New Light on Tycho's Instruments

First published commercially in 1602, reprinted as vol. v of Tychonis Brahe opera omnia (edited by Dreyer J. L. E. , 15 vols, Copenhagen, 1913–29, hereafter cited as Opera), and published in English translation as Tycho Brahe's discussion of his instruments and scientific work (Copenhagen, 1946) with almost identical pagination.

“Man hat den Eindruck, dass Instrumente gebaut wurden, nur um Arbeit zu schaffen …”, Repsold J. A. , Zur Geschichte der Astronomischen Messwerkzeuge von Pürbach bis Reichenbach 1450 bis 1830 (Leipzig, 1908), 29.

Opera, v, 97, 107. A cross-staff made in 1571 by the same artisan (Gualter Arscenius) is possessed by the British Museum: No. 86, 6–30, 1.

Opera, v, 98.

Opera, v, 99.

Opera, ii, 335; x, 10.

Opera, x, 8, 10.

Opera, v, 80–83.

Opera, ii, 335; x, 19.

Opera, ii, 342–6; v, 88–91.

Opera, v, 84–87.

Tycho's description and depiction of the instruments are in Opera , v, 12–15. Dreyer (in Tycho Brahe (Edinburgh, 1890)) states that the instrument was made at Uraniborg (p. 101), but the eclipse observation of 8 December 1573 ( Opera , x, 38) contains an unambiguous reference to it.

Tycho's discussion of the steel sextant is in Opera , iv, 369–72 and v, 76–79. He seems to imply that he already had it for his travels in Germany in 1575. Norlind picked this point up (Tycho Brahe (Lund, 1970), 278) without noticing that the Landgrave of Hesse, whom he saw in Cassel on the trip, only learned of the sextant at second hand in 1580.

Opera, v, 16–19.

Opera, v, 46, 155.

As Tycho's diagram (Opera, ii, 335, amplified by the addition of the dotted lines, Figure 8) shows, any pair of sightings through slits AB and BC intersect to one side or another of the true centre of the arc, post B. Fig. 8.

De crepusculis (Lisbon, 1542). Tycho's reference to it is in Opera, v, 12.

Delambre has delivered his characteristically trenchant judgement of this scheme in Histoire de l'astronomie au moyen âge (Paris, 1819), 402–4.

Although Tycho, in his Mechanica, labelled his first quadrant the Q. minor and his second quadrant the Q. mediocris ( Opera , v, 12, 16), this was clearly an afterthought. In fact, the first quadrant was never used after the second one appeared; and it was long forgotten by the time the larger quadrants entered the scene. Accordingly, when Tycho actually faced the need for names, it was the second quadrant that was called the Q. min. in his logs—for it, alone, was capable of providing the altitude readings to individual minutes and the azimuth readings that are attributed passim to the Q. min.

For a resumé of the history of linear transversals, see Zinner Ernst , Deutsche und Niederlāndische Astronomische Instrumente des 11.–18. Jahrhunderts (Munich, 1956), 224.

In the Mechanica Tycho provided a rigorous defence of the transversals by showing that the error involved was, at most, slightly over 3′ (Opera, v, 153–4).

Opera , ii, 157–8. For the first references to Tycho's four clocks, see Opera, x, 46, 77, 110.

Christoph Schissler; for a biographical sketch and a listing of his extant works, see Zinner , op. cit., 503–20.

Tycho appropriately discussed his great globe in the Mechanica (Opera, v, 102–5) with the rest of his instruments. The translated passages are based on the 1946 translation (see ref. 1).

Opera, x, 85, 88–89.

Opera, x, 92.

Opera, x, 181, 185, 132.

Opera, v, 92–93.

The log entries for this period involve enough different hands that it is by no means impossible that the extra instrument is simply a confusion in nomenclature. The only clearly-simultaneous reading ( Opera , x, 189) is simply an editorial mistake. The claim of the Q. max. to identification with Figure 2 (right) (besides the fact they share the same name) rests on the fact that it gave azimuths (Opera, x, 249) and that, less than a year after it was phased out, the azimuth semicircle (Figure 5 (right)) was put into service on a remarkably similar mounting. The Q. maius must have been surrounded by a “square” very like that shown on the Q. max., for all of its early readings were two-fold, the extra reading being a tangent value such as would derive from a square.

Opera , x, 134. In view of the consistent use of “mur” in reference to the mural quadrant, there is little excuse for believing with Dreyer (Tycho Brahe, 101) that observations of April 1581 per magnum instrumentum (which are identical in style to those made with the Q. maius) “were probably also made with [the mural] quadrant”.

The mural quadrant is described and depicted in Opera, v, 28–31.

Dreyer (Tycho Brahe, 101) follows Tycho in giving 5 inches and 2 inches for the breadth and thickness. But these are the archaic units of Tycho. They can be converted approximately by reference to Tycho's depiction and his statement ( Opera , v, 153) that he usually made his transversals one-fortyeighth of the radius of the instrument. According to the picture, the inside and outside borders on the arc were each roughly equal to half the size of the transveral strip itself. This would indicate that the five-inch width of the whole arc would have been one-twentyfourth the width of its five cubit radius, so that Tycho's cubit embraced 24 of his inches. In this argument lies the first indication that Tycho was using the traditional relationship 16 inches = 1 foot = 2/3 cubit.

Tycho was still adjusting the quadrant on the wall in 1583: Opera, x, 135.

Opera, x, 100.

Opera, v, 52–55.

Opera, x, 125, 127.

The sextans bifurcatus is described very briefly in Opera , v, 96. Citations to the sextantem biformen (Opera, x, 103, 129) indicate that the dual-alidade model was the first one ready.

Opera, v, 68–71.

The chronology is reconstructed from the following evidence. The sums at the foot of Opera , x, 275 establish the arcum astronomicum as Tycho's log notation for the bipartite arc. References to this instrument first appear at the beginning of 1583 ( Opera , x, 239, 246). References to an arcum parallaticum, which must be the extra sighting apparatus on the sextant, appear at the same time ( Opera , x, 275). In his discussion of the arc, Tycho states that it was built specifically to perform a task that “cannot very easily be done with … a sextant”, and then mentions, almost parenthetically, that “this drawback has been removed, it is true, by another expedient”.

Opera , v, 48–51. Observations are first found in Opera, x, 243, 236.

In a brief statement in his Progymnasmata of 1602 ( Opera , ii, 153), however, Tycho expressed himself rather bluntly on the shortcomings of the ruler.

Tycho (his disciples, actually) did very little work on the project, and did that rather late, in 1589 ( Opera , v, 301–4). For an excellent discussion of Tycho's geographical activities, see Richter Hermann , “Willem Janszoon Blaeu with Tycho Brahe”, in Imago mundi, iii (1939), 53–60.

Opera , x, 232. Tycho's description of it is on Opera, v, 20–23.

The first months of trial and use are marked very clearly in Opera , x, 289–95. Tycho's description is in Opera, v, 24–27.

The rulers are described in Opera, v, 44–47.

Ptolemy , Almagest (trans. Manitus Karl , repr. Leipzig, 1962), 254–8.

Tractatus de annulo astronomica (Louvain, 1534), cited by Dreyer, Tycho Brahe, 316.

Tycho's general dismissal of rings (after he bought one, modified it, and made another) and his specific reference to Gemma occur in a brief discussion in Opera, v, 98.

Opera , x, 292, 363. The two are discussed and depicted in Opera, v, 56–63.

Opera, x, 302, 351. Tycho's description is in Opera, v, 64–67.

Opera, xi, 3–4.

Opera, x, 427; v, 32–35.

Opera, xi, 1, 244; v, 36–39.

Opera, xi, 251; v, 40–43.

Described but not depicted in Opera, v, 96–97. Its radius was 4 feet.

Opera , xi, 319, 360. Presumably a quadrant made for, or according to a design suggested by Odd Einarson, one of Tycho's short-term collaborators who was bishop of Skalholt in Iceland: Dreyer , Tycho Brahe, 382.

Opera, xii, 108–18.

Opera , xii, 110. The armilla portatalis is described in Opera, v, 98–99. Its radius was 2 feet, and Tycho mentions that it was useful even at Hven for low-altitude observations, where the walls of the crypts interfered with observations by the larger armillaries.

The Icelandic Quadrant and the camerae obscurae (Tycho's old one dated from at least 1578: Opera , x, 52) were not mentioned in the Mechanica. Neither was the Q. maius, if it existed.

Dreyer , Tycho Brahe , 320. While he is right in saying that Tycho does not mention Nonius in the context of the azimuth semicircle, some remarks in Opera, ii, 224 make it clear that Tycho was familiar with the work in question.

Machina coelestis (Dantzig, 1673), Plates F & O.

Dreyer , Tycho Brahe, 357.

Ibid.

“Über den neun Stern vom Jahre 1572”, Astronomische Nachrichten, lxii (1864), 273–8.

Dreyer , Tycho Brahe, 351–2.

Tupman G. L. “A comparison of Tycho Brahe's Meridian Observations of the Sun with Leverrier's Solar Tables”, The observatory, xxiii (1900), 132–5, 165–71.