Observations by Thomas Harriot
Thomas Harriot (1560–1621) is the English astronomer, optician, and mathematician. His manuscripts are stored at Petworth House Archives, West Sussex, UK, while a digital version is provided by ECHO – Cultural Heritage Online. Using Harriot's archive, Herr (1978) estimated the solar differential rotation.
18 Dec 1610 – 28 Jan 1613
At Syon House (just west of London) and in London, Harriot made 200 (plus two repeated) drawings of the solar disc and its spots. Images are accompanied by Julian calendar date, observing conditions, local time, magnifying power of the Galilean type refractors (8/1, 10/1, 20/1, 30/1, and 50/1), number of sunspots, and other information.
Harriot observed through clouds or misty air, and once on 23 December 1611 he mentioned: "I observed through the thick layer & also through my coulored glasses". Harriot commonly exploited the 10/1 and 20/1 instruments; the field of view of the 10/1 instrument was smaller than the solar disc. On 26 July 1612, he noted: "With 20/1 I see a litle more the 1/3 of the diameter of the sonne. That is 11' or 12'. Magnification 8 is mentioned only once on 13 December 1611, and that of 50 once on 10 February 1612. There are a few days when Harriot stated that he observed, but did not see spots.
The method with which Harriot made drawings is not known, but apparently he did not take advantage of the projection apparatus (Bradley et al. 1833 and Chapman 1995, for more details and on the quality of observations, telescope device and eyepieces). Typical images contain a circle of the solar disc with dashed lines likely denoting the zenith and the ecliptic, which are not drawn from 12 July to 12 September 1612.
Drawings were made with a pen and ink. Harriot did not divide sunspots into umbra and penumbra. There are repeating defects (small black spots) on the sheets from May to August 1612. Accordingly, if these defects fell on the solar disc, they were not recognized by us as sunspots.
Figure 1 compares numbers of sunspot groups counted by Hoyt and Schatten (1998) and by Vokhmyanin et al. (2020). Cumulatively, we assigned 12% more sunspot groups. Notice that early drawings are poorly detailed, apparently the result of a hurried manner of looking at the Sun (Mitchell 1916). For this reason, the number of groups prior to June 1612 may be underestimated.
On a few days in 1612, Harriot stated that he observed but did not see sunspots. In the Data, on these days we assigned the sunspot area as NaN (Not-a-Number), because the size of the spots on drawings on previous or next to these days drawings suggests to us that these spots should not have disappeared the next day or have already present on the previous one. Most likely, these spots could have been smaller. For a similar statement by Harriot in 1611, we also assigned the area as NaN. Here, because earlier drawings are quite schematic, hence Harriot might not have recognized small structures.
The smallest sunspot was registered by Harriot on 17 August 1612 (9 msh), and the largest one (1918 msh) on 11 December 1611. The smallest sunspot group was registered on 22 July 1612 (20 msh), and the largest one (4088 msh) on 3 May 1612 (Figure 2a and b). In more detailed observations by Galilei in May – August 1612 by means of the projection apparatus, the same sunspot group on 3 May is also the largest with area 3898 msh.
Fig. 2. (a) and (b) are examples of Harriot's drawings. Red ovals mark the smallest and largest sunspot groups G138 and G66 correspondingly; (c) shows the probability density functions of the sunspot group area from Harriot's drawings (blue) and three 14-month periods of the RGO/USAF/NOAA catalogue (Vokhmyanin et al. 2020).
Figure 2c shows the distributions of sunspot group area by Harriot with blue bars and modern observations in magenta, orange, and green. The majority of Harriot's drawings cover a 14-month period from December 1611 to January 1613. From the modern observations, we chose three periods of the same length with the largest medians of the sunspot group area distribution (May 1874 – June 1875, April 1946 – May 1947, and April 1957 – May 1958). Namely, we compare historical observations with those periods of Greenwich observations, when the highest percentage of large groups of sunspots was recorded. We use the distribution of areas divided by the total number of groups, since there are less sunspot groups in the 14-month interval of Harriot's observations than in the Greenwich catalogue on the corresponding time interval.
Interestingly, the beginning of the Greenwich catalogue is the one closest to Harriot and is the poorest period in the RGO coincidentally. Also, Figure 2c demonstrates that Harriot's reports have a lack of small sunspot groups with an area less than 60 msh which in turn make up 45% of all groups in the Greenwich catalogue.
To evaluate the accuracy of the sunspot area drawing, we compared sunspot areas from repeated drawings made by Harriot on 22 February and 21 August 1612. Area differences vary significantly, especially for small spots. The average uncertainty is about 30%. A more accurate estimate of the area error might be given after comparing the drawings made by different observers.
Figure 3 shows the latitude–time diagram from December 1611 to January 1613 reconstructed be means of Method I (red crosses) and Method II (blue circles). Ideally, sunspot position and other parameters have to be close in these two methods. However, differences in sunspot latitudes occasionally exceed 10o. We also would like to emphasize that the near-equator region is usually spotless, while observations by Scheiner from October 1611 to January 1612 demonstrate equator occupancy. The latter are likely due to the poor quality of Scheiner's early drawings (Arlt et al. 2016).
Fig. 3. Latitude–time diagram from December 1611 to January 1613 reconstructed by two methods (Vokhmyanin et al. 2020).
Figure 4 compares results of two methods. The rotation angle Rot or the angle between solar axis and zenith direction is shown. Light blue lines mark daily limits of P−q angle (difference of the position and parallactic angles, see Heliocoordinates). 62 blue circles, which corresponds to Method II, are located out of these limits. The largest deviation occurred in the second half of May 1612 and amounts to 24o.
Fig. 4. Red crosses and blue circles define the rotation angle of an image (a), the observation time (b), the average dispersion of all sunspots on a drawing from their average latitudes (c), all calculated by Methods I and II, correspondingly. Light blue curves mark P−q limits when the Sun is above horizon. Black curves denote time of sunrise and sunset (Vokhmyanin et al. 2020).
Figure 4b shows the local time of the observations obtained by the two methods. Black curves mark the times of sunrise and sunset. Harriot usually observed in the morning hours. The differences in time of the two methods increases in warm months. Here, there are 62 circles fewer (Method II) than crosses (Method I), because the rotation angle does not match with the Sun being above the horizon. Here, we would like to emphasize that Method II itself is not aimed to precisely define the time of observation, but gives the best image rotation to define an average picture of spot positions.
Figure 4c depicts the daily average dispersion of sunspots from their average latitudes. Since spots observed on only one day gave zero dispersion, we excluded them from the figure. In the cold months, the scatter of both methods usually does not exceed 2–3o. In the warm season, the average dispersion according to Method I varies up to 6o, and only on 30 July 1612 jumps to almost 10o. The latitude scatter of Method II rises to 4o, but generally does not exceed 2o. The latter seems less than the actual plotting accuracy by Harriot, and hence Method II may be overfitting because of too much freedom in the parameters. Moreover, in Method I we do not throw away useful information (time of observation reported by Harriot). Therefore, sunspot positions defined by means of Method I could be preferable, but Method II may correct for errors Harriot made, e.g. wrong time or wrong orientation of the disk.
Figure 5 shows the sunspot trajectories (thin black curves) restored according to Methods I and II on 30 July 1612, when the average dispersion of sunspots from their average latitudes jumps to almost 10o in Method I (Figure 4c). Apparently, on this day, the observation time is incorrect. Fortunately, this is the only case.
Fig. 5. Superposition of schematic colored images of Harriot's observations on 29–31 July 1612. Images were derotated according to Method I (a) and Method II (b). The thin black curves schematically mark the trajectories of sunspots, the heliographic grid on 30 July is underlaid (Vokhmyanin et al. 2020).
Figure 6 shows a superposition of derotated drawings of the second half of May 1612, when the rotation angle in Method II deviates most of the daily limits of P−q angle (Figure 4a). Results of the two methods are compared in Figures 6a and b. The colored curves schematically mark the trajectories of several sunspots. During this time period, in Method I sunspots tend to move upwards on the grid, indicating a markable drawing uncertainty. Sunspot trajectories obtained in Method II (Figure 4b) evidently demonstrate minimal variation in latitude, while zenith lines worse match each other, and ecliptic lines are wrongly tilted.
