Fig. 1. Hoffmann's tabular computations of the positions of the largest sunspot in micrometer turns (blue circles), in arcminutes and arcseconds (green squares), and in digiti (red dashes) from 26 May to 2 June 1703 (a) and from 18 to 29 June 1703 (b). Panel c: an enlarged pencil drawing of the sunspot group of 27 – 29 May 1703. Panels d – f: superimposed ink and pencil drawings of the sunspot transit from 26 May to 2 June 1703, from 18 to 29 June 1703, and the sunspot of 16 July 1703, respectively. The images are reproduced from the Eimmart Archive Collection 998, volume 3, folios 422 – 424, and volume 37, folios 73 – 74. Red dashes indicate the tabular positions of the largest sunspot in digiti. The three heliographic grids correspond to 26 May, 18 June, and 16 July 1703. The grid intervals are 10o. The solar Equator is shown as a horizontal line, blue circles mark digiti, and times reported by Hoffmann are converted to UT (Vokhmyanin and Zolotova 2023).
Observations by Johann Hoffmann
Johann Heinrich Hoffmann (1669–1716) is a German astronomer. We examine his sunspot observations (drawings and table data) stored in the Collection 998 of the Manuscript department of the National Library of Russia, St. Petersburg.
26 May – 16 July 1703
The first portion of the observations by Hoffmann was made in Berlin, where he rented a flat from Kirch (Dick 2000), and they are stored in volume 3, folios 422, 423, and 424. Three drawings of one sunspot transit are made with black ink. The first two drawings are accompanied by tables that provide the day, time of observation, and three columns with sunspot positions measuring the linear distance from the eastern limb. The first column contains raw values in micrometer turnovers scaled to 77, the second arcminutes and arcseconds scaled to the solar diameter of 31'42'', and the third in digiti scaled to 12 (some historical researchers gave sunspot positions in "digiti", "inches", or "Zoll", all denoting the same way of dividing the solar disk into six concentric circles, where the largest circle is identical to the solar limb. The solar diameter, therefore, becomes divided into 12 parts). Figures 1a and b evaluate the reliability of Hoffmann's tabular computations. Apart from very few discrepancies, the sunspot positions are the same as the ones from the drawings.
This scientific report has been attached to a letter to Georg Eimmart. On folio 425, Hoffmann wrote: "Sonder Zweifel wird mein Patron die wenigen Zeilen, durch Einschluß des Hn Deckers, von den 10 Julij, erhalten haben; darin ich etwas von der Observatione Macularum in Sole gedacht, und zugleich einen Abriß oder Schema wo die Maculae täglich gestanden übersendet, in welchen Schemate der H Decker sich selbst erboten, die Maculas auf die annotirte loca genau zu verzeichnen, weil ich ihm öfters zu der Observation rufen, und zu sehen laßen, aber er hat weder die formam noch den situm recht in acht genommen; denn die große Macula war in dem medio ⊙ meist rund, und prope margines oval, auch sind ihr die kleinen alle Zeit von hinten gefolget. Dahero ich wieder das damahls übersendete Schema hirmit protestire, und werde meinen Patrono bey übersendung der Ephemeridum ad annum 1704 die Observationes von diesen Maculis (davon die große Macula auch das dritte mal in ⊙ erschienen) wie auch von der Eclipsi ☽ des 29 Junij mit bey legen."
We translate as follows: "Without doubt, my patron will have received the few lines of 10th July through the action of Mr Decker, in which I commemorated some observations of spots in the Sun, and as well sent a sketch or scheme with the daily locations of the spots, in which Mr Decker offered to plot the positions precisely. I had often called him to see the observation, but he neither scrutinized the shapes nor the locations; since the large spot was in the middle of the Sun mostly round, and oval near the limb. Also, the small ones always followed it behind. Therefore, I herewith again present the transmitted sketch and will, upon receiving the annual ephemeris of 1704, attach the observations of these spots (of which the large one appeared for the third time on the Sun) as well as of the lunar eclipse of 29th June for my patron."
Indeed, a copy of the table appears in volume 35, folios 42 and 43 (1, 2, 3), and the next folio titled "Observationes Coelestes Anni 1704" is blank. The only difference is that in the first table for 25 June 1703, the local time of observation is 7:10 p.m., while it is 7:0 p.m. in the second table.
The "transmitted sketch" made with a pencil was placed in volume 37, folios 73 and 74. An enlarged piece is shown in Figure 1c. The sunspot group of 27 May 1703 accurately reproduces the drawing Hoffmann sent to Kirch (Neuhäuser et al. 2018, Figure 15 therein). Recall that Hoffmann wrote that the small sunspots always followed behind the large spot (otherwise in the pencil drawing), while the ink drawing shows the transit of only the largest sunspot.
In 2026, La Hire's observations resolved this contradiction (Zolotova and Vokhmyanin, 2026): we think that when Hoffmann compiled the measurements with the individual sunspot drawings, he had forgotten to reverse and flip the sunspot drawings. We improved the pencil drawing and recalculated sunspot parameters. The improved pencil drawing was analysed in Figure 10 in La Hire.
Figures 1d–f compare the series of drawings drawn in black with the drawings with a gray pencil and the largest sunspot positions according to the digiti units from the tables (red dashes). Tabular and drawn sunspot positions match adequately except on 28 June 1703. The tabular data mention that the sunspot was observed at 19:00 and located at 10 44' digiti. However, in the drawing and according to the micrometer measurements, the sunspot was located closer to the western limb. Since the micrometer measurements and the conversions to arcminutes and arcseconds are consistent with each other and the drawing, we suppose there is an error in the digiti column. In Data, we provide three sets of sunspot parameters reconstructed from the drawings in ink, pencil, and from the tabular data in digiti.
Note that Hoffmann located the sunspots on the horizontal line passing through the center of the disc. The largest sunspot turns out to be either slightly in the northern or slightly in the southern hemisphere since the solar Equator crossed the disk center on 3 June 1703. Hayakawa et al. (2021, Figure 8 therein) defined that the sunspot group observed from 26 May to 2 June 1703 was in the southern hemisphere, but the two others of 18 – 29 June and 16 July 1703 were in the northern hemisphere, assuming the vertical points to the celestial pole. Based on the letters by Hoffmann and Kirch, Neuhäuser at al. (2018) inferred that the sunspot group from 24 May to 2 June 1703 was located on average at −0.7 ± 3.5o. In addition, they noted that Kirch had speculated that the sunspot that appeared between 18 and 29 June 1703 was the same one. Spoerer (1889) listed both sunspots from 24 May to 3 June and from 18 to 30 June 1703 with −2o latitude referring to the reports by la Hire and Cassini.
The largest sunspot of the group visible from 26 May to 3 June 1703 was also drawn by Stannyan and Hodgson (1704). We estimated its latitude to be about −2o. On 24 – 30 June 1703, the sunspot was reported by Derham (1703), who described it as "round and strong, afterwards long, and with a Nucleus. The very same Spot (I doubt not) I saw again on the Suns Eastern side on July 5 [16 July 1703 Gregorian]..." We determined the sunspot latitude from his drawing of 24 – 30 June 1703 to be a couple of degrees in the southern hemisphere.
We also reconstructed the sunspot positions from Hoffmann’s drawings. Only Method II can be exploited, as the orientation of the solar disk depicted does not match its actual appearance in the telescope. Using the drawings and the tabular data, we follow the hypothesis of a long-lived sunspot group and obtain an average latitude of the largest sunspot of −0.85 ± 0.2o for the period from 26 May to 16 July 1703.
We show that this sunspot group was also observed by Maria Eimmart and Eustachio Manfredi. We compare their drawings and find that the times of observation noted by Hoffmann were probably misspelled (morning and evening were mixed up) in several cases. Here and in Data for Hoffmann's observations, longitudes are indicated for the corrected times of observation. The average longitude of the largest sunspot from 26 May to 2 June is 270.5o, 274o for 18 – 29 June, and 278o on 16 July 1703. Hence, Hoffmann, Kirch, and Derham could have reported on a complex activity nest (Castenmiller et al. 1986) or magnetic-activity complex (Bumba and Howard 1969), where new magnetic flux emerges near a pre-existing active region (Muhamad et al. 2021). This may also be related to the phenomenon of active longitudes well seen in the period of overlap of 11-year cycles (Benevolenskaya et al. 1999; Kostuchenko and Benevolenskaya 2014; Kramynin and Mikhalina 2016). The year 1703 belongs to the ascending phase of Cycle −4. However, the near-Equator location of the sunspot group suggests that it might belong to the previous cycle overlapping with Cycle −4.