The photographic determination of the height and position of aurorae observed in New Zealand during 1937

Geddes, M. (Murray), Govt. Printer, Wellington, N.Z., 1939

DEPARTMENT OF SCIENTIFIC AND INDUSTRIAL RESEARCH.

RADIO RESKARCH PUBLICATION No. 3.

DOMINION OBSERVATORY BULLETIN No. 141.

The Photographic Determination of the Height and Position of Auroræ observed in New Zealand during 1937.

BY M. GEDDES.

Extracted from the New Zealand Journal of Science and Technology , Vol. XX,

No. (>b, pp. 289b-305b, 1939.

WELLINGTON, N.Z.

E. V. Paul, Gov I'kinter.

*939-

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The original publication details are as follows:

Title: The photographic determination of the height and position of aurorae observed in New Zealand during 1937

Author: Geddes, M. (Murray)

Published: Govt. Printer, Wellington, N.Z., 1939

289 b

THE PHOTOGRAPHIC DETERMINATION OF THE HEIGHT AND POSITION OF AURORÆ OBSERVED IN NEW ZEALAND DURING 1937.

Bv M. Geddes.

Summary.

The photographic work on fifteen aurora is reviewed, and selected plates measured according to the method developed by Stormer. Duplicate pictures secured over three different base-lines in Southland yield determinations of the height of four displays, the results for the various forms being in good agreement with those secured in Norway. Single pictures have also been measured for the determination of geographical position. An investigation is made of sunlit forms occurring at various stages of the different displays.

The positions of aurora; observed, n New Zealand before 1937 have already been discussed(l). This paper deals with the photographs taken for height and position measurements during 1937. A discussion of the height of one other display, 1936 November 11, is also included.

A base-line for height determinations was established in 193b October, and the first duplicate pictures obtained about a month later, on November 11. Including this aurora, duplicate pictures were secured of five displays, and single pictures, from one station or the other, of another nine displays. It is the successful pictures from these fourteen aurora (total of 507 photographs) that are reviewed here. The cameras used were supplied from Norway through Professor C. Stormer, and are similar to those employed in that country(3). By means of a sliding lens six pictures are taken on each 9 cm. by 12 em. plate. The plates used were Agfa Isochrome (H. and D. 4,400), although more recently these have been replaced by Agfa Isopan, with greatly improved results. Communication over the base-line was carried out by telephone—a very unsatisfactory arrangement, as no extensions were available and instructions had to be given to the secondary station some minutes before

Inset—Photographic Determination.

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the pictures were tak ' prevented shorl work and made it quite impossible to follow any rapid changes in the aurora. A further disadvantage was the closing of the telephone exchange at midnight on week nights and at 8 p.m. on Sundays : this was one of the chief reasons for the failure to secure duplicate photographs of some aurora?. However, since the period under discussion, wireless transmitters have been installed and much of the difficulty overcome.

The photographic work has been financed by the Department of Scientific and Industrial Research through the Dominion Observatory.

The cameras have been in charge of 1). ('. Berry and the writer. Table I shows the positions of the various stations, determined from data supplied by the Lands and Survey Department.

Table I. —Positions of Stations.

The co-ordinates of the three base-lines used have been determined from the following formula?, in which—

latitudes of main and secondary stations.

longitudes of main and secondary stations.

heights of main and secondary stations.

d = 2R = diameter of the earth = 12,758 km.

declination and hour angle of positive base-pole— i.e.,

point at which base-line, as seen from main station, cuts the celestial sphere.

For R we use

where M and N are the radii of curvature on the meridian and prime vertical respectively.

(4) Base-line = g = d.q.

Geddes. —Photographic Determination of Aurorae in New Zealand.

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1939.]

Table II gives the co-ordinates of the base-lines determined in this manner

Table II. —Co-ordinates of Base-lines.

The Measurement of the Photographs.

The method used is the same in principle as that described on numerous occasions by Stormer and others(s, 7, 8). Stormer has, however, very kindly

Fig. 1.

supplied the writer with a modified method developed by N. Herlofson and so far not published.* Consider Fig. 1, in which z is the zenith, P the celestial pole, A the position of the main station, and B the positive base-pole. AO is perpendicular to AB.

* Since the above was written a full discussion of the method has been published by Stormer in “ Some Results regarding Height and Spectra of Aurorae over Southern Norway during 1936 Geofysiske Puhlikasjoner XII, 7 Oslo, 1938.

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Then, if S is any star, a system of co-ordinates may be found in which its position is fully determined by the arc TS and the angle PBT, referred to respectively as c and I. It is these co-ordinates which are used. In addition, we require the altitude and azimuth, /; and a.

The transference from one system of co-ordinates to the others may be carried out by means of the formulae given in the publications already referred to*, but it is done much more easily by graphical methods. The spherical triangles are solved by using Becker’s We determine first hj and a from 8, t and the co-latitude, and then e, £ from 8, t—t , and 90°—S 0 .

In the actual measurement the negatives are projected by means of a lantern on to a sheet of paper, the projected image being on the scale of I°=l cm. at the centre of the picture. The lantern used has been supplied by the New Zealand Radio Research Committee. The correct scale is determined by measuring the angular distance of a pair of stars determined by the following formulae, where, if Sj and S 2 are the two stars,

difference in hour angle between S x and S 2 .

declinations of Si and S 2 .

Bj and B, = angles measured in the positive direction between and PS X and between and PS 2 , P being the pole.

angular distance between the two stars.

Table 111 gives a for the stars used in this studv :

Table lll.—Angular Distances of Stars.

* It should be noted thate = 90° u and £ = o> H a constant where u and cu are the co-ordinates used in the publications.

t Set' reference No. 4. The diagram is obtainable from the author. The Observatory, Dowanhill, Glasgow, W. 2. Scotland.

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Oeddes.—Photographic Determination of Aurob.e i\ New Zealand.

The outlines of the aurora are sketched in on the enlarged image er with some of the surrounding stars. At least two, and preferably three, stars must be shown on each drawing.

Using the methods already described, the co-ordinates (hj, a) and (*, £) are computed for the reference stars, and the subsequent measuring work done by means of “ nets.” A full description of these and their construction has been given by Harang and Tonsberg(s). Briefly they are diagrams giving, on a scale of 1° = 1 cm., polar co-ordinates with reference to any pole. Thus, using the ( h j, a) values for the reference stars, we may set the drawing on the correct “ net ” and read off {h, a) for any point; then, using the (e, £) values of the reference stars, we may reset it and read off (e, £) for the same points. This work requires to be done on a “ light ” table, the one used having been supplied by the New Zealand Radio Research Committee. All readings are made correct to o°*l.

The shift in any point of the aurora must take place in the plane containing the base-line and the auroral point. Hence on the two drawings from the main and secondary stations (referred to as the A and B drawings) £' for any given value remains constant. Therefore, if e and £ are determined for a point on the A drawing, the corresponding point on the B drawing is the point which has the same value of £. The system of measurement thus recognizes corresponding points automatically.

If (cj, I) and (e.,, £) are corresponding points on the A and B gs, then the parallax, //, is given by f i - e 2 .

. if

r = distance of the auroral point from the main station,

D = projection of r on the surface of the earth,

II = height of the auroral point,

we hi

and, where hj is the altitnde of the auroral point, we have the following approximate formula' for 11 and D :

■where

x = r cos hj

y = r sin hj.

In the present study h lt the height been sufficiently small to be neglected. Wl Dumber of cases are being dealt with, itli and graphii : I rsed instead. If a section ol is drawn on a scale of 1 : 1,000,000 (I rum. - I km.), then, knowing /' and r (the altitude and distance of the a ] point), roral |>oint and obtain 11 and D by irement.

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In the case of single pictures, where only the geographical position of the aurora is to be determined, the plates are treated similarly, except that it is not necessary to determine (c, £), (A, a) being sufficient. The height is then assumed, and the position determined according to the method described in a previous paper(l).

Efficiency of Base-lines.

It can be shown that the largest parallax is obtained at a point 90° from the positive base pole— i.e., where e= 0. Hence a measure of the efficiency of the base-line may be obtained by an inspection of the e values for the points measured. The average value of c 2 for the E-Ia base is 2°-5 and for the others 58°-0. Hence the advantage of the greater length of the H-Ia and H-Ib base-lines is negligible when compared with the disadvantage of the unfavourable direction. Despite this, however, the B-Ia base has proved almost useless for the measurement of arcs, as their normal direction is nearly parallel to the base. In the case of auroral forms of high altitude none of these restrictions apply. None of the base-lines used are long enough, as they yield only small parallaxes. For work in Southland it seems that the best base would be one of about 60 km. with a base pole having an azimuth of about 210°.

The Aukorj;.

Table IV shows the displays photographed, the stations in operation, and the number of duplicate and single pictures which were successful. Where only single pictures were secured one station was usually out of operation on account of clouds or the closing of the telephone exchange. No measures have been made of the plates secured on April 28, 29, June 6, October 4, 10, 24, as the presence of clouds prevents accurate measurement.

Table IV. —Aurora photographed.

All the duplicate pictures used have been drawn and measured twice, sonic three times, and a few four times, in order to remove as many inaccuracies as possible.

Geddes.—Photoobaphic Determination or Ai ix New Zealand.

1939.]

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295 V; November 11 (Base E-la. Nos. 20 27). -This was mainly a faint glow which emitted a burst of rays a 1 11 hj. 40m. 6.M.T. The exposures were made on these rays. A misunderstanding between the, two cameras resulted in only two pictures being synchronized, Xos. 20 and 23. One ray lias been measured on each plate. The large heights are to be expected as the main an' was below the horizon.

1937—March 5 (Base E-la. Nos. 28-75).—This was mainly a normal RA display.* Plate-holders, believed to be light proof and not so, resulted in the fogging of most of the duplicate sets taken. The one set measured is considered below under sunlit aurora;. No. 37 has been measured to determine the position of the arc.

1937 — March 1~) (Base E-la. Nos. 76-145). -This was a fine aurora of the normal type, developing along the usual lines :

Most of the duplicate pictures were taken during the first HA staple, when the lower border of the arc was very diffuse and quite immeasurable with such a small parallax. Fortunately, however, a vertical break persisted in the arc for some time, and this, together with a few feeble rays, gave definite points to measure. The break, which commenced about 10h. Kim. 6.M.T., represented a fold in the arc, and this gradually widened. The existence of this fold accounts for part of the variation in the measures of the arc ; the other factor to be considered is the general fluctuation of the whole display. In the case of No. 91 a temporary sharpening of the lower border of the arc permitted its measurement. Using the height determinations as a guide, a number of single pictures have been measured to determine the position of the arc at various stages.

1937 March 31 (Base 111 a. Nos. 146-176).—This was in full development at dusk as a com] ilex drapery formation, but it declined rapidly to a glow. All the photographs were taken during the period of decline, when the type was mainly HA with a few spasmodic rays and diffuse patches. : moonlight made the photography of these rather faint forms difficult, and, as a result, it is not easy to find points to measure on the nee;

1937—August 4 (Station H. Nos. 189-195).—Clouds at Invei ated duplicate work on this display —a mild RA. By assuming the height, the geographical position of the are has been determined from two pictures.

1937—October 1 (Base H-Ib. Nos. 196-251).—The maximum of this display hail already been reached by dark, when it a a complex ry formation which declined rapidly to a low, faint HA. This . for four hours, until the sky became too cloudy for observation. The duplicate pictures were all taken during the hour, and, unfortunat of them can he me: at no time was the lower border of t ; i from cloud at the two stations simultaneously. 'I position has been determined from single ial manner.

October 9 (Station H. N 3).- Tins display commenced midnight when the telephom exchange had closed, so that no duplicate work could be undertaken. It was of til'' normal t ■ night

I planation of the I (1) and (3).

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with repetitions of the HA— s■ RA—>- D—f DS—)- HA sequence. Selected single pictures have been measured to determine the geographical position. Sunlit forms are considered below.

1937—October 23 (Station H. Nos. 319-418).—This was a normal HA. The geographical position has been determined in the usual manner.

1937—November 28 (Station H. Nos. 428-469).—The early Sundaynight closing of the telephone exchange prevented duplicate work. The aurora was of the normal type varying from HA to D, but was accompanied in the early stages by sunlit rays. Two pictures have been measured to determine the geographical position of the arc.

Table V shows the results of the measurement of the duplicate pictures. The position of each point is determined by H and D, and by the azimuth a, which is measured from 0° to 360° from north through west. The parallax, p, has been included as it gives some idea of the accuracy of the result. The measurements obtained from the single pictures are given in Table VI. Here the value of H is assumed either from a general study of the evolution of the display or from the results of duplicate measures at other stages of the same display. It will be noticed that a few pictures appear in both tables. In each case an indication of the form measured is given in the remarks column.

Table V.—Measures of Duplicate Pictures,

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Table V. —Measures of Duplicate Pictures— continued.

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Table Vl.—Measures of Single Pictures.

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Table Vl. —Measures of Single Pictures — continued.

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Table Vl. —Measures of Single Pictures — continued.

Geogra cal Position.

Using the values of D and (/ it is a simple i plot on a suitable map the position of the auroral point as projected on the surface of the earth. In the present study maps have been prepared using the equidi zenithal projection. A discussion of the methods of preparing such maps will be found in any text-book on surveying. For the centre of projection the point

has been adopted. This should give an error of less than 1 per cent, in the plotting of the auroral points.

Fig. 2 shows the position of the points determined in Table V. and Fig. 3 the points determined in Table VI. In the case of Fig. 3 it has proved impossible, owing to overcrowding, to show all the points given in the table. As a result, the map has been restricted to displays not al dealt with in Table V and to the sunlit forms discussed below.

It will be seen that in general the New Zealand aurora occur in the vicinity of the Auckland and Campbell Islands, as had been found preThe general direction of the arcs, where folds do not cause complications, is in close agreemen! for the various displays. This din is probably normal to the direction of the lines of magnetic force, but this cannot be verified. The only data available on the magnetic elements in this region arc contained in the report of the Magnetic Survey of NewZealand (epoch 1903)(12). The information given there is far too scanty.

Geodes.—Photographic Determination of Auror.e in New Zealand.

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and probably too much out of date to justify an effort to plot the lines of magnetic force with a view to comparing them with the position of the various auroral forms. It is for this reason, also, that it has not been possible to make a close study of the auroral rays in the manner suggested by St6rmer(6).

Sunlit Aurora.

It frequently happens, when auroral activity is fairly intense, just after dark or just before dawn, that some portion of the display lies in the sunlit atmosphere. Various cases of this have been investigated in the Northern Hemisphere(9, 10, 11). but the type had not been recorded in New Zealand before 1937. During that year the following displays showed undoubted sunlit forms: Marchs,ls; April2B; October 1,9; November2B. No photographs were secured of the type on March 15 and April 28, but on the other occasions successful exposures were made.

In every case the sunlit forms consisted of rays which had a most typical appearance. Low down near the arc they were normal in appearance, but at the boundary of the dark and sunlit atmospheres they underwent a sudden dimming, only to reappear higher up, quite bright, and changed in colour from green or white to dull red. Such rays have been shown in Norway to reach very great heights, and it is hoped to make a very thorough study of them in New Zealand in the future.

In order to study such forms it is necessary to investigate the position of the shadow-line. We determine first the geographical co-ordinates ((f>, A) of the foot-point, S — i.e., the projection of the auroral point on the surface of the earth. The altitude, h lt of the centre of the sun above this point is then found by

where (8, t) are the declination and hour angle of the centre of the sun If desired, h lt which is negative, may be corrected for refraction. The height, Hj, of the shadow-line, above the point S, is given by

A comparison of H 1; the height of the shadow-Une, and H, the height of the aurora, determines whether or not the form is sunlit. If a large number of cases are being considered the investigation is best done by graphical methods in conjunction with Lugeon's tables(l3).

The fact that the auroral ray changes in brightness as it crosses the shadow-line makes it possible to determine the height of this point fairly accurately in cases where only single pictures are available. The point can then be plotted on a map and the direction of the ray drawn through it. The height and position of other points on the ray may then be found by determining their azimuths and finding the point where these azimuths cut the line of the ray. In the absence of definite information on the direction of the lines of magnetic force, the exact direction of the ray is somewhat doubtful, but in the cases considered below it has been determined indirectly, either from duplicate measures of other rays in the vicinity or from a study of the direction and position of the arc from which the ray has developed. Sunlit forms have been investigated, cither in this way or from duplicate pictures, in the following cases :

1937—March 5 The early Btages of this display were characterized by numerous bursts of rays which showed undoubted sunlit forms. Fortunately, the only measurable duplicate set of pictures secured depicted

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some of thi md one of them has ared. In the case of the other pictures there proved to be too much doubt about the exact geographical position for the height of the earth's shadow to be determined.

1937—October 1. —Numerous sunlit rays again characterized the early stages of this display, although, unfortunately, only single pictures of them were secured. Three of these have been measured, as it has proved possible to determine with sufficient accuracy the geographical position of the aurora and, thus, the situation of the shadow-line.

1937—October 9.—A brilliant burst of sunlit rays occurred shortly before dawn at about 15 hj. 38 m. Gr.M.T. Among others, two excellent pictures were secured of a bundle of rays which can be traced to an altitude of 42°, and these have been measured. The .summit of the rays proved to be the highest so far determined —633 km.

1937 — November 28. —The early stages after dark were characterized by rather hazy rays which appeared to be sunlit in the upper regions. Unfortunately, it has proved impossible to determine accurately the division between the sunlit and shadow portion of the rays, as the fade and rebrightening is too gradual. The shadow-line in this region was at a height of 530 km.

Table VII gives the results of the measures of the sunlit forms discussed above. The various columns are the same as for the previous tables, with the addition of Hj, the height of the shadow-line.

Table Vll. —Sunlit Aurora Rays.

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Geddes.—Photographic Dktekmination of Auroim: in New Zealand

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Projection: Equidistant Zenithal Fig. 2.

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Projection: Equidistant Zenithal Fio. 3.

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Geddes. —Photographic Determination or- Aurora in New Zealand.

In the case of No. 370 the highest point measured is not the summit of the ray as it is not shewn on the plate. No. 372 really records the upper portions of the same handle of rays some minutes later. It is interesting to note from this that these rays during the interval of eight minutes travelled approximately 150 km. towards the west.

The sunlit rays recorded above have, with the exception of No. 10. been included in Fig. 3. No. 40 appears with the other duplicate measures in Pig. '2.

Acknowledgments.

The writer would like to express his appreciation of the great amount of time which litis been devoted by 1). ('. Berry to the operation of the ra tit the InvercargiU stations. In stressing the value of his work it is sufficient to point out that without his assistance no duplicate pictures could have been secured, while the total of single pictures would have been very much smaller.

Grateful acknowledgment i.s also made of the valuable advice and assistance of Professor Stormcr in practically ever}' department of the work, and of the assistance given by the Dominion Observatory, the Department of Scientific and Industrial Research, and the New Zealand Radio Research Committee. The writer desires further to thank Dr. Becker for copies of the charts which have proved so valuable in reducing the labour of the measuring-work.

References.

(1) M. Geddes (1937) : “ Position of New Zealand Aurorae.” N.Z. Journ. of Set. rfr

Tech., 19, 1.

(2) “ Photographic Atlas of Auroral Forms.” International Geodetic and Geophysical

Union, Oslo, 1930.

(3) “ Supplements to the Photographic Atlas of Auroral Forms I.” Ibid., Oslo, 1932.

(4) L. Becker (1930): “ Graphical Solution of a Spherical Triangle.” M.N.R.A.S.,

91, 2,

(5) Habano and Tonsberg (1932): “Investigations of Aurora Borealis at Nordlys

Observatoriet, Tromso 1929-30.” Geofysiske Publikasjoner, 9, 5.

(6) Stobmbb (1926): " Resultats dea Mesures Photogrammetriques dcf

Boreales Ob la Norvege Meridionale de lull a li*J2." Ibid., I. 7.

(1921): " Rapport sur une Expedition D'Aurores Boreales a Bossekop et

Store rlorsnes pendant le printemps de I'Annee 1913." Ibid., 1921.

- (1933): "Height and Velocity of Luminous Night Clouds observed in

Norway 1932."

(1929): '"'ria- Distribution in Space of the Sunlit Aurora Rays." Xature.

January 19, 1929.

(10) (1929): “ New Evidence of the Action of Sunlight on Aurora Rays.” Ibid.

June 8, 1929.

(1937): " Divided Aurora Hays with one Pari in the Sunlil and ai

in the Hark Atmosphere." Ibid., 140, 1096.

(12) COLEBIDOE Finn (1916): "A Magnetic Survey of New /calami and Some of (la-

Outlying Islands." Wellington.

13) J. LrcKON (1934) " Tables Crepusculaires." Warsaw.

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