The fleet cruise in Hawaiian waters in May-June gave an opportunity for an unusual astronomical sight. In preparing for a daylight meridian altitude of Venus about 1500 zone time on June 2, it was noted that the declination and latitude were very nearly the same. Under these conditions the azimuth will change from east through south (or north) to west in a few minutes. The assistant navigator, Ensign F. L. Ashworth, suggested the procedure which is given below, with the end in view of obtaining a fix from the single body in a few minutes.
In Dutton the high-altitude method which employs an arc instead of a line is explained. Briefly, the position of the point on the earth which has the body in its zenith is plotted by using the declination of the body as latitude and the Greenwich hour angle as longitude. Then a circle with this point as the center and the zenith distance as the radius is the circle of equal altitudes or position circle corresponding to the line of position in the every-day sight. Two such circles with a good change in azimuth should intersect and give the ship’s position and, since the azimuth changes rapidly, the run between circles does not affect greatly the accuracy of the position circle. However, the position circles are run to a single time by applying the distances run in the usual way. The sights chosen were: (1) a few minutes before transit, (2) at transit, and (3) a few minutes after transit. The third circle is merely a check on the other two. It is not necessary.
Note that the declination does not change appreciably during the short time involved. Point 1 is to the eastward because the Greenwich hour angle, which is the longitude of the point, is smaller than the Greenwich hour angle of the later sights. Circles 1 and 3 are run up and back, respectively, to the circle at meridian transit. This is shown on the plot. The work and the plot follow.
This method was used with the sun in the same way and fix obtained at transit.
Circle (1) Circle (2) Circle (3)
G.C.T. June 3 01-11-17 01-15-12 01-18-13
*G.H.A. 151°-07.8 152°-03.9 152°-51.7= Long. of center
*Dec 23-33 N 23-33 N 23-33 N = Lat. of center
*ho 89°-04.5 89°-35 89°-08.5
*Zenith Dist. 55.5 25.0 52.5= Radius