I. An unknown star may be readily identified by means of the Star Identification Tables (H. O. Publication No. 127) when its altitude and azimuth have been observed. In cloudy weather, however, at night, when there is much motion on the ship and particularly when the altitude of the star is high, it is not convenient to obtain a compass bearing of the star.
For the purpose of star identification the azimuth may be obtained, without the use of the compass, from two observed altitudes as shown below.
From formula 285 of Chauvenet's Trigonometry (10th edition), we have
Rm may be found from the difference between two altitudes, observed in quick succession, expressed in minutes and decimals, divided by the interval between the observations in minutes and decimals of time. To be exact, unless the ship be on a course at right angles to the bearing of the body, the rate of change of altitude in one minute, Rm, found by observation must be corrected for the run of the ship; that is, if K minutes is the speed of the ship per hour, then K seconds is the speed per minute and the correction = K" cos (C~Z), where C = course and Z = azimuth of the body, which is found by using the observed rate of change per minute and Plate 1. Enter the Traverse Tables with K" as a distance and (C~Z) as a course, then the correction is found as a difference of latitude, to be subtracted from the observed change of altitude per minute when the ship is moving towards the body, and to be added when moving away from the body; in other words, when (C~Z) is less than 90°, subtract; when (C~Z) is greater than 90°, enter with the supplement of (C~Z) and add the correction. The above rules apply when the body is rising; when falling, add when approaching, and subtract when separating. As a rule, this correction is not necessary for finding the approximate azimuth for the identification of stars, except in very fast ships whose courses are nearly towards or away from the observed body.
After finding Rm find the azimuth from Plate 1 by taking Rm on a vertical scale, the intersection of the horizontal line through this point with the curve corresponding to the latitude of the ship fixes a vertical line which determines the azimuth at the bottom or top of the diagram, depending upon the compass quadrant in which the body lies, and this should be noted roughly at the time the altitudes are observed. The enlarged part of Plate 1 is for altitudes near the meridian.
2. To find the hour angle of the star from Table 1:
Table 1 was computed with a view to having a compact Time-Azimuth Table for all latitudes and declinations and for finding the great circle courses when the distance is not known, as well as for finding the hour angle in star identification ; in other words, it was designed to solve the following equations :
Here we are concerned with formulas (9) and (10) only, and the altitude, h, is always given the same name as the latitude, L.
To find the hour angle, given the true altitude and azimuth of the star, from the elevated pole, and the latitude of the observer.
Enter Table 1 with ½Z in column A, and opposite ½Z and under ½(L~h in the headline AB take out log X; under 90°—½(L~h) in the headline AB find this log X, and take out the angle X opposite in column B.
Opposite ½Z in column A and under 90° — ½(L — h) in the headline AB take out log Y; under ½(L + h) in headline AB find log Y and the corresponding angle, Y, opposite in column B.
Then, when L>h we have, t =X+ Y, and when L<h we have, t = X-Y.
Hour Angle from Azimuth Tables
3. As Table 1 contains about 36 pages it is too long to reproduce here, nor is it necessary for the purposes of this paper, as the Azimuth Tables may also be used for finding the hour angle of a star when its altitude and azimuth are given when the Star Identification Tables are not available. Table 1 is shown in skeleton form to indicate its use.
To find the hour angle:
Enter the Azimuth Tables in the latitude of the ship with the azimuth as an hour angle and the altitude as a declination; the corresponding azimuth is the hour angle of the star.
In order to find the hour angle from the Azimuth Tables it is necessary to first determine the name of the declination, which may be readily done from Table II, for which the writer is indebted to Commander H. L. Rice, Professor of Mathematics, U. S. Navy.
through a rift in the clouds, bearing to the S'd and E'd, altitude cor.—9'; G. S. T. of 2d observation 8h12mI7s.
As the ship was rolling heavily at the time no accurate bearing could be taken. What star was observed?
the hour angle column, and in the 26° declination column we find 58°04'= 3h52m18s for the hour angle of the star.
Example 2.—At sea, February 26, 1901, 6.30 p. m., L. M. T., weather overcast and cloudy; the altitude of an unknown star of about the 2d magnitude, seen through a break in the clouds, was 29°30' (true) , bearing N. 74° W. Lat. by D. R. 35° N., Long. 60° W. What was the name of the star?
that the hour angle, 7h22m=110°30', is not given, so we enter with the supplement of this hour angle, 4h38m and the supplement of the corresponding azimuth, 115°30', or 64°30' = 4h18m, is the hour angle required.
The right ascension and declination here found correspond to a Leonis (Regulus).
After finding the hour angle and declination enter the Azimuth Tables with these to see whether the azimuth so found agrees with that given, thus verifying the work.
5. When the star is on or very near the meridian, so that its hour angle is practically o, the star's right ascension may be assumed equal to the local sidereal time and its declination may be readily found by applying its zenith distance to the latitude by dead reckoning. •
6. The writer has found Plate II very convenient for finding the altitude at which to set the sextant in order to pick up a particular star in the early evening twilight, or to find Venus or Jupiter by day.
From the local apparent time, at which it is desired take the observation, find the local sidereal time, to which apply the star's right ascension to obtain its hour angle and take its azimuth from the tables.
Enter Plate II with the hour angle on the margin; the intersection of the horizontal line through this point with the declination curve of the body fixes a vertical line, the intersection of which with the horizontal line through the given azimuth determines the altitude curve of the star.
Example 4.—In the early evening twilight, at sea, February 26, 1901, Lat. 35° N., Long. 60° W., what was the altitude of a Andromedæ at 6.30 p. m., L. M. T., when the star's hour angle was 4h49m12s and its azimuth N. 74° W.? Star's declination 28°30' N.
From Plate II the altitude was 29°30'. Set the sextant to this altitude and at the proper time by watch sweep the horizon over the pelorus set at N. 74° W. Thus the reflected image of the star may be easily seen on the horizon long before the eye can catch the direct image in the sky.