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The Total Solar Eclipse of 21–22 October 1930.
[Read before the Wellington Philosophical Society, 25th September, 1929; received by the Editor, 1st October, 1929; issued separately, 30th November, 1929.]
1. Summary.
The times of the various contacts, the position angles and Sun's altitude are established for the position 175° 38′ West Longitude, 15° 34′ South Latitude on the island of Niuafou, and differential corrections are established for the determination of these times for stations within a few minutes of longitude and latitude of the initially selected station. Data are also given for a moving plate carrier for use with a fixed telescope at the initial station, and differential corrections are established for the adaption of these data to stations in the vicinity of the initial one.
2. The Initial Station.
The suitability of Niuafou Island as an observing station for the eclipse has been discussed by Mr. Andrew Thomson* (Director, Apia Observatory), who showed that, of the two land areas in the track of totality, this one will be unquestionably the most advantageous since it is closer to the central line and also since the Sun's altitude will be greater there at mid-eclipse than at Nurakita, the other island in the track of totality. The accompanying map has been prepared from Admiralty Chart No. 987—for a tracing of which I am indebted to Dr. Adams—and shows the central line of the eclipse passing about 5.1 geographical miles from the selected initial station which is a point on the hill Piu-ofa-hefa of altitude 557 feet. The co-ordinates of this point are those given above and were determined in 1895 by Lieut. B. T. Somerville of H.M. Surveying Ship “Penguin.”
The island is purely a volcanic one, and serious activity has been recorded on five occasions since 1853. The activity in 1853 resulted in the loss of many lives and the destruction of a village, but the author does not know the location of the outburst. In 1867 serious activity took place in the south of the island. There was another violent eruption in 1886 when Falcon Island was also elevated 50 feet. Another eruption took place in 1912 when lava flowed near the coastal village of Futu. Finally, the eruption of July 1929, which destroyed the village of Futu, was very unfortunate since it destroyed the best landing place on the island, the only one sheltered from the prevailing winds which blow from East or South-East for 65 per cent. of the period from September to November. However, arrangements for an observing expedition should not be dropped or
[Footnote] * Andrew Thomson, “Report on Niuafou Island as Station for Solar Eclipse Observation,” Popular Astronomy, vol. 36, Nr. 8, 1928.
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discountenanced on this account, as the landing place will probably be reconstructed before the eclipse, or if not, there is still another landing place at Anagaha in the north, and another on the east though they are not so easily accessible as Futu.
It may be noted here that the discrepancy between the longitude given at the beginning of Mr. Thomson's paper and that given on the map accompanying it is due to the fact that the first mentioned longitude was scaled from a general map of the Pacific, while the map was added after the paper was in the press. Comparison of Mr. Thomson's map with the Admiralty Chart reproduced here reveals a number of minor discrepancies; but Mr. Thomson had to rely on a map supplied to him, and did not have access to the Chart.
The calculations for Mr. Thomson's paper were performed by Mr. C. J. Westland, F.R.A.S., before the arrival of the 1930 Nautical Almanac, and were for the position 175° 41′ West Longitude, 15° 35′ South Latitude, and the discrepancies between his results and those set forth in this paper are attributable to these two factors.
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.
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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.
Figure 2.
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.
4. Sun's Altitude: Position Angles.
The following table gives the position angles from the north point and from the vertex together with the altitude of the Sun's centre for the second and third contacts at the initial station.
[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.
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[The section below cannot be correctly rendered as it contains complex formatting. See the image of the page for a more accurate rendering.]
| Position from North. | Angle from Vertex. | Altitude of Sun's Centre. | |
|---|---|---|---|
| 2nd Contact | 147° | 248° | 51° 39′ 48″ |
| Mid-Eclipse | — | — | 51° 51′ 05″ |
| 3rd Contact | 299° | 40° | 52° 02′ 24″ |
The Sun's altitude for the first and fourth contacts will be approximately 34° and 71° respectively. It will be noticed that the position of the sun at mid-eclipse is excellent for observing purposes. The above altitudes are not corrected for refraction.
5. Moving Plate Photography.
In order to photograph the eclipsed Sun, a fixed telescope directed to the Sun's centre at mid-eclipse may be used in conjunction with a moving plate.* Following are the numerical data required for the erection of such an instrument at the initial station.
| Z = zenith distance of Sun's centre corrected for refraction and parallax | 38° 08′ 15″ |
| A = Sun's azimuth (from North to East) | 87° 30′ 41″ |
| B = azimuth of track carrier in direction in which it rises | 282° 08′ 46″ |
| T = inclination of track carrier to horizon | 37° 13′ 24″ |
| P = angle between track carrier and photographic plate | 8° 58′ 34″ |
| h = Sun's hour angle | —38° 54′ 06″ |
| δ = Sun's geocentric declination | —10° 40′ 23″ |
| Δδ = variation in δ per hour | —53.5″ |
| q = Sun's parallactic angle | 258° 20′ 12″ |
| z = uncorrccted z.d. of Sun's centre | 38° 08′ 55″ |
| k = coefficient of refraction | 58.2″ |
| Q = angle made by direction of Sun's motion with the horizon | 258° 23′ 39″ |
For a small change Δλ, Δφ in longitude and latitude, the following differential corrections may be applied to the above values of Z, A and Q.
Δ Z = 1.2502 Δλ + 2.3915 Δφ
Δ A = 0.4178 Δλ + 1.3533 Δφ
Δ Q = 0.0245 Δλ + 1.6222 Δφ
The new values of P, T and B may then be obtained from tan P = cos Q tan Z, sin T = sin Q sin Z, cot (B-A) = tan Q cos Z where P and T are always in the first quadrant and that one of the two values of B is chosen so that the moving carriage descends when the Sun is East and ascends when it is West of the meridian.
The rate of the moving carriage may be determined by substituting for f, the focal length of the lens, in
R = 0.004289f,
[Footnote] * See L. J. Comrie, loc. cit. for further details and references.
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the result being the rate per minute in the same unit as f. This will not be affected by small changes in λ and φ.
The error due to the use of a straight track and a uniform rate, at the end of an exposure of t minutes, will be E = 0.03634 t2.
6. Conclusion.
These computations have been performed primarily in the hope that they be of use in an attempt to organise an observing expedition from New Zealand. They certainly show that the situation of the sun is good for observing purposes at the time of totality, and that the duration of totality is sufficient to permit of a fairly extensive observing programme. From the meteorological standpoint, the eclipse will take place at the best possible time of the day for there to be the most attractive prospects of good weather, clear sky and excellent visibility. In fact the eclipse seems to be especially favoured except in the number, location and distribution of possible observing stations, and the author hopes that some encouragement will be given to the proposal to organize an observing expedition from this country especially as it is now understood that no official expedition will be going from England.
It is with pleasure that the author records his indebtedness to Dr. C. E. Adams, Dominion Astronomer, whose independent calculations have been such a reliable and valuable check on those, the results of which are set forth in this paper.
Christchurch,
1929, September 7.
Note Added in the Press.
At the request of the Dominion Astronomer, an investigation for an eclipse observing site on Niuafou was made by the Commander of H.M.S. “Veronica” who selected a position on a spur some 40 feet above sea level and close to Anagaha. The Commander gives the coordinates of this site as West Longitude 175° 37′ 54″, South Latitude 15° 32′ 04″, which position, according to Admiralty Chart No. 987 on which the author based his computations, would be out at sea.
For this position, the times of the phases are:—
| Totality begins | 1930 October 21d | 20h 50m 49s U.T. |
| Mid-Eclipse | 20h 51m 36s U.T. | |
| Totality ends | 20h 52m 24s U.T. |
The duration of totality is thus 95 seconds. The position is 3.7 geographical miles from the central line; that is 1.4 geographical miles closer than the point for which the computations were originally made.
The results of the investigations by the Commander of H.M.S. “Veronica” were not available until after the paper had gone to press.
P.W.G.
1929, October 24.