“Annulo Cingitur”: The Solution of the Problem of Saturn

Gassendi P. , Opera omnia (Lyons, 1658), iv, 480.

Van Helden A. , “Saturn and his Anses”, Journal for the history of astronomy, v (1974), 105–121.

Clerke A. M. , A popular history of astronomy during the nineteenth century, first ed. (Edinburgh, 1885), 111.

Van Helden , op. cit., 110, fig. 1; 117, fig. 8.

The realisation that Saturn is surrounded by not one but several rings dates from J.D. Cassini's discovery of the division named after him. In order to avoid confusion and anachronism, therefore, I shall treat the two bright rings as one ring in this paper.

I have put the word “seeing” in inverted commas here because seeing a globe also involved mental interpretation. Properly speaking, in the absence of surface markings and shadow effects, observers before about 1660 could only see a disk.

Grant R. , History of physical astronomy (London, 1852), 257.

On 8 March 1656 Huygens wrote to Hevelius: “Only last year did I learn the art of making telescopes, nor do I have earlier observations”. Oeuvres complètes de Christiaan Huygens (The Hague, 1888–1950), hereafter O.C., i, 388.

O.C., xv, 172, 238.

O.C., i, 332, 335. The anagram, Admovere oculis distantia sidera nostris vvvvvvv cccrrhnbqx, is a popular line from Ovid's Fasti. Huygens also inscribed this line (without the supplementary letters) on the objective lens of the 12ft telescope with which he discovered the satellite. O.C., xv, 11.

O.C., i, 392. The solution was: Saturno luna sua circunducitur diebus sexdecim horis quatuor.

O.C., xv, 15, 238, 246.

O.C., i, 380.

Hevelius to Boulliau, 9 December 1659, Bibliothèque Nationale MSS Fonds Français 13043, f. 89v-90r. Wallis to Huygens, 1 January 1659, O.C., ii, 306.

O.C., xv, 176.

Between the construction of his first pendulum clock in December 1656 and the publication of Horologium in September 1658, Huygens made virtually no progress in the preparation of his “System of Saturn” for publication (see e.g., O.C., ii, 220–221), although he did continue his observations of the planet and its satellite.

Hevelius to Boulliau, 22 June 1656, Observatoire de Paris MSS “Epistolae Hevelium”, iv, no. 458.

The tract was not written as a response to Huygens's challenge (O.C., i, 411–12, 434–5).

Hevelius J. , Selenographia (Gdansk, 1647), facing p. 42. See also Van Helden, “Saturn and his Anses”, 116, fig. 7.

Holwarda Johannes Phocylides , Philosophia naturalis seu physica vetus-nova (Franeker, 1651), 259–60.

Johannis Hevelii Dissertatio de nativa Saturni facie, ejusq; variis phasibus certa periodo redeuntibus (Gdansk, 1656), 1–4.

Ibid., 12–13; 29–30; plate G, facing p. 12; plate H, facing p. 30.

Ibid., 6.

Ibid., 16, 17.

Ibid., 21.

Huygens to Hevelius, 25 July 1656, O.C., i, 413. Antonius Vatier to Hevelius, 3 April 1656, British Museum MSS Sloane 652, 189–90. For Wren's comments on this hypothesis see O.C., iii, 422–3, and Van Helden A. , “Christopher Wren's De Corpore Saturni”, Notes and records of the Royal Society, xxiii (1968), 213–29, p. 224.

O.C., i, 488–9.

See e.g., Van Helden , “Saturn and his Anses”, 117–18.

O.C., i, 474–6; ii, 165–6; xv, 288–90.

O.C., i, 474–6.

O.C., i, 486.

O.C., ii, 175.

Odierna G. B. , Protei caelestis vertigines seu Saturni systema (Palermo, 1657), 22.

The tract was dated 20 December 1656, but bears the publication date 1657.

Odierna , op. cit., 5.

Ibid., 3–4.

O.C., iii, 140; xv, 290–2.

O.C., iii, 420; Van Helden , “Christopher Wren's De Corpore Saturni”, 221.

O.C., ii, 305.

Van Helden , “Christopher Wren's De Corpore Saturni”, 223–4; O.C., i, 481. See also, Armitage A. , “William Balle, frs (1627–1690)”, Notes and records of the Royal Society, xv (1960), 167–72.

O.C., i, 482.

Ibid.

O.C., iii, 417.

Van Helden , “Christopher Wren's De Corpore Saturni”, 221–2.

Ibid., 221. Wren also wrote: “Then, with Saturn reaching about mean longitude, [the anses] are seen to suddenly disappear. At that time, the globe appears indeed solitary because both the sun and the eye are in the plane of the corona, which, because it has no sensible thickness–-although it is perhaps a few miles thick–-must escape the keenest of sight because of the great distance, thus leaving the globe utterly bare” (ibid., 222).

Ibid., 224.

Ibid., 223.

O.C., iii, 417.

O.C., xv, 176.

O.C., xv, 39, 238–9; i, 322.

The anses became visible again in October 1656 (O.C., xv, 246), seven months after Huygens had published De Saturni luna.

O.C., xv, 238–40, 296.

E.g., O.C., xv, 239, 240.

O.C., xv, 294–6.

O.C., ii, 109–10, 157–61, 166, 169, 173–6. See also Brown H. , Scientific organizations in seventeenth century France (Baltimore, 1934), 84.

O.C., ii, 330–1.

O.C., xv, 228–38.

He calculated the sidereal period to be 15^d22^h39^m, and the synodic period 15^d23^h13^m. These values were based on about 68 circuits of the satellite. In 1683 Halley corrected the sidereal period to 15^d22^h41^m6⁸, which differs from the modern value by only a few seconds (Philosophical transactions, xiii, no. 145 [10 March 1683], 82–88).

O.C., xv, 270.

O.C., xv, 298.

O.C., xv, 309.

See e.g. the illustration on O.C., xv, 299.

O.C., xv, 318.

O.C., xv, 318–20. The editors of the Oeuvres complètes point out that on at least four occasions between 1655 and 1659, cited in Systema Saturnium, Huygens shows a dark band on the planet adjacent to the exterior edge of the ring, while on the dates in question the shadow of the ring on the body should have appeared adjacent to the interior edge of the ring. The only explanation, according to the editors, is that on those occasions Huygens saw the contrast between the bright ring and one of the darker equatorial belts of Saturn (O.C., xv, 202–3).

O.C., iii, 18.

O.C., ii, 510.

O.C., xv, 214.

O.C., ii, 510–11.

Bibliothèque Nationale MSS Fonds Français 13043, f. 89v-90r.

Ibid., f. 90v.

Ibid.

Ibid., f. 92r.

Ibid., f. 90v.

O.C., iii, 92–93.

O.C., iii, 95, 134.

Ibid.

O.C., xv, 210.

Prince Leopold very often ordered his academicians to perform certain experiments. See Middleton W. E. Knowles , The experimenters, a study of the Accademia del Cimento (Baltimore, 1971), 56–61.

Eustachii de Divinis Septempedani brevis annotatio in systema Saturnium Christiani Eugenii … (Rome, 1660), reprinted the same year with Huygens's response, Brevis annotatio … una cum Christiani Hugenii responso (The Hague, 1660), in O.C., xv, 401–37.

O.C., xv, 426–36. See also, Van Helden A. , “The Accademia del Cimento and Saturn's Ring”, to appear in Physis.

Christiani Hugenii Zulichemii brevis assertio systematis Saturnii sui (The Hague, 1660), O.C., xv, 462–4.

Eustachius de Divinis Septempedanus pro sua annotatione in systema Saturnium Christiani Hugenii adversus ejusdem assertionem (Rome, 1661), 56–58.

Ibid., 106.

O.C., v, 176, 193. Fabri H. , Dialogi physici, in quibus de motu terrae disputatur (Lyons, 1665), 212. See also Fabri , Synopsis optica (Lyons, 1669), 49–59.

O.C., iii, 151, 157, and the figure between 154 and 155.

O.C., iii, 154–5.

See e.g., O.C., iii, 149–50.

O.C., iii, 194–7.

O.C., xv, 109–10, 153.

O.C., xxi, 786.

O.C., iii, 351–2.

O.C., iii, 283, 352.

O.C., iii, 350–3.

O.C., iii, 350–1, 338.

O.C., iii, 332, 368. Birch T. , The history of the Royal Society of London (London, 1756–57), i, 43.

O.C., iv, 34.

O.C., v, 257, 368.

O.C., xv, 483–4. See also “Observation de Saturne faite a la Bibliotheque du Roy”, Journal des scavans, 11 February 1669, 11–12.

O.C., xv, 479. The ratio 9:4 is very close to the modern value.

He finally observed this shadow effect in the summer of 1664 (O.C., v, 109–10.) For a discussion of the relative merits of the telescopes of Huygens and Divini, see Van Helden A. , “Eustachio Divini versus Christiaan Huygens: A Reappraisal”, Physis, xii (1970), 36–50.

Campani G. , Ragguaglio di due nuove osservazioni (Rome, 1664), facing p. 8.

Ibid., 18.

Auzout A. , Lettre à M. l'Abbé Charles (Paris, 1665), 7. This letter was written in October 1664.

When the so-called crêpe ring was discovered in 1850, it was quickly pointed out that it had been sighted on several occasions in the seventeenth century, Clerke , op. cit., 113.

Campani to the Abbé Charles, quoted in O.C., v, 117, n.l.

Auzout , op. cit., 9.

E.g., Hooke's observation of June 1666 was published in the Philosophical transactions, i, no. 14 (2 July 1666), 246, and plate.

Riccioli G. B. , Astronomiae reformatae tomi duo (Bologna, 1665), 367–8.

O.C., vii, 101.

Cassini J. D. , Suite des observations des taches du Soleil faites à l'Académie Royale. Avec quelques autres observations concernant Saturne (Paris, 1671). Oldenburg printed the prediction in the Philosophical transactions of 18 December 1671. See also O.C., vii, 115–16.

“Extraict d'une Lettre de M. HUGENS de l'Academie Royale des Sciences à l'Auteur du Journal des Sçavans, touchant la figure de la Planete de Saturne”, Journal des sçavans, viii (12 December 1672); O.C., vii, 235.

Hevelius , De nativa Saturni facie, 17.

O.C., vii, 237.

The first eight satellites of Saturn were discovered when the ring was in or near its edgewise poition. Phoebe, discovered by Pickering in 1898, was the first satellite of Saturn to be discovered when the ring was not near its edgewise position, but this discovery was made with the help of photographic techniques.

O.C., xv, 46.

“Observations Nouvelles de M. Cassini, touchant le Globe & l'Anneau de Saturne”, Journal des sçavans, 1 March 1677, 32–33. The claim that William Balle had already noticed this separation in 1665 (e.g., Grant , op. cit., 526), is erroneous. Balle's observation can be found in O.C., v, 543. This figure was omitted from the article in the Philosophical transactions, i, no. 9 (12 February 1666), 152.