Fig. 1. Plausible position of the two sunspots based on Boyle's note. Red arc shows the possible latitude-longitude range where the second sunspot could be located (Zolotova and Vokhmyanin 2025).
Observations by Robert Boyle
Robert Boyle (1627–1691) was an Anglo-Irish natural philosopher, chemist, and physicist, best known for Boyle's law.
7 May – 4 June 1660
Cassini (1671) cites notes by Boyle (originally Boyl): "Friday, April 27, 1660 [7 May in the Gregorian calendar], about 8 of the clock in the Morning, there appear's Spot in the lower limb of the Sun a little towards the South of its AEquator, which was entred about 1/40 of the Diameter of the Sun, it itself being about 1/165 [the last digit is poorly printed, but we interpret it as 5] in its shortest Diameter, of that of the Sun; its longest, about 1/40 of the same. It disappear'd upon Wednesday Morning (May 9th) [19 May Greg.] though we saw it about day before about 10 in the morning to be near about the same distance from the Westward limb a little South of its aequator, that it first appear'd to be from the Eastward limb, a little South also of its aequator, It seem'd to move faster in the middle of the Sun then towards the limb. It was a very dark spot almost of a quadrangular form, and was enclosed round with a kind of duskish cloud, much in this form and in this proportion to the Spot [the text is supplemented by a schematic sketch of the sunspot]. We first observ'd this very same Spot both for figure, color and bulk, to be re-enter'd the Sun May 25th [4 June Greg.], when it seem'd to be in a part of the same line it had formerly traced; and was enter'd about 4/33 of its Diameter about 7 of the clock in the afternoon. At the same time there appear'd another Spot, which was just entred and appear'd to be entred not above 1/132 part of the Sun's diameter. It appear'd to be longest towards the North and South, and shortest towards the East and West. There seem'd to be dispers'd about it divers small clouds here and there.". These observations were reported to have been conducted using an excellent telescope.
Using the sketch and measurements provided, we mapped the sunspots onto the solar disk (Figure 1). For the first sunspot (indicated in blue), we arbitrary interpreted the description “a little towards the South of its equator” as −5o in latitude. Since no specific latitudinal constraint was provided for the second active region, we initially assumed its latitude to fall within ±30o. However, considering the reports by Johannes Hevelius (1679), we narrowed the latitude range to ±10o (Figure 1c, red arc). The Electronic Supplementary Materials include the reconstructed sunspot parameters derived from these interpretations (Figure 1). Note that the observations by Boyle and Hevelius share a common group numbering (G). Also note that Boyle referred to the sunspot's umbra as the "spot", while describing its penumbra as a "duskish cloud".
Precise measurements of the first sunspot's position on 7 May and 4 June 1660 yield a sidereal sunspot rotation rate of 14.4 ± 0.1o d-1. This implies that on 18 May 1660 the sunspot was located at approximately 32o in longitude (Figure 1b).
Speculating that the sunspots or sunspot groups could have persisted for seven solar rotations due to weakened convection, we modeled the transit of two objects across the solar disk between February and August 1660. The rotation rate for the first sunspot as previously mentioned, is 14.4 ± 0.1o d-1. For the second sunspot, whose rotation rate is unknown, we applied the rotation law derived by Balthasar, Vazquez, and Woehl (1986): ω(B) = ω0 + 2.87 sin2B, where B represents the heliographic latitude, and ω0 is set to 14.4 ± 0.1o d-1. Continued here...
