Fig. 1. Sunspot drawings and engravings from 5 to 9(!) May 1684: (a–f) from La Hire (1683 – 1684) and (g) Le Monnier (1741). For details Zolotova and Vokhmyanin (2025).
Observations by Philippe de La Hire
Philippe de La Hire (1640–1718) was a French painter, mathematician, an observational astronomer, and a key figure in the French Academy of Sciences. Here, we consider La Hire’s hand-written observational journals stored in the Bibliothèque de l’Observatoire de Paris.
Journal from 25 January 1683 to 10 October 1684
The first 194-page journal was also published as a part of Le Monnier (1741). We analyze both sources. In total, 313 measurements of the solar limb passages and 269 midday altitude measurements were reported. A typical observation provides the time between a solar limb and a midday altitude measurement. The observation days in La Hire's journals coincide with the spotless days according to the sunspot-group-number tables (based on La Hire's observations) in Hoyt and Schatten (1998) database. Presumably, Hoyt and Schatten assumed that the observer also saw the passage of sunspots, if there were any on the disk, while measuring the passage of solar limbs.
The journal also provides measurements of the Sun's altitude in the morning and evening hours and notes on the accuracy of the pendulum. Solar observations are mixed with numerous reports on the passage of other celestial bodies: the Moon, Jupiter with its satellites, Saturn, Mercury, Venus, Mars, Sirius, Regulus, Arcturus, the Pole star, the brightest stars of Leo, and etc. The Sun was observed through a telescope equipped with a micrometer and the passage of a sunspot through a system of wires was measured by a pendulum and a chronicle. More about observational techniques and instruments can be found in Ribes and Nesme-Ribes (1993) and Boistel (2004).
Figure 1 illustrates several original sunspot images from the journal on scale. Figure 1a shows a small sketch of a sunspot on a poorly drawn solar disk. Figure 1b shows a modified image (resized, reversed, and flipped) with the heliographic grid corresponding to the equatorial mount of a telescope. According to the sketch, this sunspot appeared in the northern hemisphere, while the sunspot position measurements placed this active region in the opposite hemisphere. In this work, we therefore do not rely on such schematic drawings to reconstruct sunspot coordinates.
Figure 1(c – f) shows the sunspot group from 5 to 8 May (or supposedly 9 May 1684). The journal also contains a tracing paper from the image on 7 May, probably prepared for engraving. Figure 1g shows the same sunspot on 5 and 8 May engraved in Le Monnier (1741). Drawings and engravings are somewhat different, hence they could have been based on other drawings. Le Monnier (1741) also contains sunspot drawings from 1 to 9 July 1684 differing slightly from those in La Hire (1683 – 1684).
Fig. 2. (a – d) Sunspot position derived from the measurements by La Hire (1683 – 1684) from 5 May to 28 July 1684. Reliable data are represented by filled circles, whereas unreliable and incomplete data are shown as unfilled circles and annular sectors. The heliographic grids correspond to the equatorial mount. (d) Sunspot longitudes and rotation rate (Zolotova and Vokhmyanin 2025).
Figure 2(a – d) shows the sunspot positions aligned with the rotation axis according to the measurements made by La Hire (1683 – 1684) on 5 May to 28 July 1684. There are two measurements at midday on 6 May that determine the sunspot position in the horizontal plane, giving two possible sunspot locations. We mark a more reliable position with a filled circle. The electronic supplementary material includes two versions of the derived sunspot parameters.
On 11 – 12 June 1684, the sunspot group consists of leading and trailing parts, which we schematically illustrate with linked circles (Figure 2a).
For the entire time interval, midday observations yield an average sunspot latitude of −9.8 ± 1.4o. Note that referring to Cassini's publications in Mémoires, Spoerer (1889) gave the following estimates for the latitude of this sunspot: −11o from 5 to 17 May, −10.8o from 28 June to 9 July, and −9o from 26 to 28 July 1684.
Figure 2(e) illustrates the derived longitudes. Based on the most reliable observations (filled circles, which were usually made at midday, and when the sunspot was far from the limb), we determine that the rotation rate was 14.1 ± 1o d-1 between 7 and 9 May, 14 ± 1o d-1 between 11 and 12 June, and 14.2 ± 1o d-1 between 26 and 28 July. The uncertainty is large for such short time measurements of one or two days apart. The average rotation rate between adjacent observations (i.e., the average of all rotation rates between two adjacent observations) from 29 June to 7 July is ⟨V●⟩ = 14.3 ± 0.9o d-1 and the mean rotation rate (the rotation rate between the distant measurements) is V[29Jun−7Jul] = 14.5 ± 0.2o d-1.
Similarly to Flamsteed, we also calculate the rotation rate assuming a recurrent activity nest. The mean rotation rates are determined to be V[9May−11Jun] = 14.3 ± 0.1o d-1, V[12−29Jun] =14.5 ± 0.1o d-1, and V[7−26Jul] =14.2 ± 0.1o d-1. Overall, in Figure 2 (e), the longitude gradually increases, indicating that the active region rotated faster than the sidereal Carrington rotation at 14.2 − 14.5o d-1 aligning well with the measurements by Flamsteed.
Fig. 3. Visualization of sunspot transits reconstructed from the measurements and sunspot drawings by La Hire (1683 – 1684). Yellow denotes faculae. Black circles indicate objects with the size of 30'' and 40''. The orange sunspot out of the solar disk reproduces the horizontally and vertically mirrored sunspot engraving from the Journal des Sçavans (1684). For details Zolotova and Vokhmyanin (2025).
Observations in the morning hours in La Hire (1683 – 1684) are usually accompanied by sunspot drawings. By reversing and flipping these drawings and combining them with the measurements, we present our assumption of the active regions t