Analyses of Early Sunspot Records by Jean Tarde (1615 – 1617) and Jan Smogulecki (1621 – 1625)

Jean Tarde and Jan Smogulecki carried out sunspot observations in the 1610s and 1620s at the dawn of the telescopic era. We analysed their original observational records to revise their sunspot-group numbers in the existing database. In this study, we provide a new counting as a basis for future scientific discussions. Furthermore, we compared Smogulecki’s sunspot observations with those of Scheiner and Schönberger on the same observation days. We also detected a big sunspot group on 2 – 3 February 1622 in Smogulecki’s sunspot drawings and estimated its area to be approximately 1600 millionths of the solar disc. In addition, we measured the sunspot positions in Tarde’s and Smogulecki’s sunspot drawings to construct a butterfly diagram for this early period.


Introduction
Sunspots have been observed for several millennia, although they started to be more systematically recorded since 1610, after the use of the telescope as an astronomical instrument (Yau and Stephenson, 1988;Vaquero and Vázquez, 2009;Hayakawa et al., 2017;Willis et al., 2018). The number of sunspot groups and individual sunspots observed on the solar disc were used to calculate the indices of the relative sunspot number and group sunspot number (Hoyt and Schatten, 1998;Clette and Lefèvre, 2016). These indices, derived from their counting, have been extensively used to characterise long-term solar activity, as they have been constructed from direct solar observations for the last four centuries. Recent studies have detected some problems with these sunspot-number indices (Clette et al., 2014). This was also the case with their background database (Hoyt and Schatten, 1998), which has been significantly revised and updated based on the original records (Vaquero et al., 2016). Currently, there is an ongoing global effort to address these problems and recalibrate the different sunspot-number indices (Muñoz-Jaramillo and . Harriot recorded the first known sunspot observations using a telescope on 18 December 1610 (Arlt and Vaquero, 2020;Vokhmyanin, Arlt, and Zolotova, 2020). In the dawn of the telescopic era, Scheiner and Galileo were two of the most important sunspot observers and antagonists of a famous historical debate on the nature of sunspots (Galilei and Scheiner, 2010). Other outstanding sunspot observers at the time were Malapert, Mögling, Tarde, and Smogulecki. Recently, some studies have analysed the earliest telescopic sunspot records and provided new information on the solar activity that occurred at that time. These studies also detected significant errors in the number of sunspot groups included in both the Hoyt and Schatten (1998) database and the most recently revised collection of sunspotgroup numbers by Vaquero et al. (2016) (hereafter V16). For example, Zolotova (2020, 2021) studied the group numbers, latitudes, and areas of the original records of Harriot, Cigoli, Galileo, Cologna, Scheiner, and Colonna. Carrasco, Gallego, and Vaquero (2020) showed a significant number of observations made by Galileo and Scheiner in the 1610s that had been missed in V16. These authors also detected a change in the observation method carried out by Galileo (from observations through a telescope to the projection method) that influenced the number of groups recorded by him before and after this change. Neuhäuser and Neuhäuser (2016) revised early sunspot records made by Marius, Saxonius, Malapert, and other sunspot observers at the time. Carrasco et al. (2019) also analysed the sunspot observations made by Malapert for the period 1618 -1626, obtaining a greater solar-activity level from these records than previously known. Hayakawa et al. (2021) consulted the original manuscript of Mögling's sunspot observations and derived his sunspot-group number and sunspot positions for the period 1626 -1629. Arlt et al. (2016) calculated the areas, latitudes, and tilt angles from sunspot drawings recorded by Scheiner in his book Rosa Ursina (Scheiner, 1630); further, Vokhmyanin and Zolotova (2018a,b) determined the group numbers, positions, and areas from Galileo's and Gassendi's observations. All of these recent studies have allowed us to improve our knowledge of solar activity at the dawn of the telescopic era. However, further studies are required because the observational coverage of sunspot observations in the earliest period of the telescopic era is still scarce (Muñoz-Jaramillo and Vaquero, 2019).
In this context, we consulted Tarde's and Smogulecki's original Latin texts describing their sunspot records. Thus, we detected significant problems in the existing number of sunspot groups assigned to Tarde and Smogulecki in V16. The main objectives of the present work are: i) to provide a new group counting as a basis for future scientific discussions on the sunspot-group number, and ii) to calculate the sunspot latitudes recorded in Tarde's and Smogulecki's drawings. The remainder of this article is organised as follows: Section 2 includes biographical details about Tarde and Smogulecki that are relevant for interpreting their sunspot records. Section 3 presents our analyses and discussion of the number of sunspot groups. Section 4 shows the butterfly diagram obtained from the sunspot positions measured and computed from their drawings. Finally, Section 5 presents the main conclusions of this study. Jean Tarde (1651-1636 was born in La Roque-Gageac (France; 44 • 49 N, 1 • 11 E). Tarde earned his doctorate in law at the University of Cahors and continued his studies at the University of Paris (Saridakis, 2014). He held different religious positions throughout his life. He was ordained as a priest and moved to the parish of Carves. Later, he was promoted to canon theologian of Sarlat's cathedral, and then the bishop of Sarlat appointed him vicar general in 1594. Moreover, Tarde became a member of the Conseil du Roi (Dujarric-Descombes, 1971). Regarding his scientific career, he carried out studies in several disciplines, including mathematics, physics, and geography (Baumgartner, 1987). Tarde was interested in sunspots and was in contact with contemporary astronomers such as Galileo and Grünberger. In fact, Tarde visited them in Italy in 1614. Thereafter, he returned to Sarlat (44 • 53 N, 1 • 13 E) in 1615 and constructed a small observatory. His main scientific work was on sunspots. Tarde published his study on sunspots in the book Borbonia Sidera in Latin (Tarde, 1620) and its French translation in Les astres de Borbon (Tarde, 1627).

Jean Tarde and Jan Smogulecki: Two Jesuit Sunspot Observers
Jan Smogulecki (1610Smogulecki ( -1656 was born in Kraków (Poland; 50 • 03 N, 19 • 56 E) (Kosibowiez, 1929;Witkowska, 2009;Roegel, 2011). He studied mathematics and astronomy in Freiburg and philosophy and law in Italy. When he returned to Poland around 1630, he was elected as mayor of Nakło and a local parliament member. In 1636, he joined the Jesuit order, studied theology in Kraków, and was ordained in Rome in 1641. He declared his intention to be a missionary and was sent to China in 1644. He learned the Chinese language and customs and taught astronomy and mathematics in China. Smogulecki introduced, for the first time in China, the calculation of logarithms to his students. Spreading his fame, he was invited to the Chinese Imperial Court in Beijing. Shortly after this, Smogulecki requested permission to leave the Chinese imperial court to continue his missionary travels. Regarding sunspot observations, he started to observe sunspots at Freiburg (48 • 00 N, 7 • 51 E) when he was only 11 years old in 1621 until the year 1625. Then, under the supervision of his mentor, Georg Schönberger, he published his work on sunspots Sol illustratus (Smogulecki, 1626).

Tarde and Smogulecki's Sunspot Observations
Tarde (1620) published his sunspot observations for the period 1615 -1617 in Borbonia Sidera. In this book, Tarde published six sunspot drawings and textual reports to present his observations. One of them includes all the sunspot groups observed by Tarde on 25 August 1615. The other five drawings include a selection of sunspots among all those observed by Tarde to show some paths of sunspots crossing the solar disc. Two examples are presented in Figure 1 (top panel). Tarde indicated the solar disc orientations by letters A (centre), B (east), C (west), F (north), and G (south). The letters D and E represent the initial and final points of the path followed by each sunspot, and H, I, K, L, and M are letters assigned to the five sunspots that were depicted (Tarde, 1620, p. 32). The numbers included in these drawings indicate the day of the month when the sunspots were observed. The textual descriptions of the drawings were limited to the interval when each sunspot was observed. Tarde probably used the projection method to observe sunspots, as he himself explicitly described it (Tarde, 1620, p. 3). However, we could not find specific details about the observational method nor the sizes of Tarde's telescopes used in his observations. Smogulecki also recorded sunspot drawings and textual reports to describe his observations. In his drawings, he recorded the groups to show their paths on the solar disc. Sometimes, he also recorded a selection of groups based on his observations. Figure 1  interpretation is sometimes challenging, because Smogulecki used the term "star" to design both individual sunspots and sunspot groups. For example, on 22 August 1625, the following observation was made (Smogulecki, 1626, p. 43): "(English translation) 22 August. Two stars. That above the Ecliptic was composed by many." We also detected some discrepancies between the observational period indicated in one of his drawings and the information recorded in the textual report, namely, in the middle-left of his drawings, Smogulecki indicated that the observation period of the sunspot "a" located in the northern hemisphere started on 30 May 1625 (Smogulecki, 1626, p. 45). However, in the annotations, he wrote that sunspot "a" (in the northern hemisphere) was observed for the first time on 1 June 1625, such as another sunspot recorded by Smogulecki in the southern hemisphere also named sunspot "a". Moreover, Smogulecki (1626, p. 47) indicated that he had an optimal tube of eight spans in length (approximately 1.8 m, see Cardarelli, 2003), whereas we could not find any information regarding his observation methods. Smogulecki indicated that he made many more sunspot observations in other months and years. Nevertheless, he only published a part of them in Sol illustratus. One of the reasons for this was that it was enough for his purpose, and moreover, as indicated by him, a complete work on sunspots was about to be published in Rome (he probably referred to Rosa Ursina by Christoph Scheiner) (see Smogulecki, 1626, p. 47).
Tarde and Smogulecki explained some facts related to sunspots from their observational experience. According to Tarde: i) sometimes, only one sunspot can be seen on the Sun, and sometimes multiple sunspots can be seen (Tarde indicates that he counted 30 spots on 25 August 1615); however, there are no sunspots on the Sun for many days (Tarde pointed out that no sunspots appeared on the Sun during an entire month, but unfortunately he did not specify when it occurred); ii) it is possible that some sunspots can return to the solar disc after rotating on the other solar hemisphere (with different shapes), and they can be used to describe periodic motions that had not been analysed yet; iii) sunspots are not clouds or something similar but "stars" composed of opaque and non-transparent matter; iv) many sunspots are surrounded by filaments that are partly whitish and blackish; and v) these sunspots describe a uniform motion in a straight line, parallel to the Ecliptic and from the East to the West. Some of the interesting conclusions provided by Smogulecki that he deduced from his observations were the following: i) sunspots take around 12 -14 days to cross the solar disc and move regularly and circularly, slower in motion when next to the limbs and faster around the disc centre, where they also seem bigger; ii) sunspots furthest from the Ecliptic cross the solar disc faster than those located close to the Ecliptic; iii) the path crossing the solar disc is not parallel to the Ecliptic, as assumed by some observers; iv) very few sunspots are perfectly round and they frequently have irregular shapes; v) the outline of almost all sunspots is a duller black than in the centre, and vi) some sunspots have a size equivalent to the Earth's radius (note that Smogulecki underestimated the relative size of the Sun with respect to the Earth since he recorded that the Sun diameter was equivalent to around only eleven Earth radii).
We now know that some of these conclusions were erroneous. However, despite this and their thought that sunspots were "stars" or "planets" orbiting the Sun, these astronomers demonstrated themselves to be rigorous observers, recording everything that they observed. The English translations from the original Latin texts of the reports made by Tarde and Smogulecki can be consulted on the website of the Historical Archive of Sunspot Observation (haso.unex.es).

Sunspot Group Numbers
Tarde and Smogulecki's sunspot records were previously analysed by Wolf (1859a, 1859b) and Hoyt and Schatten (1998) and then incorporated into the revised database of V16 without any change. In the latest database, the number of observational days assigned to Tarde is 69 for the period 25 March 1615 -6 June 1617 and that for Smogulecki is 82 for the period 5 October 1621 -1 November 1625. Thus, Tarde's sunspot observations are located in the declining phase of the first solar cycle of the telescopic era and those from Smogulecki in the rising phase and the maximum of the second solar cycle. Figure 2 shows these records. Although we acknowledge that these are not a significant number of observations, Tarde and Smogulecki were two of the most active sunspot observers of their time. In fact, Tarde was the most active observer regarding his observation interval, followed by Saxonius (12 records) and Scheiner (5 records). Moreover, no other astronomers carried out observations on any of Tarde's observational days. In the case of Smogulecki, he was the second most active sunspot observer during his observing period. Only Scheiner recorded observations over more days in this interval (372 records). The other astronomers who made sunspot observations during this observation period were Malapert (17 records) and Hortensius (2 records (Tarde, 1620, pp. 33 and 35 -37). The five sunspot groups represented in Tarde's five drawings were selected by Tarde from all the sunspot groups that he observed to explain his sunspot observations (see Tarde, 1620, p. 32). Therefore, Tarde's descriptions indicated that not all the observed sunspot groups on those observation days could have been recorded in the drawings. Tarde (1620, p. 37) only indicated in the drawing for the period 27 May -6 June 1617 that the sunspot group represented in that drawing was the only one observed on the Sun during those days. Therefore, the number of groups for 27 and 28 May 1616 should be corrected in future versions of the sunspot-group number database and those for the periods 17 -27 November 1615, 3 -14 March 1616, 16 -27 April 1616, and 17 May -6 June 1616 should be removed, as they only indicate the lower limit of the sunspot-group number for those dates. Regarding Tarde's sunspot drawing on 25 August 1615 (Tarde, 1620, p. 24), there are two observations in V16 assigned to Tarde related to this record. One of them includes a misinterpretation of the date of observation because ten groups were recorded by Tarde on 25 March 1615 (i.e. just five months before the real date of observation: 25 August 1615). Thus, this record should be removed from the database as well. The other record indicates that five groups were observed by Tarde on 25 August 1615. Unlike V16, we counted nine different sunspot groups for that day (Figure 1, top-left panel).
In the case of Smogulecki, the most significant problem detected was related to the number of groups observed by Smogulecki in the period 5 -11 October 1625 (up to eight and nine groups in V16). Regarding all of the observers in V16, the second highest number of sunspot groups recorded during the second solar cycle of the telescopic era (in the 1620s) was nine groups by Smogulecki (the highest was ten groups observed by Scheiner on 4 July 1625). First, it seems that V16 misinterpreted the observational year of these records as 1625, unlike the actual observation year of 1621. In addition, the number of sunspot groups assigned to Smogulecki in V16 for those wrong dates was actually the number of individual sunspots. Therefore, there were two groups on 5 and 6 October. Subsequently, only one sunspot group was recorded on 9, 10, and 11 October. Furthermore, Smogulecki did not record his sunspot observations on 7, 8, and 12 October 1621, unlike what was described in V16.
We found five days of Smogulecki's sunspot observations (2 and 3 November 1621 and 2, 3, and 12 February 1622) that were overlooked in V16, whereas we found nothing for Tarde's sunspot observations. In contrast to V16, we counted a different number of sunspot groups in one record for Tarde (25 August 1615) and discarded 57 days of Tarde's records, where it is not possible to know the real number of the observed sunspot groups. Regarding Smogulecki's data, we removed 18 days of the misinterpreted observations included in V16, because Smogulecki did not provide any information on sunspots on those dates. Moreover, we corrected the number of groups determined for the other 25 days. It was not possible to determine the number of groups on 17 observation days because of a lack of information. Therefore, the revised numbers of observation days for Tarde Table 1 lists the differences between the sunspot group counting made in this work and that in V16. Carrasco et al. (2021) have recently revised the sunspot observations recorded by Scheiner (1630Scheiner ( , 1651 in his books Rosa Ursina and Prodomus for the period 1611 -1632 correcting significant problems in the number of groups related to those observations in V16. Figure 3 Table 1 Differences between the sunspot-group counting in this work and that in V16. The first column indicates the observation period or date, the second column gives information on the astronomer (Tarde -TAR, Smogulecki -SMO) responsible for the observation, the third and fourth columns provide the number of groups according to V16 and this work and the fifth column includes the explanation of the differences in the number of groups between this work and V16. The two final rows contain the number of observation days assigned to Tarde and Smogulecki in V16 and,in brackets,from   same observation day on 24 dates ( Figure 4). Scheiner recorded a larger number of groups than Smogulecki on 10 days, the number of groups recorded by both observers was equal on 13 days and Smogulecki only observed more groups than Scheiner on 10 August 1625 (2 versus 1). Moreover, the averages of the number of recorded sunspot groups in the common observation days from Smogulecki's data and Scheiner's data are 2.5 and 3.1, respectively, i.e. Scheiner systematically recorded approximately a quarter more sunspot groups than Smogulecki. In addition, Schönberger recorded one group for the period 30 April to 3 May 1624 according to Carrasco et al. (2021), whereas Smogulecki recorded two groups on 30 April and three groups on the remaining dates.
Smogulecki observed a great sunspot on 2 and 3 February 1622. He recorded the following information on this sunspot (Smogulecki, 1626, pp. 47 -48): "(English translation) The spot represented by the letters 'X' and 'Y' [see sunspot 'Y' depicted between the sunspot drawings of Figure 1, bottom panel] was the only one observed in 1622. I could observe it here in Freiburg, but also Father Adam Tanner and Johann Baptist Cysat in Ingolstadt. It was certainly exceptional in size since its longitude was equivalent to one thirteenth of the solar diameter and its latitude, in its most voluminous part, was equivalent to one twenty-fourth of the solar diameter. Thanks to the tube, we have distinguished its inner shape on 2 (as it is represented in the image 'Y') and 3 February 1622 (as it can be seen in the image 'X'). This spot had inside very black corpuscles as all those that generally take that form, and they were surrounded by a more tenuous matter. All these corpuscles recorded on the paper represented the figure of a single star or a very black spot that occupied the thirteenth part of the solar diameter. It moved below the Ecliptic, and during those days when it was close  to the centre of the Sun, it was composed of seven tiny stars arranged in a 'V' shape not surrounded by any cloud. This set reached a larger size the next day [February 3rd]; after that day, neither this spot nor the other large one could be seen because the sky was never clear at any time. On 12 February, when it was clear again, nothing else could be seen in the Sun with the tube." Thus, Smoguleki recorded a sunspot whose projected area on the solar disc was approximately one-thirteenth in longitude of the solar diameter and one twentyfourth in latitude. If we assume an elliptical shape, we can estimate its projected area as A = π a b, where a and b are the semi-axes of the ellipse. Thus, this sunspot occupied a projected area of approximately 1600 millionths of the solar disc. Furthermore, candidate auroras were sighted in multiple European sites even down to Switzerland on 3 February 1622 (Abelinus, 1746, p. 619;Link, 1964, p. 514). Therefore, this great sunspot recorded in Smogulecki's account could have been responsible for the mid-latitude auroras and a plausible geomagnetic storm on 3 February 1622. It is known that the Sun can cause significant geomagnetic storms even during low solar activity (Garcia and Dryer, 1987;Hayakawa et al., 2020;Silverman and Hayakawa, 2021). As such, despite its location in the early rising phase of the solar cycle of the 1620s, this active region could be associated with a significant geomagnetic storm, as found in parallel cases.

Sunspot Positions from Tarde's and Smogulecki's Drawings
We calculated the sunspot positions in Tarde's and Smogulecki's sunspot drawings. In this study, we used Soonspot, a program created to calculate sunspot positions and areas (Galaviz et al., 2019). Areas were not computed in this work because both observers represented the sunspot groups as simple dots (see Figure 1).
We defined the sunspot groups in Tarde's and Smogulecki's records for the period 1615 -1625 and calculated the latitudinal average of each group over time. Since the observation by Tarde on 25 August 1615 was made at noon, we assume that the orientation of the drawing is based on the Earth's axes. Moreover, we assume that the orientation of both Tarde's and Smogulecki's sunspot drawings are according to erect images. All latitudes obtained in this work are represented by green (Tarde) and yellow (Smogulecki) in Figure 5 Mogling's drawings. Thus, we calculated the latitudes for 14 sunspot groups recorded by Tarde and another 14 groups using Smogulecki's records. Nine of the 14 sunspot groups in Tarde's records were in the northern hemisphere and five in the southern hemisphere. The group furthest from the solar Equator was recorded at −29.8 • , and six groups appeared at latitudes between −10 • and +10 • , according to Tarde's records. The sunspot positions computed in this work from Tarde's observations are the only calculations of the sunspot positions available in that period. Regarding Smogulecki's data, eight groups were recorded by this observer in the southern hemisphere and six in the northern hemisphere. The group with the highest latitude was located at −33.0 • , and only one group was recorded near the solar Equator between −10 • and +10 • . The latitudes calculated in this work from Smogulecki's records are similar to those computed by Arlt et al. (2016) from Scheiner's drawings on the same dates, which are depicted by small blue dots in Figure 5.

Conclusions
We have revised the sunspot observations made by Tarde in 1615-1617and Smogulecki in 1621-1625. These astronomers published their observations in the books Borbonia Sidera and Sol illustratus, respectively. In their documentary sources, these observers recorded both sunspot drawings and textual reports to explain their observations. In their drawings, Tarde and Smogulecki sometimes recorded only some of the groups that they observed on the same day. This has led to misinterpretations of these records in existing databases (Hoyt and Schatten, 1998;Vaquero et al., 2016). In this study, we identified these problems and provided a revised group counting. We acknowledge that the number of observations made by these observers does not have a large observational coverage, but they are important because most of their records are the only ones available of sunspot records on those observing dates.
We compared Smogulecki's sunspot observations to those of other observers at that time. For example, we found that Scheiner recorded an average of approximately a quarter more groups than Smogulecki. Smogulecki also recorded an exceptionally large sunspot group on 2 -3 February 1622. Based on his descriptions, we estimated its area to be 1600 millionths of the projected area of the solar disc. In addition, we calculated the sunspot latitude of the sunspot groups in Tarde and Smogulecki's records. No sunspot latitude is available from previous reconstructions of the butterfly diagram fot the years when Tarde conducted observations. The latitudes computed from Smogulecki's data were similar to those obtained by other observers on the same observation days. The group counting and sunspot positions obtained in this work and the English translation from the original texts will be publicly available on the website of the Historical Archive of Sunspot Observation: haso.unex.es.

Disclosure of Potential Conflicts of Interest
The authors declare that they have no conflicts of interest.
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