3. Times of Contact.
These have been calculated according to the method of the American Ephemeris, and are given below both in U. T. and in Local Mean Time.
|U. T.||L. M. T.|
|Eclipse begins||1930 October 21d||19h 38m 07s||07h 55m 35s|
|Totality begins||20h 50m 52s||09h 08m 20s|
|Mid-Eclipse||20h 51m 39s||09h 09m 07s|
|Totality ends||20h 52m 26s||09h 09m 54s|
|Eclipse ends||22h 13m 47s||10h 31m 15s|
In order to deduce the times of beginning and ending of totality at a station whose co-ordinates are λ + Δλ, φ + Δφ where λ and φ are taken positive to West and North respectively, it is necessary first to determine the time of mid-eclipse at the new station from the equation*:—
T = 20h 51m 39s − 1s.196 Δλ − 1s.012 Δφ
where Δλ and Δφ are in minutes of arc, due regard being paid to their signs, and T is the required time expressed in U.T. The next step is to compute the semiduration S in minutes of time as follows:—
Δ = − 0.00138 − 0.000172 Δλ − 0.000176 Δφ
sin ψ = − Δ/0.00561
S = − 0.80796 cos ψ
The two solutions for ψ give two equal and opposite values of S. Then the times of beginning and ending of totality will be given by T + S, the negative value of S being used for the beginning and the positive value for the ending. This method should give times accurate to within a second anywhere on the island.
[Footnote] * The method followed here is that due to Dr. L. J. Comrie, “Some Computational Problems arising in Eclipses,” M.N., R.A.S., vol 87, Nr. 6. April, 1927.
It will be noticed that the duration of totality at the initial station will be 94 seconds, a sufficient time to enable a fairly extensive observing programme to be undertaken.
To convert the times in U.T. to L.M.T., it is merely necessary to subtract 11h 42m 32s.
It is very fortunate that the eclipse will occur at about 9h local time, as this is about the time of best visibility in these parts, and as an average of about 44 hours of sunshine are recorded between 8h and 10h during October at Apia which is in approximately the same latitude and not greatly distant.
Sketch showing position of eclipsed Sun, relative to Mercury and some of the neighbouring stars in the constellation Virgo, 1930, October 21, 20h. 51m. 39s.
Figure 2 shows the position of the eclipsed Sun relative to the planet Mercury (which is near the star θ Virginis) and some of the neighbouring stars in the constellation Virgo. The spot representing the eclipsed Sun is to scale. It may be noted here that the Sun's true semidiameter is 16′ 04.3″ and that the Moon's true semi-diameter is 16′ 10.6″. The stars plotted in the figure comprise all Nautical Almanac stars and all stars listed in Eichelberger's Cataloguo* as well as a few others.
[Footnote] * W. S. Eichelberger, “Positions and Proper Motions of 1504 Standard Stars for the Equinox 1925.0” Astronomical Papers of the American Ephemeris, Vol. 10, Part 1, 1925.