Since the pole star performs its apparent daily circuit around the celestial pole in 24 sidereal hours, it follows that an interval of 6 hours is required to pass from one of the positions indicated in Fig. 7 to the next. Consequently, it is only at every sixth hour that a simplification in the process of finding the latitude by Polaris is possible. At any intermediate position, the latitude should be determined according to the rule of the preceding article, which may be classified as a less intricate form of reduction to the meridian.

The latitude thus found is, of course, only an approximation (correct, perhaps, only to within 4 or 5 minutes of arc), but at the same time it may serve as a useful check on the latitude by account, especially so, after a continued run in fog and thick weather. The main difficulty in observing the pole star (and, for that matter, any other star) is to measure the altitude, because of the indistinctness of the sea horizon at night and the small size of the star. It requires considerable practice with the sextant before altitudes measured on the sea horizon at night can be considered trustworthy.

38. Additional Method by Polaris.-On the last page of the Nautical Almanac for each year is given a table for computing the latitude approximately from an observed altitude of Polaris at any time (whether the star is on the meridian or not), its hour angle being known to a close approximation. As full instructions accompany the table, they need not be repeated here. However, it is well to remember that the table given in the Nautical Almanac is good only for that year and should not be used in other years without the proper corrections.

39. Present and Future Pole Stars.-The reason for the precaution mentioned in the preceding article is that the pole star is gradually changing its position relatively to the celestial pole, which makes the formation of new values of the table necessary; the annual change of the declination of Polaris is 19" (increasing), and that of its right ascension 25$ (increasing). Our present pole star did not always and will not forever bear the distinction of being the most important

of stars in the northern celestial hemisphere. Owing to the motion of the pole, as described in Nautical Astronomy, Part 1, Polaris will in course of time, about 2095 A. D., approach to within 28' of the north celestial pole, and will then commence to recede from it. Hence, up to that year, the polar distance of the present pole star will decrease gradually until its value is only 28', after which it will increase again. At the time of Hipparchus (156 B. C.) this star was 12°, and in the year 1785 it was 2° 2′, distant from the pole. Two thousand years ago the star & Ursa Minoris was the pole star, and about 2,300 years before the Christian era the star a Draconis was not more than 10' from the celestial pole, while 12,000 years from the present time the brilliant star Vega (a Lyræ) will be within 5° of it. These changes, requiring thousands. of years, are caused by the precession of the equinoxes.

EXAMPLES FOR PRACTICE

1. On October 29, 1899, in longitude 179° 14' E, the observed altitude of Polaris was 19° 25'. Index error 3' 20". Height of eye 23 feet. Greenwich mean time at instant of observation 23h 24m 10s. Required, the latitude. Ans. Lat. 18° 1.6' N

2. On December 9, 1899, at 7h 10m 30s P. M., local mean time, the observed altitude of Polaris was 10° 17' 10". Index error = + 3' 20". Height of eye 26 feet. Longitude 37° W. Find the latitude. Ans. Lat. 8° 58.7' N

=

=

3. On April 27, 1899, at 11h 24m 6s P. M., local mean time, the observed altitude of Polaris taken in an

78° 20' 10". Index error the latitude.

artificial horizon was

4. On March 15, 1900, an altitude of Polaris was measured when exactly on a horizontal line with Alioth; it was found to be 40° 15′ 30′′. Index error 14 feet. Find the latitude. Ans. Lat. 40° 9′ N

- 1' 40". Height of eye

=

40. Compound Altitudes. In the foregoing examples of methods for determining the latitude of an observer, a single altitude of the celestial object observed has uniformly been regarded as the altitude at the time. However, as it is not always possible to measure an altitude with sufficient

precision, it is advisable, where a certain degree of accuracy is required, to take several altitudes, or compound altitudes (usually three or five), in rapid succession-that is, within a minute or two of one another-and to note the corresponding times either on a chronometer or on a watch; the interval between these observations should be as nearly equal as practicable. The mean of the altitudes thus observed is then considered as the correct observed altitude corresponding to the mean of the times.

41. To illustrate this, assume that an observer is about to measure an altitude of a star near the meridian, or ex-meridian altitude, as it is commonly called. An assistant is stationed in the chronometer room and is ready to note the time when the prearranged signal is given (which may consist of either a call or the touching of an electric push button connected with a bell in the chronometer room), the result being as follows:

Since the mean of these altitudes and the corresponding chronometer times are likely to be more accurate than any single observation, the observer now proceeds as if the observed altitude of the star were 24° 19′ 12′′ and the corresponding time by the chronometer, 4" 42m 6.4s.

42. Hack Chronometer.-In measuring a set of altitudes, the chronometer is not always consulted directly, but a good second's watch, or Hack chronometer, is used. The mean of the times by watch corresponding to the mean of the altitudes being found, the watch is then compared with the chronometer and its error on chronometer time ascertained.

This error being allowed for, the time by chronometer corresponding to the mean of the altitudes is obtained; or, the error of the watch may be found by comparing it with the chronometer immediately before the observations are taken. Whether the comparison takes place before or after, it should be within a short interval of the observations, and the observer should never neglect to compare the two timepieces at each observation, no matter how frequently they may occur.

LONGITUDE AND AZIMUTH

DETERMINATION OF LONGITUDE

LONGITUDE BY CHRONOMETER

(Time Sight of the Sun)

1. Explanation. The determination of longitude at sea is a problem of first consequence to the navigator. From statements previously made, it is known that the longitude of any place on the surface of the globe is established as soon as the time at that place and the time at Greenwich at the same instant is determined. The difference between these times, whether mean or apparent, converted into degrees, minutes, and seconds, is the desired longitude, which is west when the time at Greenwich is greater than that at the place, but east if the time at Greenwich is less than the local time. Now, the chronometer, when properly corrected for error and accumulated rate, will furnish the time at Greenwich; hence, the problem of determining longitude is simply a problem of determining the local time at ship. How this is accomplished, by means of observations of celestial bodies, will now be explained.

According to a previous statement, it is known that at any instant

apparent solar time = hour angle of the true sun From this it follows that when the sun's hour angle is found, the local apparent time is at once determined, which, by the application of the equation of time, may be converted Copyrighted by International Textbook Company. Entered at Stationers' Hall, London

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