Libration of the Moon,Hevelius's Theory,and its Early Reception in England

See Kozieł K. , “Libration of the Moon”, in Kopal Z. (ed.), Physics and astronomy of the Moon (New York and London, 1962), 27–59, pp. 27–9; Kopal Z. Carder R. W. , Mapping of the Moon: Past and present (Dordrecht, 1974), 50–3.

The journals of Leonardo da Vinci contain well-preserved drawings of the lunar disk, originating from 1505–8 and 1513–14, with the dark spots portrayed fairly accurately; see Reaves G. Pedretti C. , “Leonardo da Vinci's drawings of the surface features of the Moon”, Journal for the history of astronomy , xviii (1987), 55–8. Also preserved are Leonardo's notes, in which he mentions that careful observations of the dark spots on the Moon reveal that the spots undergo changes (ibid., 57). It appears however that this remark does not refer to the phenomenon of libration, of which Leonardo was not a conscious observer, but rather to the effects associated with the variable illumination of the Moon, since in another passage he states: “… the spots on the Moon, as they are seen at full moon, never vary in the course of its motion over our hemisphere”; see Whitaker E. A. , Mapping and naming the Moon: A history of lunar cartography and nomenclature (Cambridge, 1999), 9.

Idem, “Selenography in the seventeenth century”, in Taton R. Wilson C. (eds), Planetary astronomy from the Renaissance to the rise of astrophysics. Part A: Tycho Brahe to Newton (Cambridge, 1989), 119–43, pp. 121–2. The famous telescopic observations of the Moon, carried out by Harriot, extended over a period from July 1609 until October 1612. His map of the full moon — A feather drawing, with a diameter of about 15cm — Most likely originates from 1611. See Shirley J. W. , “Thomas Harriot's lunar observations”, in Hilfstein E. Czartoryski P. (eds), Science and history: Studies in honor of Edward Rosen (Studia Copernicana, xvi; Wrocław, 1978), 283–308. One needs to add that in England Harriot had a predecessor in William Gilbert, who around the year 1600 drew a map of the lunar disk (about 28cm in diameter; based on observations with the naked eye) and proposed as many as thirteen names for the dark and light regions of the Moon. See Whitaker , Mapping and naming the Moon (ref. 2), 10–15. Recently Stephen Pumfrey showed that William Gilbert did notice the optical libration of the Moon with the naked eye before Thomas Harriot: See Pumfrey S. , “The Selenographia of William Gilbert: His pre-telescopic map of the Moon and his discovery of lunar libration”, Journal for the history of astronomy , xlii (2011), 193–203. However, still there is no evidence that Gilbert's discovery made any impact on seventeenth-century selenographers.

Knowledge of their existence was popularized in 1785 by von Zach F. X. , through publication in the Berliner astronomisches Jahrbuch für das Jahr 1788. A modest collection of prints, along with the above-mentioned map, was for the first time published in Strout E. , “The very first maps and drawings of the Moon”, Journal of the British Astronomical Association, cxxv (1965), 100–5.

Whitaker , op. cit. (ref. 2), 37–8.

The Latin text of the legend has been transcribed by Van de Vyver O. S.J. , “Lunar maps of the XVIIth century”, Vatican Observatory publications, i (1971), 69–83, pp. 82–3.

Whitaker , op. cit. (ref. 2), 44–5 (four copies of the van Langren map have been preserved). The works of Claude Mellan (1598–1688) also point to the fact that libration in latitude in particular accounted for the significant errors on the early maps and drawings of the surface of the Moon. This French artist, having conducted selenographic observations under the eyes of Pierre Gassendi (1591–1655) and Nicolas de Peiresc (1580–1637), presented a map of the full moon early in 1637. It had to have been produced on the basis of two different maps — Of the waxing and of the waning moon — Since the left part of the map clearly corresponds to a different libration in latitude than the right (ibid., 34). Righini in turn attempted to prove that in two illustrations of the Moon (in the first and the last phase) included in Galileo's Sidereus nuncius, the auspicious crater visible on the terminator line had been drawn at various values of libration in latitude; see Righini G. , “New light on Galileo's lunar observations”, in Bonelli M. L. Righini Shea W. R. (eds), Reason, experiment, and mysticism in the Scientific Revolution (London, 1975), 59–76, pp. 72–4. Yet, as was observed by Whitaker, other features of the surface, which can be identified in both prints, contradict this conclusion; see Whitaker E. A. , “Galileo's lunar observations and the dating of the composition of Sidereus nuncius”, Journal for the history of astronomy , ix (1978), 155–69, p. 164.

Drake S. , Galileo at work: His scientific biography (New York, 1995), 311.

It is worth noting that a reference to the geometric conditions responsible for libration in latitude can be found as early as in Johannes Kepler's Book IV of the Epitome astronomiae Copernicanae (Frankfurt-am-Main, 1620). However, Kepler makes this comment in passing, without analysing the phenomenon. See Włodarczyk J. , “Kepler's Moon”, in Kremer R. L. Włodarczyk J. (eds), Johannes Kepler: From Tübingen to Żagań (Studia Copernicana, xlii; Warsaw, 2009), 119–29, p. 124.

Galileo , Dialogue concerning the two chief world systems, Ptolemaic and Copernican, transl. by Drake S. , 2nd rev. edn (Berkeley, Los Angeles and London, 1967), 65.

Ibid ., 66–7. Galileo most likely had in mind formations known today as Mare Crisium and Grimaldi; see Righini , op. cit. (ref. 7), 62.

Galileo , op. cit. (ref. 10), 66. This is a reference to parts of the Moon's orbit farthest to the north and to the south from the ecliptic.

See Kopal Carder , op. cit. (ref. 1), 58.

See Righini , op. cit. (ref. 7), 62.

Among works discussing this well-known problem occurring in Ptolemaic astronomy is Gabbey A. , “Innovation and continuity in the history of astronomy: The case of the rotating Moon”, in Barker P. Ariew R. (eds), Revolution and continuity: Essays in the history and philosophy of early modern science (Washington, D.C., 1991), 95–129, pp. 115–20.

Galileo , op. cit. (ref. 10), 65.

Ibid., 462. This third argument, or more precisely the way it was used by Galileo, came to be the source of a long-standing debate among historians of science. The most important recent studies on the topic include: Smith A. M. , “Galileo's proof for the Earth motion from the movement of sunspots”, Isis , cxxvi (1985), 543–51; Hutchinson K. , “Sunspots, Galileo, and the orbit of the Earth”, Isis , cxxxi (1990), 68–74; Topper D. , “Galileo, sunspots, and the motion of the Earth: Redux”, Isis , xc (1999), 757–67; idem, “‘I know that what I am saying is rather obscure…’: On clarifying a passage in Galileo's Dialogue”, Centaurus, xlii (2000), 288–96; Mueller P. M. S.J. , “An unblemished success: Galileo's sunspot argument in the Dialogue”, Journal for the history of astronomy , xxxi (2000), 279–99; Topper D. , “Colluding with Galileo: On Mueller's critique of my analysis of Galileo's sunspots argument”, Journal for the history of astronomy , xxxiv (2003), 75–7; Gingerich O. , “The Galileo sunspot controversy: Proof and persuasion”, Journal for the history of astronomy , xxxiv (2003), 77–8.

Galileo , op. cit. (ref. 10), 347.

Copernicus N. , On the revolutions, ed. by Dobrzycki J. , transl. and commentary by Rosen E. (Warsaw and Cracow, 1978), 22–5.

Galileo , op. cit. (ref. 10), 398–9.

Ibid., 410–11.

Boulliau I. , Astronomia Philolaica (Paris, 1645), 178–9. One can surmise that this argument was the consequence of Boulliau's rejection of Kepler's model illustrating the Sun's physical effect upon the planets by way of quasi-magnetic infuence, because this would require the “magnetic axes” to have a fixed position in space; ibid., 22–4.

Le opere di Galileo Galilei: Edizione nazionale , ed. by Favaro A. (Florence, 1890–1909), xvii, 214–15. English translation from Drake, op. cit. (ref. 8), 385; cf. also Righini , op. cit. (ref. 7), 62–3.

Le opere di Galileo Galilei (ref. 23), xvii, 291–6.

Ibid., 215; English translation from Drake, op. cit. (ref. 8), 385. Although W. R. Shea interpreted this fragment to mean that Galileo had abandoned the tidal ebb-and-flow model, in which the Moon played a marginal role, for theories based predominantly on the influence of the Moon (see Shea W. R. , Galileo's intellectual revolution (London, 1972), 186), Drake's reading of the same fragment seems more plausible, cf. Drake , op. cit. , 503, n. 13.

Hevelius J. , Selenographia: Sive, Lunae descriptio (Danzig, 1647), Figure P (between pp. 222–3), Figure Q (226–7) and Figure R (262–3).

Ibid., 236–9.

Ibid., 80.

Van de Vyver , op. cit. (ref. 6), 71–2; Whitaker , Mapping and naming the Moon (ref. 2), 25–33.

Hevelius , op. cit. (ref. 26), 435–8. Gassendi's observations used by Hevelius were later published in Gassendi P. , Opera omnia (Lyon, 1658), iv, 355–65.

Hevelius , op. cit. (ref. 26), 242. For detailed description of the grid see below.

Ibid., 409–11.

Ibid., 438–9.

Hevelius J. , Epistolae II. Prior: De motu Lunae libratorio … (Danzig, 1654). This letter was also reprinted in much rarer publication: idem, Epistolae IV (Danzig, 1654).

Riccioli G. B. , Almagestum novum, Part 1 (Bologna, 1651), 214–15.

Ibid., Figure 6 after p. 204.

Riccioli presented his theory of the Moon, together with the numerical parameters, on pp. 279–80 of Almagestum novum (ref. 35).

The relation between orbital eccentricity and the angle of libration in longitude will be included and explicitly discussed in the description of Hevelius's model (see Figure 9, below).

Hevelius , op. cit. (ref. 34), 3 and 46.

All the results of Grimaldi's observations used by Hevelius were published also in Almagestum novum (ref. 35), 211.

Hevelius , op. cit. (ref. 34), 25–35.

Ibid., 24.

Ibid., 6.

Ibid., 7–8.

Ibid., 14–17.

Ibid., 18.

Gian Domenico Cassini, who in the 1680s was the first ever to determine through observation the inclination of the lunar equator towards the ecliptic, obtained a result over half a degree greater than the actual value. It was not until the mid-1700s that a result closer to the true value was obtained by Tobias Mayer. See, e.g., Grant R. , History of physical astronomy (London, 1852), 73.

Looking at the proportions of the matrix, one can see that relative to the degree of libration in latitude, the degree of libration in longitude was underestimated.

Hevelius's libration values were transferred to a rectangular coordinate system, representing selenographic longitude and latitude (this transformation had little effect on the shape of the curves, since the coefficient used was the cosine of 17.5^o = 0.95); the range of variation within both librations was scaled to match the actual values.

Hevelius , op. cit. (ref. 34), 46–8.

Turnbull G. H. , “Samuel Hartlib's infuence on the early history of the Royal Society”, Notes and records of the Royal Society, x (1953), 101–30, p. 114.

Museum British , ms. Add. 25,071, ff. 92–3. Quoted after Bennett J. A. , “A study of Parentalia, with two unpublished letters of Sir Christopher Wren”, Annals of science , xxx (1973), 129–47, p. 147. There are strong indications that during their observations of the Moon in Oxford, Wren and Hooke used a prototype of micrometer; cf. idem, The mathematical science of Christopher Wren (Cambridge, 1982), 39–40.

Bennett J. A. , “Christopher Wren: Astronomy, architecture and the mathematical sciences”, Journal for the history of astronomy, vi (1975), 149–84, p. 164.

Sprat T. , The history of the Royal Society of London (London, 1667), 315; Wren S. , Parentalia; or, Memoirs of the family of the Wrens (London, 1750), 198.

Birch T. , The history of the Royal Society of London (London, 1756–57), i, 21.

Letter written by Henry Oldenburg to Christiaan Huygens on 7 September 1661. Quoted after The correspondence of Henry Oldenburg, ed. by Hall A. R. Hall M. B. (Madison, 1965–86), i, 422.

Bennett , The mathematical science (ref. 53), 40. The issue of Wren's lunar globe was still being discussed at meetings of the Royal Society in 1667, cf. Birch , op. cit. (ref. 55), ii, 156, 160.

Hooke R. , Micrographia (London, 1665), 246.

See Gabbey , op. cit. (ref. 15), 97–9.

In modern literature, this discussion is presented in: ibid., 99–104.

Mercator N. , Institutionum astronomicarum libri duo (London, 1676), 286.

“5 circiter gradibus … in limbo Lunae computandis” (ibid.); “ad quinque circiter grad. in limbo Lunae numeratos” (Hevelius, op. cit. (ref. 34), 41).

“hypothesis elegantissima”. Mercator, op. cit. (ref. 61), 286.

In his discussion, Gabbey (ref. 15) considers the actual configuration, determined later (see ref. 47), in which the Moon's equator does not overlap with the ecliptic, but is inclined towards it. The depiction of this in Figure 2 of Gabbey's article differs from Mercator's description.