An Overview of Sunspot Observations in 1727–1748

From 1610 onward, astronomers have used telescopes to observe the solar surface and record the variability and appearance of sunspot groups there (Vokhmyanin et al. 2020; Arlt & Vaquero 2020). This multicentury endeavor has been regarded as one of the longest-running scientific projects in human history (Owens 2013). Individual sunspot observation records provide ground truth with which to evaluate and calibrate long-term variation in solar activity, including regular solar cycles and longer-term variability in terms of sunspot group number, relative sunspot number, and sunspot positions (Clette et al. 2014; Hathaway 2015; Arlt & Vaquero 2020). These data form the bases of numerous scientific analyses and discussions of solar dynamo activity (Arlt & Weiss 2014; Hotta et al. 2019; Charbonneau 2020), solar cycle predictions (Svalgaard et al. 2005; Iijima et al. 2017; Upton & Hathaway 2018; Petrovay 2020), space weather (Cliver & Dietrich 2013; Hayakawa et al. 2019a), space climate (Barnard et al. 2011; Usoskin et al. 2015), and climatological impacts (Gray et al. 2010; Anet et al. 2014; Ineson et al. 2015; Owens et al. 2017), among others.

These data are composites of various observations using different methods at different locations. Even after initial modern compilations (Hoyt & Schatten 1998a, 1998b, referred to hereafter as HS98), sunspot observation data sets have been continuously improved with analyses of individual sunspot observations to revise existing data and additions of new data (Arlt 2008; Vaquero et al. 2011; Carrasco et al. 2015; Svalgaard 2017). Indeed, after compilation of the initial revised data set in Vaquero et al. (2016, hereafter V+16), multiple historical records have been analyzed to improve existing data sets and derive sunspot positions (Arlt et al. 2016; Carrasco et al. 2019, 2021; Hayakawa et al. 2018b, 2020,2021; Karoff et al. 2019; Vokhmyanin et al. 2020). Furthermore, numerous sophisticated methods have been introduced to recalibrate raw sunspot observation data (Clette and Lefèvre 2016 (CL16); Svalgaard & Schatten 2016 (SS16); Usoskin et al. 2016, 2021; Chatzistergos et al. 2017 (C17); Muñoz-Jaramillo & Vaquero 2019).

However, it remains challenging to extend such data reconstruction methods to sunspot records in the early half of the 18th century. As shown in Figure 2 of Muñoz-Jaramillo & Vaquero (2019), existing reconstructions of sunspot group number remain particularly controversial and sunspot positions are still missing especially from the 1720s to the 1740s. This is partially because this interval is mostly out of long-term observers' coverage (SS16; C17), and so few records are available for each individual year (Vaquero et al. 2007). These difficulties remain even after improvements with new data (Vaquero et al. 2007; Arlt 2018 (A18)) and revisions of known data (Vaquero & Trigo 2014; Carrasco et al. 2015; Hayakawa et al. 2018b).

Figure 1 shows a great scarcity of the number of days with observational records of sunspots (<50 days per year) in 1727–1748 (V+16), even when including Wargentin's observations in 1747 (A18). This data scarcity has prevented us from understanding the transition of solar activity from the Maunder Minimum to regular solar cycles, despite its significance. Likewise, existing reconstructions of sunspot group number by SS16 and of the International Sunspot Number (CL16) divided by 20 (Muñoz-Jaramillo & Vaquero 2019) show significantly different trends, for example, in the amplitudes, shapes, and time series of each solar cycle in this interval. In particular, Solar Cycles −2 and −1 in SS16 show somewhat strange shapes about their expected maxima around 1726–1728 and 1736–1739. Therefore, this study tries to improve the source data in 1727–1748, by adding four forgotten data sets collected in 1728–1729, 1736, 1737, and 1748 (Section 2), thereby revising the known records in this interval (Section 3). The study then derives sunspot positions using the expanded sunspot records available for this interval (Section 4).

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To provide additional sunspot observations for the target interval of 1727–1748, we located several data sources hitherto overlooked in the scientific community. For 1728–1729, we exploited Conrad Zumbach Van Coesfelt's sunspot observations, as originally published in one of his publications (Van Coesfelt 1730). Conrad Zumbach Van Coesfelt (1697–1789) was a scientist who taught mathematics and philosophy, and engaged in astronomical and meteorological observations (NNBW 1927). His observations were likely conducted in Leiden (N52°09', E004°29'), where he based himself mainly from 1713 July onward. Van Coesfelt (1730) summarized his observations in a plate with 24 composite sunspot drawings (e.g., Figure 2). We identified 83 days of sunspot observations from 1728 December 12 to 1729 December 23 and classified their sunspot group numbers from 1 to 3 in 1728 (4 days) and from 0 to 8 in 1729 (79 days) using the Waldmeier classification. As these data overlap with no known observations in V+16 in 1728, and with 3 days of observations in 1729, they fill 4 days and 76 days without records in 1728 and 1729, respectively. The improvement is even more striking given that none of the known data for 1728 in V+16 (comprising 25 days) included the sunspot group number but it instead consisted only of the individual sunspot number, and thus has been recommended to be removed from discussions on the sunspot group number (Carrasco et al. 2015).

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For 1736, we exploited Dclos's sunspot observations published in a Paris journal (MHSBA 1736, p. 321). Jean Baptiste Dclos (1695–1743) was a Jesuit mathematics professor in Lyon who also engaged in astronomical observations (MHSBA 1736 p. 2176; Pernetti 1757, p. 310). On this basis, this study assumes his observational site to be Lyon (N45°46', E004°50'). Dclos recorded his sunspot observations for 10 days during 1736 March 16–28 (Figure 3). These observations overlap with existing observations in V+16 for three days during 1736 March 22–24. In this interval, Dclos recorded five sunspot groups, while Christfried Kirch reported five groups on March 23 and Schutz reported three and five groups on March 22 and 24, respectively. Dclos's observations are found to be broadly consistent with these contemporary observations. Otherwise, his records fill seven days on which no sunspot records are known to date (V+16).

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For 1737, we exploited Benjamin Martin's sunspot drawing at 7 in local time on 1737 August 25 (Figure 4; Martin 1738, Figure 47). As this observation was obtained using the Julian calendar, this date was converted to 1737 September 5 in the Gregorian calendar. Benjamin Martin (1704–1782) was known as a lexicographer and instrument maker from Worplesdon in Surrey, and became a resident of Chichester in Sussex in 1735 (Brayley 1842, p. 46). Therefore, his observational site is assumed to be Chichester (N50°50', W000°47'). As shown in Figure 4, his sunspot drawing shows six sunspot groups on the solar disk. This observation fills a data gap in the hitherto known sunspot records, helping to improve our understanding of sunspot activity in 1737, for which only three days with sunspot records are documented in V+16.

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For 1748, we exploited three days of observations from Cassini and Maraldi published in HARS (1748, p. 105). On July 22, Cassini and Maraldi reported two clusters (amas) of sunspots in the SE and NW quadrants of the solar disk. On July 24, they observed the same sunspots moving westward and one additional group that was not visible two days before on July 22. On July 25, Cassini and Maraldi witnessed an eclipse and reported the contact time of four spots with the solar limb, which probably indicates the presence of four sunspot groups. Accordingly, we consider that Cassini and Maraldi observed two sunspot groups on July 22, three groups on July 24, and four groups on July 25. As previous data for 1748 (V+16) include only one day of sunspot observations (July 25), the additional two days of observations (July 22 and 24) fill a gap in the existing data and improve our understanding of sunspot behavior in 1748. To support the data from Cassini and Maraldi, we additionally located two records for the same eclipse in Paris Observatory manuscripts from Laurent Béraud (MS B1/4-155) and Samuel De Schmettau (MS B1/4-164).

We consulted original references of the known sunspot observations included in V+16, to review the latest revisions and revise their observational details accordingly. For 1727, we revised Manfredi's and Cassini de Thury's group number on September 14–15 to 5 and 4, respectively, and removed Poleni's report as a misinterpretation of Manfredi's (Carbone et al. 1727; HARS 1727, p. 397). We also considered the actual sunspot observer in Carbone et al. (1727, p. 473) as not Carbone but Blanchini, mainly because they show almost the same descriptions in the main texts and group annotations in the sunspot drawings (Carbone et al. 1727, p. 473; Blanchini 1737, p. 249). We also removed Walther's data in HS98 and V+16, as his original descriptions did not provide quantitative details and should be associated not with Walther as a supervisor but with Weidler as a presenter (Weidler 1729b, p. 5; Wolf 1866, p. 47). Furthermore, caveats must be noted for Alischer's records in 1727, which are not found in Wolf's report (149) for the Sammlung of Breslau (Wolf 1866, p. 28). These records are instead found in Büchner (1731 p. 53 and 110), indicating reference mislabeling in HS98.

All known sunspot records in V+16 for 1728 were derived from Weidler's observations; however, Carrasco et al. (2015) determined that these observations were not sunspot group numbers but individual sunspot numbers. Therefore, these data should be removed from quantitative discussions of sunspot group number in 1728, making Van Coesfelt's records, introduced in this study, the only quantitative data for sunspot group number in this interval.

For 1729, three sunspot observers were included in V+16: Weidler, Krafft, and Beyer. Following the analyses of Carrasco et al. (2015) on Weidler (1729a), Hayakawa et al. (2018b) removed Weidler's data except for two days (February 1 and March 18) and added a new record from Beyer (December 14). Krafft was associated with 14 days of sunspot records in V+16. In his source records, Krafft described the Sun as "completely clear from all spots" from July 20 to 24, whereas a small spot was confirmed in the eastern limb on July 24 (NNZG 1731, p. 162). In existing studies, this report has been associated with the spotless days observed on July 20–23 and the one sunspot group on July 24. The remaining nine days of Krafft's records were probably derived from his report on an occurrence of a notable sunspot on May 3, its disappearance on May 10, and its recurrence on May 22 (NNZG 1731). These records do not allow us to interpret the sunspot group number in the entire solar disk. Therefore, we removed these data from our revised data set. Likewise, we removed Beyer's record of July 31 because it was likely derived from Krafft's correspondence to Beyer (not Beyer's own observation), indicating a sunspot was visible on the last day (am letztern Tage) of the stretch of spotless days during July 20–24 (Wolf 1866; see also NNZG 1731, p. 162). This date was probably misinterpreted as "the last day" of July, namely July 31.

We made moderate revisions to the record in the 1730–1732 period. For 1730, four observers were included in V+16: Beyer, Adelbulner, Hallerstein, and Wasse. Following Hayakawa et al. (2018b), we removed Adelbulner's observations, revised Beyer's data, and revised Hallerstein's records to Hell's. We further revised the sunspot group numbers in Beyer's records for the four days of April 29–30 and May 2–3. We also consulted Wasse's sunspot report (RS MS CLP/8ii/27) to revise the group number dating from the Julian calendar (1730 September 25) to the Gregorian calendar (1730 October 6) and removed one naked-eye sunspot record collected on 1730 October 4.

No datable sunspot records were hitherto available for 1731 (Vaquero et al. 2007; V+16; Hayakawa et al. 2018b). For 1732, two records were provided from Christfried Kirch (September 17) and Cassini de Thury (December 17) in V+16. While HS98 relied on Ref. 151 of Wolf (1866) for the latter, no observations for 1732 were mentioned in that reference. Instead, we located mention of sunspot observations in 1732 in Triesnecker & Bürg (1801 p. 343), where three sunspot groups were reported during the observation of an eclipse in Ingolstadt.

V+16 based the 30 spotless days in 1733 on Beyer's record in April and Le Monnier's record in May. We identified Beyer's original report with NNZG (1734, p. 259), which was dated April 16 and described the recent absence of sunspots on the solar disk. Given this date, Beyer's data after April 16 should be removed (April 17–30). Moreover, this general description of a spotless Sun should be treated with caution. Le Monnier (1751, p. 1) reported a solar eclipse on May 13 without any reference to sunspots, while an anonymous observer at Leipzig viewed the solar disk through 4 ft and 8 ft telescopes and reported that the Sun was without any sunspots (Adelbulner 1735, p. 28). Therefore, we removed Le Monnier's record and added this anonymous report indicating a spotless day on May 13.

The only known sunspot record for 1734 is associated with an anonymous eclipse observation from May 4 (V+16). According to HS98, this reference "needs to be re-checked." We identified the source report for this reference as Manfredi's eclipse report from Rome (Manfredi 1735). Although no sunspots are mentioned in this report, it is questionable whether this indeed indicates a spotless Sun.

The known records for 1735 in V+16 were derived from Wolf (1876), except for the record dated October 16, which was associated with Hallerstein but was actually reported by Simonelli (Hallerstein 1768). This has been pointed out in Vaquero et al. (2007), but this modification has apparently not been incorporated in V+16. Consulting Wolf (1876), we determined that these records were cited from Prof. Winnecke's correspondence based on Adelbulner (1736) and De L'Isle's manuscripts in Pulkovo Observatory. Wolf (1876) based the other records on Adelbulner (1736). HS98 and V+16 have associated these records with Baratier and Rukkehr. Here, we associate the latter observations with Baratier, as Wolf (1876, p. 393) described "Rükkehr" not as a personal name but as Baratier's "return." Taking this correction into consideration, Baratier's reports on March 8, April 29, and May 1 indicate individual sunspot numbers, whereas it is virtually impossible to robustly derive their group number. Baratier also reported he saw a sunspot on April 23 or 24, but he did not clarify which date was true. Therefore, in Adelbulner (1736, p. 90 and 107), we can confirm only two days of reports with robust dates and sunspot group numbers (March 19 and June 14 in 1735). Meanwhile, De L'Isle's original manuscripts should be searched for and investigated in future studies.

Available data for 1736–1743 have been scarce but intermittently improved in several studies (Vaquero et al. 2007; V+16; Vaquero & Trigo 2014). Furthermore, we corrected the dates of observations by Huxham, Bradley, and Weidler from 1736 October 31 to 1736 November 11, from 1737 February 18 to 1737 March 1, and from 1739 July 24 to 1739 August 4, respectively, as they were not the corrected dates in the Julian calendar format (Weidler 1739; Huxham 1744, p. 645; Bradley 1832, p. 368) and were not corrected to the Gregorian calendar format. In this context, we also corrected Bradley's two other records to 1722 December 8 and 1726 September 25 and associated the former with Molyneux (Bradley 1832, p. 359 and 391). We removed Weidler's record on 1738 August 15 following Vaquero et al. (2007). We also removed two reports on 1739 December 30, as they did not involve sunspot observations (see also Vaquero et al. 2007). Finally, we removed Shaw's record on 1739 February 17, as it was misdated in Shaw's supplementary chapter ("a collection of such papers as serve to illustrate the foregoing observations") and misidentified with Shaw (Shaw 1738, p. 56).

For 1739–1742, Mucio Muzano (known as "Musano" in HS98 and V+16) and John Winthrop provided relatively rich sunspot observations. Muzano's datable observations are summarized in eight disk drawings on plates in Muzano (1754), as illustrated in Figure 5. We removed 14 days of undocumented records from V+16, as Muzano (1754) stated nothing about spotless days between his observations. We also consulted John Winthrop's records including his original manuscript (MS HUM 9 Box 3, Harvard University Archives; see Figure 6) to revise his data. Winthrop worked at Harvard University (N44°23', W071°07') in New England, where he conducted sunspot observations with an 8 ft telescope and followed the Julian calendar (Kilgour 1938). As previous studies misinterpreted his observational dates as being in the Gregorian calendar format (HS98; Vaquero & Trigo 2014; V+16), we modified his dates from the Julian to the Gregorian calendar. We also removed two of Winthrop's records from V+16 (1739 April 19 and 1740 May 2 in the Julian calendar), as they described a naked-eye sunspot observation and a Mercury transit without mentioning sunspots, respectively. We also added one day from Winthrop's forgotten record for 1741 January 24, consulting Tuckerman (1841).

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For 1747–1748, the known records in V+16 were derived from Pehr Wargentin's observations in 1747 (A18) and several eclipse observations on 1748 July 25. We added Pehr Wargentin's eclipse observation for 1748 July 25 (Wargentin 1751, Table III) and revised Eustachio Zanotti's record during this eclipse based on his manuscript (MS B1/4-180) in Paris Observatory.

Figure 7 shows our additions of forgotten sunspot records as well as our revisions and confirmations of existing sunspot records for 1727–1748, contextualizing these data into the overall sunspot records for 1725–1749. While the data coverage remains scarce, our revision clearly improved the details describing Solar Cycles −2 to 0, potentially addressing the existing controversial understanding of these cycles (Figure 1). Indeed, this study located the minimum of Solar Cycles −2/−1 in 1733, confirming previous reconstructions (CL16; SS16). No records with visible sunspots were confirmed in 1733 and 1734, unlike in adjacent years. In 1733, Beyer and an anonymous observer at Leipzig reported a spotless Sun in April and May. This year is contrasted with 1734, known only through Manfredi's eclipse report in 1735, which simply had no explicit reference to sunspots.

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This study located the minimum of Solar Cycles −1/0 in 1743; this minimum has previously been controversially located in 1743 (SS16) or 1744 (CL16). Few datable records are known for 1742–1743 and none have been identified for 1744–1746 (Figure 7). Here, additional support was found from Benjamin Martin's curious general description, in which he stated: "And in this Century the Spots were frequent and numerous until the Year 1741, when for three Years successively very few appeared. I saw but one in all that Time; and now since the Year 1744 they have again appeared as usual" (Martin 1747, p. 321). While we can derive neither datable records nor quantitative data from this description, it does indicate a significant decrease in sunspot occurrence during 1742–1743 and its recovery since 1744. This allows us to locate the minimum of Solar Cycles −1/0 in 1743.

However, it is extremely challenging to calibrate sunspot observation records and derive reliable time series before 1749 because, prior to Staudach's observations in 1749–1796 (Arlt 2008, 2009; Svalgaard 2017), available records are notably scarce even after our revisions and do not overlap well with each other. Indeed, these observations are neither regular nor abundant enough to systematically record spotless days (Figure 7) and do not allow the use of the active day fraction either (Usoskin et al. 2016, 2021). Likewise, these problems do not allow us to derive the scaling factors for individual observers except for von Hagen's records (1739–1751), which overlap with Staudach's observations (SS16; C17).

It is also challenging to extend the existing data using von Hagen's data because his records are known only through Wolf's table; the original records have not been further analyzed in the scientific community. Wolf explicitly declared that he acquired von Hagen's records through correspondence with Mr. Wagner, who consulted von Hagen's manuscripts in Pulkovo Observatory (Wolf 1866). Von Hagen's manuscript was entitled Collectanea astronomica colligente et observante F. de Hagen ("Astronomical collection collected and observed by F. von Hagen"). While this manuscript is mentioned in contemporary bibliographic catalogs (e.g., Struve 1860, p. 824), it could not be successfully located in Pulkovo Observatory (Y. Nagovitsyn 2020, private communications). In order to reliably use von Hagen's records, his original manuscripts should be located and analyzed in detail according to modern viewpoints (e.g., Arlt et al. 2013; Svalgaard 2017; Hayakawa et al. 2020; Vokhmyanin et al. 2020).

Alternatively, SS16 used the brightest star method to roughly estimate the annual sunspot group number on the basis of the greatest sunspot group number for each year before Staudach's observations. This procedure allows for the estimation of the annual sunspot group number in 1725–1749 (see Figures 28, 30, and 35 in SS16), as shown in Figure 8. Here, we have applied a scaling factor of 0.88, which SS16 used to derive the sunspot group number from the brightest star method. Caveats must be noted on the reliability of this approach, as little is known about the scale factor of each observer in this interval and any variability can immediately affect the resulting estimates (e.g., C17).

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With these caveats in mind, Figure 8 locates the maxima of Solar Cycles −2, −1, and 0 in 1730, 1736, and 1748, respectively. The cycle configuration has been significantly improved in Solar Cycle −1, where SS16 showed a significant dip in sunspot group number for 1737–1738 (Figure 1). While this dip is still visible in our reconstruction, we consider this to be an artifact of data scarcity in 1737 and 1738, for which only three days and one day of observations are known, respectively. The maximum of Solar Cycle −2 was moved from 1728 to 1730 mainly because Weidler's data were removed, Beyer's data were updated, and some exaggerated data were adjusted (Carrasco et al. 2015; Hayakawa et al. 2018a). This resulted in a dip in sunspot group number for 1726–1730, likely owing to the contrast between the abundant record availability for 1726 and the scarce record availability for 1727–1728. The sunspot records for 1726 should be revisited in the future, as long-term observers' records (e.g., Plantade and C. Kirch) have remained publicly inaccessible so far. Notably, we have revised the greatest sunspot group number in 1726 from 10 to 8, as Godin's original records for 1726 September 26 reported not 10 (dix) groups but 2 (deux) groups (HARS 1726 p. 330; Wolf 1866, p. 35).

We next analyzed these sunspot records and derived sunspot positions in 1727–1748. We first manually fitted the observations to a circle to remove potential geometrical distortions, as described in Fujiyama et al. (2019), and then set their disk orientations. Either the chronological sequences or the explicit time stamps of the observations are required for this process; otherwise, it is challenging to infer the exact disk orientations and depicted sunspot positions. Therefore, it is important to clarify that we could not derive all sunspot positions from the sunspot drawings acquired for the target interval.

When the sunspot groups were recorded in chronological sequence (e.g., Figures 2–3 and 5–6), we combined the directions of their depicted motions, their track inclinations, and annotations of their disk orientations to interpret the orientations of the sunspot drawings by Van Coesfelt, Beyer, Dclos, and Muzano as erect images and those by Winthrop as inverted images. Thus, we followed the recorded sunspot motions and located the associated sunspot positions, minimizing latitudinal variations for individual sunspot groups. Among the observations, Van Coesfelt's sunspot drawings were sometimes particularly challenging to interpret, as he did not provide exact time stamps and did not explicitly date some sunspot groups. In this case, we only derived positions for the datable sunspot groups.

When the sunspot drawings were chronologically isolated, we consulted their time stamps to set their disk orientations. Alternatively, some observations were associated with specific astronomical events such as a partial solar eclipse or Mercury transit (e.g., Figures 9 and 10; Vaquero et al. 2007). In these cases, we computed the disk orientations and heliographic coordinates of the sunspot observations and compared their relative positions with the lunar shade or transit path of Mercury or Venus for each observational site (Figures 9 and 10). We used the rotation elements of Archinal et al. (2011a, 2011b), the ephemeris data of JPL DE430 (Folkner et al. 2014), and the values of the difference of the terrestrial and universal times (ΔT) of Stephenson et al. (2016), as per Hayakawa et al. (2019b, 2021). Likewise, we derived sunspot positions from sunspot drawings with known disk orientations and explicit observational time stamps.

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Using the sunspot observation data analyzed in this study, we derived and visualized the sunspot positions for 1727–1748 and contextualized them into the known data from Wargentin in 1747 (A18) and Staudach in 1749 (Arlt 2009). Our results filled the data gap in the existing butterfly diagram (e.g., Figure 2 of Muñoz-Jaramillo & Vaquero 2019), showing sunspots in both solar hemispheres with latitudinal distributions that are mostly consistent with the regular solar cycles (e.g., Arlt 2009; Muñoz-Jaramillo & Vaquero 2019), in contrast with those during the Maunder Minimum (Ribes & Nesme-Ribes 1993). Most of the sunspots were located at heliographic latitude φ fulfilling ∣φ∣ < 35° in both solar hemispheres. Despite their scarcity, the latitudinal distributions of these sunspot observations appear to be consistent with the cyclic behaviors of the sunspot group number (Figures 7 and 8). Figure 11 locates the border between Solar Cycles −2 and −1 in 1731–1735 and that between Solar Cycles –1 and 0 in 1743–1746, confirming the observed sunspot group number minima in 1733 and 1743. Solar Cycle −2 accommodates sunspot positions mostly at heliographic latitude φ fulfilling ∣φ∣ < 35° in both solar hemispheres, whereas Van Coesfelt's observations in 1729 show asymmetric sunspot distributions with southward concentrations in January–May (ranging between 20° and −40°) and northward concentrations in August–December (ranging between 35° and −20°), with a transition interval in June–July. Interestingly, Beyer's only sunspot drawing in 1729 December shows three sunspot groups in the northern hemisphere and one sunspot group in the southern solar hemisphere, in which their latitudinal distribution supports the result from Van Coesfelt's observations. Further independent records are required to determine if the time-dependent latitudinal asymmetry of the sunspot distributions in 1729 is real or an apparent result of instrumental problems. Solar Cycle −1 shows clear equatorward migrations in the latitudinal distributions of sunspot groups from 1736 to 1742. In Solar Cycle 0, the latitudinal distributions of sunspot groups migrated equatorward from 1747 to 1748, but extended toward higher heliographic latitudes in Staudach's observations for 1749 (Arlt 2009), even when compared with those for 1747 (A18). Further analyses are therefore required to clarify the sunspot group positions in Solar Cycle 0.

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In this study, we added forgotten sunspot records to the existing V+16 database for the 1727–1748 period, reanalyzed accessible sunspot records on the basis of their original source documents, revised sunspot group numbers, and derived sunspot positions in three solar cycles (Solar Cycles −2, −1, and 0). Analyses of these solar cycles were especially challenging due to insufficient data availability, contaminations from misinterpreted data, and lack of chronological overlaps between individual observers.

For the interval considered in this study, we located several series of hitherto forgotten sunspot records. We located Van Coesfelt's observations from 1728–1729, identifying 83 days of observations and deriving corresponding sunspot group numbers ranging from 0 to 8. These records form a unique and irreplaceable reference, as all the known sunspot group numbers for 1728 in V+16 are contaminations by individual sunspot numbers (Carrasco et al. 2015) and only eight days of sunspot observations provide exact sunspot group numbers in 1729 after our revisions. We located Dclos's sunspot observations from 1736, identifying 10 days of observations and deriving corresponding sunspot group numbers ranging from 2 to 5. These records fill seven days without data in V+16 and broadly agree with existing observations from three other days. We located Benjamin Martin's sunspot drawing from 1737 September 5 and identified six sunspot groups within, adding another day of observation to the three days of observations for this year in V+16. Finally, we identified two days of hitherto unknown observations from Cassini and Maraldi in 1748, adding to the single day of observation (1748 July 25) in V+16. We also located two additional sunspot records for the same eclipse—Béraud and De Schmettau (MS B1/4-164)—supporting the data from Cassini and Maraldi.

We also analyzed the source documents comprising the existing sunspot records for the target interval and revised their sunspot group numbers accordingly. Our revisions have removed Walther's records in 1727, most of Weidler's records (except for two days; see Carrasco et al. 2015), nine days of Krafft's records in 1729, Wasse's records in 1730, Beyer's records in late 1733 April, and Shaw's record in 1739. While we associated the anonymous eclipse observation from Rome in 1734 with Manfredi, we found no explicit description of sunspots in this record. We also revised Bradley's records in 1726–1739; Manfredi's, Cassini de Thury's, and Blanchini's records in 1727; Beyer's records in 1729–1733; Wasse's records in 1730; Huxham's record in 1736; Weidler's record in 1739; Muzano's records in 1739–1742 ("Musano" in HS98 and V+16); and Winthrop's records in 1739–1741. Furthermore, we relabeled Bradley's record in 1722 as Molyneux's, Cassini de Thury's in 1732 as an anonymous record from Ingolstadt, Le Monnier's record in 1733 as an anonymous observation at Leipzig, and Hallerstein's record in 1735 as Simonelli's. Finally, we located Pehr Wargentin's forgotten sunspot record and revised Eustachio Zanotti's record according to a comparison of observations during the solar eclipse on 1748 July 25.

We summarized our additions and revisions during Solar Cycles −2, −1, and 0 in Figures 7 and 8, and presented that the solar minima of Solar Cycles −2/−1 and Solar Cycles −1/0 were located at 1733.5 ± 0.5 and 1743.5 ± 0.5, respectively. As the solar minimum of Solar Cycles 0/1 was located in 1755.2 (Table 2 of Hathaway 2015), these chronological estimates indicate that the lengths of Solar Cycles 0 and −1 were 11.7 ± 0.5 yr and 10.0 ± 1.0 yr, respectively. However, it was challenging to extend the annual sunspot group number observations to this interval owing to the scarcity of relevant data and the absence of overlapping or systematic observations. Still, applying the brightest star method described in SS16 to our revised data set tentatively visualized the maxima of Solar Cycles −2, −1, and 0 in 1730, 1736, and 1748, respectively. Caveats must be noted here, as this tentative visualization can and should be easily updated/modified with additional data, reasonable scaling factors for individual observers, and better calibration methods.

On the basis of our revised data set, we derived sunspot positions and reconstructed butterfly diagrams to fill the existing gap in the data (e.g., Figure 2 of Muñoz-Jaramillo & Vaquero 2019). Despite the data scarcity, our reconstruction (Figure 11) located most of the sunspot groups at heliographic latitude φ fulfilling ∣φ∣ < 35° in both solar hemispheres. Solar Cycle −2 generally showed sunspots at heliographic latitude φ fulfilling ∣φ∣ < 35° in both solar hemispheres, whereas their positions in 1729 showed apparent hemispheric asymmetry; this difference should be further examined using independent source records. Solar Cycle −1 especially showed equatorward migration of the reported sunspot groups. The ascending phase of Solar Cycle 0 was consistently reported and showed equatorward migrations during 1747–1748, whereas this trend was somewhat blurred in 1749 within Staudach's observations. These results robustly confirm regular solar dynamo activity during Solar Cycles −2 to 0 and chronologically fill the gap between the regular solar cycles and the Maunder Minimum. Further analyses are required especially during the 1710s and 1720s to bridge the gap between the revised data set and the Maunder Minimum.

We thank the Harvard University Archives, the Royal Society, Paris Observatory, and Bibliothèque Nationale de France for providing digital copies of Winthrop's manuscripts, Wasse' s sunspot records in 1730, eclipse drawings in 1748, and Dclos's sunspot observations in MHSBA. H.H. has benefited from discussions within the ISSI International Team ("Recalibration of the Sunspot Number" series, "Solar Extreme Events: Setting Up a Paradigm", and "Modeling Space Weather And Total Solar Irradiance Over The Past Century") and the ISWAT-COSPAR S1-01 and S1-02 teams. This work was financially supported in part by JSPS Grants-in-Aid JP20K22367, JP20K20918, JP20H05643, and JP21K13957; the JSPS Overseas Challenge Program for Young Researchers; the ISEE director's leadership fund for FY2021; the Young Leader Cultivation (YLC) program; the YLC collaboration project of Nagoya University; the young researcher units for the advancement of new and undeveloped fields of the Institute for Advanced Research (Nagoya University) under the Program for Promoting the Enhancement of Research Universities; and Tokai Pathways to Global Excellence (Nagoya University) of the Strategic Professional Development Program for Young Researchers (MEXT). H.H. also thanks Víctor M. S. Carrasco for his advice on some sunspot records in 1727.

Winthrop's manuscript is available at MS HUM 9 Box 3 of the Harvard University Archives. Wasse's manuscript is available at MS CLP/8ii/27 at the Royal Society. Laurent Béraud's, Samuel De Schmettau's, and Eustachio Zanotti's records in 1748 are available at MS B1/4-155, MS B1/4-164, and MS B1/4-180 in Paris Observatory, respectively.