Sunspots from the past

  John Flamsteed (1646–1719) was an English astronomer and the first Astronomer Royal, and Edmond Halley (1656–1741) also was an English astronomer, mathematician and physicist.

   4 – 15 August 1676

  Sunspot observations made by John Flamsteed in August 1676 (Gregorian calendar; the original dates correspond to the Julian calendar) were published in Flamsteedius (1725) as a table of detailed measurements obtained using a micrometer. However, this table contains several misprints. A shortened version of Flamsteed's measurements, along with those by Edmond Halley in Oxford, was included in Flamsteed and Halley (1676) and accompanied by the engraving. Additionally, Flamsteed’s measurements on 6 August 1676 with a sunspot sketch are included in a letter to Jonas Moore (Flamsteed, 1676). The transcription of this text can be found in Carrasco and Vaquero (2016). Flamsteed (1676) described the spot as significantly large, appearing slightly divided in the middle, with two thin, cloudy spots following it. Although, the sunspot was understood to refer to its umbra, the linear dimensions provided for the large sunspot correspond its penumbra (highlighted by a yellow rectangle; the original image is located at the bottom left of Figure 1). This sunspot group was also reported by Hook, Picard, and Cassini.

  Flamsteed used an alt-azimuth mount for his eight-foot telescope, which was occasionally shaken by the wind. He took the measurements over periods ranging from a few minutes to an hour, introducing uncertainty into the mapping of sunspot. An example of this is shown in Figure 1. During the observation, which lasted from 9:51 to 10:04, the change in the Equator’s position is represented in different colors. The reversed and flipped reproduction of the sunspot group and the Ecliptic from Flamsteed's original sketch (Flamsteed, 1676) is shown in green, while the measurements are depicted in black. Additionally, we have overlaid the sunspot group from the engraving (Flamsteed and Halley, 1676) in black. To reconcile all the measurements, the Ecliptic from the sketch was used. Relying on the measured Ecliptic, the sunspot group is placed 1.5^o farther from the Equator, which is inconsistent with other measurements. These cumulative uncertainties affect the final determination of the sunspot's position.

  Figure 2(a) reproduces the original engraving (Flamsteed and Halley, 1676) with an imposed heliographic grid. Corrections were made for the asymmetry of the solar disk caused by uneven sizes of vertical and horizontal diameters, which differed by up to 6%. On 6 August 1676, the penumbra line appears broken and does not fully close. Flamsteed mentioned observing a crack, confirming that this is not merely an engraving inaccuracy. On 13 August, three sunspots (Maculae tres) were observed, with the southernmost one having a thin penumbra (tenuis nubeculisa). The latitude of the sunspot group ranged from −4^o to −10^o, with an average of −7.9 ± 1.1^o. Spoerer (1889) later estimated the latitude to be approximately −6^o.

  In measurements by Flamsteedius (1725), the solar diameter varied from 31' 46'' to 31' 55'', but it was not provided for every observation, introducing some uncertainty. Note that routine measurements at the Paris observatory from 6 to 14 August 1666 – 1670 showed a gradual increase in the solar diameter from 31' 45'' to 31' 48.5''. For the observation on 12 August, we corrected a typo in the recorded distance to the center of the solar disc (9' 49'' instead of 9' 19''). Sunspot positions were reconstructed for each day by adjusting the image sizes and aligning them with the solar rotation axis, as shown in Figure 2(b). The results reveal uncertainty in sunspot position indicated by the red-filled and gray unfilled circles. These uncertainties arose from measurements that sometimes spanned up to an hour. Heliographic coordinates were determined based on the more reliable positions represented by the filled symbols, yielding an average latitude of −7.1 ± 1.4^o.

  Figure 2(c) illustrates the sunspot position derived from Edmond Halley's measurements in Oxford. Flamsteed and Halley (1676) provided a brief table of observations and, therefore, we aligned the sunspots with the Ecliptic. The average latitude obtained from these measurements is −8.3±1.5^o. On 15 August, Halley observed the sunspot at 8:35 UT when it was near the limb. However, due to projection shortening and the high altitude of the Sun, he was unable to take accurate measurement. Both Flamsteed and Halley measured the distance to the center of the largest sunspot (media Macula) or the midpoint of sunspots (Maculae medium), which also introduced some degree of uncertainty in sunspot mapping.

  Figure 2(d) shows the longitude derived from the engraving (sunspot number 2 in the corresponding Supplementary Materials) and the measurements. Observations by Flamsteed, represented by black and red symbols, exhibit a consistent pattern: larger longitudes before 10 August 1676 and smaller longitudes afterward. We attribute this pattern to inherent observational uncertainties, as similarly noted in Cassini (Fig. 1 therein) and Siverus (Fig. 1 therein). Longitude variations based on the engraving (black points) indicate rotation rates of 14.2 ± 0.7^o d^-1 and 14.8 ± 0.7^o d^-1, before and after 10 August 1676, respectively, marking these results as unreliable. The measurements (red filled symbols) suggest rotation rates of 14 ± 0.6^o d^-1 and 14.2 ± 1^o d^-1 for the same periods. Additionally, Figure 2(d) includes measurements from Oxford, indicated by blue stars. To determine the rotation rate, we utilized only reliable sunspot positions (dark blue symbols) and calculated a rate of 14.25 ± 0.3^o d^-1.

  Figure 2(e) illustrates the position of the sunspot (la tache) as retrieved from the measurements by Picard and/or Cassini at the Paris observatory using quadrants with radii of 3 foot and 32 inches, recorded from 9 to 14 August 1676 and later published by Le Monnier (1741). Additionally, we embed sunspot drawings from Cassini (1676a, 1676b) in green. The sizes of these spots are chosen arbitrarily, and the observation times were not noted. The latitudinal position of the sunspots (3' from the disk center, as stated by Cassini) align well with the measurements of Flamsteed and Halley.

  To derive the heliographic coordinates of the sunspot, we assume the angular size of the solar disc to be 31' 46'' based on Picard's measurements. The resulting latitudes range from −4.6 to −9.6^o, with an average of −7.6 ± 1.8^o. Figure 2(f) shows the corresponding longitudes with a derived rotation rate of 14.2 ± 0.3^o d^-1, which aligns with Flamsteed's and Halley's measurements. This result is considered more reliable due to small scatter in longitudes (less than 1^o).

   24 October – 25 December 1676

  On 27 October 1676 (17 October in the Julian calendar), Flamsteedius (1725) noted that D. Haynesius (presumably Domino Edvardo Haynesio, or Sir Edward Haynes) visited him and reported observing a sunspot. Together, they used a 16-foot tube to study its shape, as illustrated in the referenced figure. Flamsteed measured its position using a shorter 8-foot tube. Despite locating several copies of Historia Coelestis Britannica, volumen primum, page 367 — which contains the referenced figure — was missing. In a letter to Towneley, Flamsteed men- tioned that the sunspot appeared on 24 or 25 October (Carrasco and Vaquero, 2016).

  Adverse weather conditions on 28 and 29 October interrupted the observations. On 2 November, Flamsteed reported that careful observations made on 27 and 30 October indicated that the Macula would have been near the central meridian at Noon on 28 October. He further predicted that the sunspot might reappear again on the limb on 18 or 19 November and return to the central meridian by 24 November.

  On 19 November, thick "vapours" allowed Flamsteed to observe the Sun with the naked eye. Using a longer tube without the red glass typically employed to protect the eyes, he clearly observed the sunspot, as depicted in figure (apparently on page 367). Flamsteed noted that the penumbra (nubecula) appeared completely elliptical and expressed surprise that it was significantly wider on the limb side, while the sunspots (Maculae) near the disc center seemed almost adjacent (cohaerere). Remarkably, Flamsteed described a projection effect nowadays known as the Wilson effect, nearly a century before it was formall