Boulliau,Mercator,and Horrocks's “Venus in Sole Visa”: Three Unpublished Letters

Opera posthuma , ed. by Wallis John (London, 1672, 1673, 1678); Venus in Sole visa, seu tractatus astronomicus , ed. by Hevelius Johann and printed with Hevelius's Mercurius in Sole visus (Gdańsk, 1662), 111–45. The latter work was dedicated to Boulliau.

Chiefly through his Astronomia Philolaica (Paris, 1645) and Astronomiæ Philolaicæ fundamenta clariùs explicata … (Paris, 1657).

“Some considerations of Mr. Nic. Mercator, concerning the geometrick and direct method of Signior Cassini for finding the apogees, excentricities, and anomalies of the planets …”, Philosophical transactions, v (1670), 1174–5; see also his Institutionum astronomicarum libri duo … (London, 1676), 144–5. While attracted to Kepler's linking of ellipse and area rule to cosmological principles and insisting that the methods of approximation required by the former did not disqualify them from consideration, Mercator was non-committal on their standing as laws. See Wilson Curtis A. , “From Kepler's laws, so-called, to universal gravitation: Empirical factors”, Archive for history of exact sciences, vi (1970), 89–170, p. 133.

Scott Edward J. L. , Index to the Sloane manuscripts in the British Museum (London, 1904), 253, 262.

Cambridge University Library, MS (Baker B) Mm 2.23, f. 82 (MS 77b); published in Diary and correspondence of Dr John Worthington, ed. by Crossley James and Copley Richard , vols. xiii, xxxvi, cxiv of Remains, historical and literary, connected with the Palatine Counties of Lancashire and Chester (Manchester, 1847, 1855, 1886), cxiv, 366. The name of Horrocks's village is corrected to Toxteth Park in the printed version.

British Library, Add. MS 32,498, f. 16; Diary and correspondence of Worthington, xiii, 130–1.

Mercator to Aubrey John , n.d., Bodleian MS 25286 (Aubrey 12), f. 332; Mercator to Collins John , 16 July 1668 O.S., in Royal Society of London, Letter-Book M1, no. 53.

It seems to have been Hartlib's practice to allow Mercator to copy those letters in which Hartlib referred to him directly or indirectly. See, for example, Mercator's copies of Hartlib's letters in Sheffield University Library, Hartlib MSS, 56/1/12-16.

Boulliau's copy of the Hartlib letter at the Bibliothèque de l'Observatoire, Paris, is preceded by a single folio (also in Boulliau's hand) comparing calculations from the Rudolphine tables for the transit of Venus of 4 December 1639 N.S. (B5 12, pp. 545–6). A summary of this information is found in Letter II (MS Birch 4255, ff. 87–88), Boulliau to Hartlib. The original has not been located nor has the draft that Boulliau customarily retained.

Hartlib to Worthington , 26 June 1659 O.S., British Library, Add. MS 32, 498, f. 19.

Correspondence of Henry Oldenburg, ed. by Hall A.R. and Hall Marie B. (Madison and London, 1965), i, 289.

The manuscript gives only the dates without the year. The eclipses, however, may be identified further in Alexandre-Guy Pingré, Annales célestes du dix-septième siècle , ed. by Bigourdan G. (Paris, 1901), 238.

Ibid., 251.

Ibid. It was followed by Hevelius from 3 February to 10 March. The previous comet was that of 1653. Ibid., 207.

Astronomia Philolaica , Prolegomena, 4, and 355 for accuracy of ellipses. See especially Book I, chaps. 13–15 for a description of his system which represents the planetary orbit as a section of an oblique cone whereby the cone's central axis passes through the empty focus of the ellipse, the aphelion being closer to the apex of the cone and perihelion at the farthest. An element of the cone should generate equal arcs in equal times about the central axis (and of all sections of the cone parallel to the base), while in equal times tracing larger arcs at perihelion than at aphelion.

See especially Opera posthuma, 287 ff.

Ibid., 331.

About 20 April 1640, ibid., 33, 334.

Ibid., 337. The autographs are in Royal Greenwich Observatory, Herstmonceux, MSS Flamsteed 76 and 68 (Notebook C). MS Flamsteed 76, f. 8 and Hevelius's printed text (ref. 1), 116 give the latitude of Liverpool as 53°20′, whereas Mercator's letter and MS 68 (Notebook C), f. 16, on which it was based, give it as 53°25′. This establishes the order and dating of the drafts, as Horrocks wrote to Crabtree on 12 September 1640 O.S. that, owing to an improved division of his quadrant, he had redetermined the latitude of Liverpool as 53°25′ (Opera posthuma, 334). Horrocks's revised figure is quite accurate by modern standards.

Huygens to Moray Robert , 30 December 1661 N.S., Oeuvres complètes de Christiaan Huygens (The Hague, 1888–1950), iii, 438. See also Huygens to Hevelius , 22 August 1661 N.S., iii, 315. It is not clear which manuscript was seen by Thomas Streete, who was acquainted with both Mercator and Neile. He referred to Horrocks's treatise in his Astronomia Carolina (London, 1661), 12, 61.

Several instances are found in Boulliau's correspondence at the Bibliothèque Nationale, the Bibliothèque de l'Observatoire, and elsewhere. For published examples see Boulliau to Huygens , 10 October 1659 and 11 July 1661 N.S., Huygens , Oeuvres, ii, 492 and iii, 290; Philosophical transactions, vi (1671), 2273. See also Hatch Robert A. , The Collection Boulliau (BN, FF. 13019–13059): An inventory (Philadelphia, 1982).

de Pagan Fran&çois Blaise , La Théorie des planètes … (Paris, 1657); Ward Seth , In Ismaelis Bullialdi astronomiæ … inquisitio … (Oxford, 1653).

Wilson , op. cit. (ref. 3), 117–18; see also Maeyama Yasukatsu , Hypothesen zur Planeten-theorie des 17. Jahrhunderts (Frankfurt-am-Main, 1971), chaps. 4–6.

In Astronomiæ Philolaicæ fundamenta clariùs explicata.

The next five paragraphs are taken with only minor changes and with some change in the order of the text from the revised autograph of Venus in Sole visa, MS Flamsteed 68 (Notebook C), ff. 14–17.

Hoole , where Horrocks resided from June 1639 to July 1640 (Opera posthuma, 323, 333). The first draft of Venus in Sole visa (Flamsteed MS 76), f. 8, gives the distance between Hoole and Liverpool as “quindecim circiter milliaribus”, as does Hevelius's printed text of 1662 (ref. 1), 116.

See ref. 19.

Flamsteed MS 76 and Hevelius text, loci cit.: 53°35′.

The doubt expressed here is Mercator's, not Horrocks's.

Following “ab Insulis Fortunatis”, both of Horrocks's drafts add: “quas iam Canarias dicunt.”

The Hevelius text (ref. 1), 115, has “à vertice ad dextram”, exhibiting a confusion between the projected image with a Galileian telescope and the appearance in the sky without the use of a telescope. The same confusion is found in John Wallis's comment on Horrocks's observation, that for “ad sinistram lege dextram”, Opera posthuma, 393. As projected, owing to the position of the observer, there is only a partial inversion, top to bottom, but not left to right, which Horrocks seems to have realized since both manuscripts of Venus in Sole visa have “ad sinistram”. The actual transit occurred from the left (Venus in retrograde) and below the centre of the Sun's disk.

Horrocks probably used what he had described a year earlier as a well-made clock ( Horrocks to Crabtree , 14 September 1639 O.S.; Opera posthuma, 327).

The first draft—Flamsteed 76, f. 8—and the Hevelius edition, 115, have 14′24″. The 14′25″ of Horrocks's second draft, however, is repeated in his record of the observation (Opera posthuma, 393).

See ref. 32.

Horrocks went on to a more precise estimate: 30′: 1′10″, i.e., 1/25.71, Flamsteed 68 (Notebook C), f. 16.

Astronomia Philolaica, Prolegomena, 14, and 172, 246, 278, 326, 327, 346. Only one of the observations was made at Athens (p. 172). The same request was made a short time earlier by Mercator using similar language through an intermediary other than Hartlib. Bibliothèque Nationale, Fonds Français 13028 (Collection Boulliau, X), f. 224r is an unsigned and undated fragment in Mercator's hand (followed by a horoscope of Oliver Cromwell) requesting information about the two observations. For possible references to this fragment, see British Library MS Add. 32,498, f. 41; Oldenburg , Correspondence, i, 281, 311; and cf. the letters of Pinocci to Boulliau, Collection Boulliau XI, ff. 147, 152, 160.

Almagest, VII, 3. Ptolemy cites two observations of Menelaus in connection with the determination of the motion of the equinoxes and as a check on Hipparchus's figure for the same.

Eichstadt Laurence , Pars prima, in luminarium motibus & eclipsibus ex Tabulis Danicis Christiani S. Longomontani, in reliquis planetis ex Tabulis Rudolphinis … (Szczecin, 1634). This is in close agreement with Horrocks's calculation that, according to the Rudolphine tables, conjunction would occur at 9.03 a.m. (letter of 26 October 1639 O.S., Opera posthuma, 331). Both figures are for the meridian of Uraniborg.

The text contains an error by the copyist and should read: H. 21 15′. Elsewhere, Boulliau gives the calculation from Eichstadius as 3 December H.21. “sed revera H.21′15” (Bibliothèque de l'Observatoire, Paris, Boulliau MSS, B 5 12, 546).

Horrocks has true conjunction at 12°28′35″. From his observation, Horrocks calculated the latitude at conjunction as 8′30″ S (MS Flamsteed 68, C, f. 41; cf. Bibliothèque de l'Observatoire, Paris, Boulliau MSS, B 5 12, p. 546).

It is not clear how Boulliau arrived at “2 hours 30^m at most”; it is an obvious blunder or an error by the copyist. Using the difference of 57^m between Liverpool and Uraniborg (supplied by Mercator and Horrocks), conjunction would have occurred about 6.49 p.m. at Uraniborg. In this case, the Rudolphine tables would anticipate conjunction by 9^h34^m, the Philolaic by 4^h52^m. The former figure is consonant with Horrocks's calculation that Kepler anticipated true conjunction by 9^h46^m (MS Flamsteed 76, f. 46).

Following the transit of 1631, a similar question arose concerning the “entirely paradoxical smallness” of Mercury. Given Gassendi's observation of Mercury's diminutive size, Wilhelm Schickard proposed an argument adopted here by Boulliau. Briefly, since the Sun is much larger than Venus, it illuminates more than one half the planet's diameter. Hence, viewed from the Earth as a dark spot against the Sun, Venus would appear smaller than its true diameter. For background see Van Helden Albert , “The importance of the transit of Mercury of 1631,” Journal for the history of astronomy, vii (1976), 1–10.

See ref. 36.

Astronomia Philolaica, 172. The date of the observation was 474 February 18; it was probably made by Heliodorus (Otto Neugebauer, A history of ancient mathematical astronomy (Berlin and New York, 1975), ii, 1038).

Probably made at Alexandria, 503 February 21/22 and 509 March 11/12, also by Heliodorus.

Boulliau's own record of the eclipse has its beginning at 13^h57^m40^s and ending at 16^h38^m (Pingré, op. cit. (ref. 12), 240).

See ref. 46.

Neither Hartlib nor Boulliau took part in the publication of Horrocks's work. See ref. 20.

Hollenstein Samuel Karl Kechel à (b. 1611) lived at Leiden after 1632. He made many observations, some of which found their way to Boulliau, Huygens, Hevelius, and Van Schooten.

Kechel's Systema novum attempted to account for the appearances according to Mercator “manentibus Sole et tellure in suo loco, vel non procul inde dimotis, rotâq[ue] circa, amber ipsâ fixarum sphærâ …”. Mercator's “animadversiones” are in Sheffield University Library, Hartlib MS 56/1/143b–46a.

See ref. 22.

Ward Seth , De cometis (Oxford, 1654). Ward proposed that comets were eternal, had circular orbits, and chided Kepler for failing to realize that they were subject to gravitational attraction and changing velocities, pp. 30–31.

The note is not in Mercator's hand.