Fig. 1. (a) and (b) Reproduction of three original drawings by Georg Christoph Eimmart (Eimmart Archive Collection 998, v. 16, f. 71); (c) sunspot positions and the time of observation defined by Method I in UT. Colors denote the reconstructed sunspot trajectories for three combinations of the original drawings. The heliographic grid corresponds to 5 July 1684; the solar axis is set vertically, i.e. excluding diurnal rotation. Blue thin circles mark inches. (d) Reconstruction of the sunspot transit by Method II (Vokhmyanin and Zolotova 2023).
Observations by Georg Eimmart
Georg Christoph Eimmart (1638–1705) is a German astronomer, mathematician, painter, and engraver from Nürnberg, appointed correspondent by Jean-Dominique Cassini on 4th March 1699. The archives were gathered from the Collection 998 of the Manuscript department of the National Library of Russia, St. Petersburg, which stores 59 volumes containing documents left by the Eimmart family and their assistants as well as correspondence with representatives of science, culture, art, and politics from a number of European countries during the period 1583–1723.
Eimmart's observatory was equipped by quadrants, sextants, telescopes (length 16, 12, and 10 foot, mounted on a pillar), astronomical (pendulum) clocks, two cameras obscuras, a helioscopium for weakening of the sunlight during the observation, and a machina helioscopia exploiting the projection technique (engraving by Delsenbach 1716, see Hayakawa et al. 2021, for details).
2–8 July 1684
A single sunspot transit was reported by Georg Christoph Eimmart at his observatory in Nürnberg. Five drawings are stored in volume 16, folio 1 (two drawings: 1 and 2) and folio 71 (three drawings). The illustrations are accompanied by a date and a time; sunspots a and bb are also reported to have been observed when the altitude of the Sun was 12o and 11o, respectively. Figures 1a and b show original drawings from folio 71. In Figure 1a, each sunspot is placed on the disk according to its own vertical ("ejus verticalis"") marked on the top of the limb with letters. A short note says that there is a full copy of these two drawings (folio 1). In Figure 3b, sunspot positions were corrected so that all verticals coincide.
As already noted by Hayakawa et al. (2021), the annotations of compass directions in folio 1 (indicating a rotation by 180o) lead to positions incompatible with other observers at the time. We, therefore, reflected the images from right to left and considered three com-binations of drawings: i) the two images from folio 1; ii) the two first images from folio 71 (Fig. 1a); iii) the third image from folio 71 (Fig. 1b). In the first two cases, we pre-aligned the verticals. Intercomparison of these three versions aims at assessing the uncertainties related to redrawing.
Figure 1c shows sunspot trajectories and observing time (UT) reconstructed by Method I. Note that for 8 July we assume that the observation was done at 16:00 local time in accordance with the description, "hor. qs. ante ⊙ occ., which most likely means "hora qui supra, i.e. the hour as before. Much later times would place the sunspot even below −20o and can be discarded. The largest discrepancy between the reconstructions is slightly above 3o in latitude and reaches 1.5o in longitude.
The first and the third observations are reported to belong to the evening of two successive days. According to the synodic rotation, the sunspot should have moved about ~13o, but the reconstruction yields a shift in longitude slightly over 20o (Fig. 1c). Such a discrepancy may be caused by either the inaccuracy of the drawing or by an incorrect note on the time of observation. A substantial shift of 17o in the central meridian distance (CMD) is also found between the sunspots on two successive days: 4 and 5 July. According to the description, two observations on 6 July are separated by only 15 minutes, while the sunspot displacement in CMD exceeds 4o. These inconsistencies cast doubt on either the accuracy of the timing or the accuracy of the drawing.
Figure 3d shows the sunspot transit reconstructed by Method II. Recall that this approach minimizes cumulative discrepancy of sunspot latitudes and is not tied to the times of observation. The third sunspot location (evening of 3 July) deviates from the most relevant track. This sunspot is located close to the disk center, and no image rotation can compensate for the displacement. If we force the method to ignore this sunspot, the average latitude of all spots will be between −11o and −12o for all three combinations of drawings.
Neuhäuser, Arlt, and Richter (2018) analyzed reports by Kirch and Schultz that describe that on 5 July (time is unknown, presumably local Noon) the sunspot was three inches from the disk center (thin blue dotted circle in Fig. 1c), and that on 6 July at 6 p.m. local time (around 17:20 UT), the sunspot was four inches from the disk center (thin blue dashed circle). This description closely matches Eimmart's drawings.
Combining the mentioned discrepancies, we assume the uncertainty of sunspot observation by Eimmart is, on average, 3o – 4o in both latitude and longitude. For the drawing from Figure 1b, the average latitude provided by Method I is −11.2 ± 2.4o (red curve in Fig. 1c). Hayakawa et al. (2021) inferred that this spot emerged around −13o in latitude. The average longitude, as given by Method I, is about 280 ± 3.5o. This yields about 14.46o d-1 solar differential rotation at 10o absolute latitude following the estimation by Balthasar et al. (1986). We find that using the Carrington angular velocity of 14.1844o d-1 the spot must have been at a 7o lower longitude on 12 June, i.e. at 272 – 274o , which is within the range of 260o – 280o as derived from the Wurzelbau report.
Spoerer (1889) wrote that Kirch observed this sunspot from 6 May to 27 July 1684 during four rotations. On the second rotation, a spot appeared on 11 – 13 June 1684. With reference to Cassini, Spoerer provided a latitude of −11o on 5 – 17 May, −10.8o from 28 June to 9 July, and −9o on 26 – 28 July 1684. Analyzing drawings by Kirch and Ihle, Neuhäuser, Arlt, and Richter (2018) provided the latitudes −21.9o (Ihle) and −19.2o (Kirch) on 6 May 1684. They argued that the sunspot of 5 and 6 July may not have been the same as that on 6 May, since these spots do not match in longitude. Our rough estimation of these reports gives a sunspot Carrington longitude of 260o – 290o on 5 – 6 July (Kirch and Schultz) and ~40o on 6 May 1684 (Kirch and Ihle).
Therefore, we suggest that the observers reported on more than one sunspot group at latitudes of about −10o and −20o. An object living for four rotations may be rather an active longitude. Otherwise, it should have been a large complex of activity showing some sort of evolution. Note, however, that the observers did not always draw the real sizes of sunspot groups.
