essential charac teristic of the micrometric measurement of the difference between the nearly equal zenith dis tances pf two stars which culminate within a few minutes of each other, one north and the other south of the zenith and not very far from it; such pairs of stars can always be found. When the method was first introduced, a special instrument, known as the zenith tele scope, was generally employed, but at present a simple transit instrument, with declination micrometer and a delicate lever attached to the telescope tube, is ordinarily used. The telescope is set at the proper altitude for the star which first comes to the meridian and the ((latitude level ,D as it is called. is set horizontal; as the star passes through the field of view its dis tance north or south of the central wire is measured by the micrometer. The instrument is then reversed and so set by turning the tele scope up or down, then the level is again hori zontal. After this reversal and adjustment, the telescope tube is then evidently elevated at ex actly the same angle as before, but on the op posite side of the zenith. As the second star passes through the field, we measure with the micrometer its distance north or south of the centre of the field; the comparison of the two micrometer measures gives the difference of the two zenith distances. The great advantage of the method consists in its dispensing with a graduated circle, and in avoiding almost wholly the errors due to refraction it virtually utilizes the circles' of the fixed observatories by which the star declinations have been measured, without requiring them to be brought into the field. Years ago it was not always easy to find accurate determinations of the declinations of the stars employed, but at present the star cata logues have been so 'extended and improved that the difficulty has practically disappeared, so that this method of determining the latitude is now not only the most convenient and rapid, but is quite as precise as any, if the level is sufficiently sensitive.

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