De Zeventiende Eeuw. Jaargang 12

[p. 106]

Between Friends: Huygens & Boulliau
Robert A. Hatch

Le vrai peut quelquefois n'être pas vraisemblable. Boileau, L'Art Poétique, vol. 3, p. 48.

Although they might be distinguished by generation, nationality, religion, and class, Huygens and Boulliau became fast friends. As is clear from their correspondence, they shared similar scientific interests, and during the crucial decade 1655-1666 their association intensified around common concerns and considerable controversy.^1. That the most dramatic period in Huygens' life began with his visit to Paris in 1655 is not news. Accompanied by his older brother and two cousins, Christiaan attended musical performances and fashionable centers of learning, among them, the prestigious Cabinet Dupuy. As he reported to his father, it was here, at the Bibliothèque du Roi on the Rue de la Harpe, that Huygens first met the ‘fameux mathématiciens’ Gassendi and Boulliau.^2.

In 1655 Ismaël Boulliau (1605-1694) was widely recognized as the foremost astronomer in Europe. An early Copernican and Keplerian, Boulliau was situated in the ‘very seat of learning’ and assisted Jacques Dupuy as librarian and moderator of his famous Cabinet. The last member of a generation that included Descartes, Mersenne, Riccioli, Peiresc, and Gassendi, Boulliau was arguably one of the senior statesmen of European science, and as an ‘intelligencer’, played a significant role in the Republic of Letters.^3. In sum, when the son of Constantijn Huygens visited Paris in 1655, Boulliau was at the height of his career.^4. He was fifty years old, Christiaan twenty six.

But the decade brought dramatic change. As the ‘Young Archimedes’ became the acknowledged Ornament of the prestigious Académie des Sciences, Boulliau's career went into steep decline. And if the decade 1655-1666 marks the ‘Triumph of Huygens’ - his most creative and productive period - it also signaled a turning point in the Scientific Revolution. The relationship between Huygens and Boulliau, a counterpoint in individual careers, reflects similar shifts in authority, shifts in the practice and patronage of science.

Although a number of studies focus on Huygens' dramatic decade - several citing his friendship with Boulliau - the relationship has been largely ignored.^5. This essay explores that association, not to highlight Huygens' success or Boulliau's decline, but to illustrate shifts in authority across three phases of an extended episode: the priority dispute surrounding the pendulum clock, the controversy concerning the rings of Saturn, and the personal exchanges between Huygens and Boulliau regarding planetary motion.

1. Beyond their correspondence, secondary literature teems with discussions and allusions to their friendship and association. The purpose of this paper is to explore that relationship in the context of their respective scientific interests.

2. Chr. Huygens to Constantijn Huygens, 6 Aug 1655, O.C., vol. 1, p. 342. Although Huygens' father knew of Boulliau for some time, the first mention of Boulliau's work seems to be a letter of Daniel Lipstorp to Chr. Huygens, 10 April 1653, O.C., vol. 1, p. 230. Huygens latter reports to his father that he has conferred with Boulliau, who showed him the telescope given by the Grand Duc of Tuscany. ‘Vous m'avex promis un desseing de Jupiter avecq ses Zones, je vous prie de me l'envoyer, afin que j'en puisse conferer avecq Mr. Bulliau. Ananthier il me monstra sa grande lunette que le duc de Florence luy a envoyée, qui me semble assez bonne, mais decouvre trop peu à la fois, comme estant de 10 pieds, et n'ayant aupres de l"oeil qu'un vierre concave.’ Chr. Huygens to Const. Huygens, 1 Oct 1655, O.C., vol. 1, p. 352.

3. To gauge one measure of Boulliau's role as intelligencer see Robert A. Hatch, The Collection Boulliau (BN, FF. 13019-13059), An Inventory, Phildelphia, 1982, and the excellent study of H.J.M. Nellen, recently translated into French, Ismaël Boulliau (1605-1694). Amsterdam, 1994.

4. Huygens' principal correspondents during this period were Boulliau, Jean Chapelain (1595-1674) and Pierre Petit (1594-1677). Each correspondent represented different talents. As Huygens' earliest Parisian contact, Boulliau was also responsible for introducing others. Chapelain would become a major figure in the formation of the Académie des Sciences. Several years later, in October 1658, Boulliau forwarded a letter of Petit, and felt sufficiently confident to suggest that Petit was a person who could ask more questions than anyone could answer, further drawing a comparison with Mersenne. One of Boulliau's functions was to serve as buffer, to screen queries and protect Huygens from unwanted contacts. Petit, whose daughter was widely noted for her beauty, would eventually become quite close with Huygens during his years in Paris. Like Boulliau, Petit was overlooked when the Académie was formalized; both were elected to the Royal Society in 1667.

5. J. Mesnard suggested Huygens' early contact with Boulliau could not have suited him better, that Boulliau was ‘le meilleur interlocuteur possible à en matière d'astronomie’. ‘Les première relations Parisiennes de Christiaan Huygens’, in: Huygens et la France. Paris, 1981, pp. 33-40, p. 34. It has been also been suggested that theirs was a durable and mutually fruitful friendship. See U. Frankfourt and A. Frenk, Christiaan Huygens, trans. from Russian by I. Sokolow. Moscow, 1976, p. 67.

Plagiarism, Priority & the Pendulum Clock

Huygens' career was born in controversy. His first steps on the stage of European science were greeted not by cheers of adoration but cries of plagiarism. If we ignore

[p. 107]

the extraordinary outcome of his career, it is well to recall the difficulties Huygens faced from the very outset. In the course of the decade, he would be accused of plagiarism by Prince Leopold de Medici, Galileo's patron; Vincenzio Viviani, Galileo's devoted disciple, and most members of the Accademia del Cimento. From other quarters similar charges would be leveled by Hooke, Wallis, Roberval, Hevelius, and a coterie of clockmakers.^6. It was an inauspicious beginning to a promising career.

The most disturbing yet fruitful part of Huygens' first controversy began shortly after the publication of the Horologium of 1658. Since the outlines of the dispute are well known,^7. I focus on the challenge of Prince Leopold, an accusation sent to Boulliau. A longtime friend and sometime patron, Leopold de Medici and Boulliau had met a decade earlier, in 1645, when Boulliau, along with Nicolaas Heinsius, visited Florence; the long and fruitful correspondence between Boulliau and Leopold continued from 1649 until the Prince's death. But it was in a letter in the Spring 1659 that the patron of the Cimento wrote Boulliau the following:

‘Concerning the clock regulated by a pendulum, certainly the invention is beautiful, but one must not steal any of the glory due to our forever admirable Galileo, who already in 1636, if I am not mistaken, proposed this same useful invention to the States General of Holland, and I have rediscovered a model already built by the same Signor Galileo, although in part different in the combination of gears.’^8.

As widely noted, Boulliau dutifully defended Huygens' honor^9. while exercising tact and sound judgment.^10. But here we dwell on the obvious: Boulliau was caught between two friends with much at risk.

As bearer of bad news, Boulliau sent Huygens' a copy of Leopold's allegations, as well as an outline of his own defense to Leopold protesting Huygens' character and credibility:

‘I have responded on this matter to His Most Serene Highness that I know that you would consider it an honor (and that you believe to merit the glory) if you had fallen upon the same thoughts as Galileo had made; and that you are so much a man of honor and so sincere that you would never rob the reputation of another in order to attribute it to yourself; that you have an extraordinarily fertile mind for very beautiful inventions, no need of the of another.’^11.

Though the pendulum clock promised significant scientific,^12. practical, and perhaps monetary rewards,^13. the dispute left young Huygens feeling smitten.^14. But his inauguration was not complete. In introducing the simple pendulum clock, Huygens was forced somehow to defend himself; and as he put it, ‘the negative is difficult to prove.’ An irony of the dispute is that while Huygens had cleverly embodied an explicit and highly original design in his working models, he was forced by circumstance to carry the complete burden - the charge of plagiarism, the burden of proof, and the weight of an undisclosed rival design. To avoid being taken as a ‘rascal plagiarizer’, as he put it to Boulliau, Huygens needed information.

But if Huygens was unknown he also represented a continuing threat to the master's legacy. Protocol required a proper introduction, honor demanded a delicate defense. Interceding on Huygens' behalf, Boulliau requested that Leopold provide diagrams of Galileo's pendulum clock as well as evidence of the model that

6. See D.S. Landes, Revolution in Time: Clocks and the Making of the Modern World. Cambridge, Mass., 1983, pp. 116-121.

7. This discussion owes much to conversations with Jody Yoder in concert with her excellent study, Unrolling Time: Christiaan Huygens and the Mathematization of Nature. Cambridge, 1988.

8. Leopold to Boulliau, 31 March 1659, BN Paris, f. fr. 13039, f. 85r, O.C., vol. 3, p. 462; trans Yoder, Unrolling Time (n. 7), p. 130.

9. ‘The complaint had been sent to Ismael Boulliau, who wasted no time in defending Huygens' honor.’ Yoder, Unrolling Time (n. 7), p. 131.

10. Middleton alludes to the celebrated argument concerning the pendulum clock ‘which would have caused ill feeling except for the tact of Boulliau.’ W.E.K. Middleton, The Experimenters: A Study of the Accademia del Cimento. Baltimore, 1971, p. 302.

11. Boulliau to Huygens, 9 May 1659, O.C., vol. 2, p. 403.

12. I have not found exact figures on the accuracy of Huygens' various clocks. What is clear is that the simple pendulum clock represented a dramatic change from previous clocks, which could vary by some fifteen minutes per day, to an accuracy now in the range of ten or fifteen seconds per day. There is evidence that Huygens' later clocks were more accurate. See Landes, Revolution in Time (n. 6), p. 116.

13. On 21 June 1658 Boulliau wrote Huygens that the Chancellor Séguier has always responded that ‘he did not want all the master clock makers of Paris crying after him, and besides it was always possible that someone had found this same clock design.’ O.C., vol. 2, p. 185.

14. Fifteen years later, in his Horologium oscillatorium (Paris 1673), Huygens found it necessary to defend his honor from hints of plagiarism, counter-claims to priority, and at from others selling his ‘construction’ as their own. See Huygens' introduction in Christiaan Huygens' The pendulum clock or geometrical demonstrations concerning the motion of pendula as applied to clocks, R.J. Blackwell, trans., pp. 12-13.

[p. 108]

was said to be constructed by Galileo's son. Leopold agreed, and in addition, he attempted to add further weight to the Florentine's claim by including an historical account composed by Galileo's student Viviani. Acting as intermediary, Boulliau made copies for himself and sent the two drawings to Huygens. But here, I would argue, Boulliau took full advantage of his position. Judging Viviani's history as a complicating factor, Boulliau did not forward the document to Huygens, nor did he raise the issue again with the Prince of Tuscany. The evidence (or circumstances) of Boulliau's failure to forward the document to Huygens, particularly his silence on the matter with Leopold, suggest this was not a clerical error but a strategic gesture based on his diplomatic experience. In retaining Viviani's history, Boulliau withheld fuel from the fire. The delay and silence worked. As attention shifted to Huygens' theory of Saturn's ring Viviani's history was quickly forgotten.^15.

15. From a scientific standpoint, Boulliau had few criticism of Huygens' first pendulum clock, and consistently provided praise in claiming Huygens' as true inventor. Boulliau's concern, dating from mid-1659, was that the pendulum must swing freely without interference from the train of the clock (24 July 1659). Huygens reassured Boulliau in his response that (O.C., vol. 2, pp. 430-431 and 441-442) that his clocks were designed to provide the smallest impulse to the pendulum - no more than a breath - and hence the mechanism would not disturb the pendulum's rate of oscillation. At this point, in mid- 1659, Huygens believed that small impulses would generate swings of equal amplitude, but experience and further reflection proved otherwise. See Landes, Revolution in Time (n. 6), p. 418-419, n. 8.

Saturnian Delights

In the midst of defending his reputation against charges of plagiarism - the death knell of a promising career - Huygens was characteristically immersed in another project, his Systema Saturnium (1659). In the first of several carefully considered projects, Huygens shrewdly dedicated the work to Leopold.^16. The strategy and timing were as perfect as the irony. Just as he was claiming priority for the invention of the pendulum clock, Huygens now threw a companion piece into the mix that demonstrated scientific brilliance as well as social savvy. Intended or not, Huygens' success with Saturn at once demonstrated that he was no plagiarist but an ally. By substituting Saturn for the pendulum clock, Huygens became the legitimate heir to his Italian hero. Far from contradicting the master, Huygens' work would now recall and extend Galileo's pioneering efforts - and the Medici name.

The story of Saturn's rings can be read as a case study in publication strategy. The core of the story is a novel scientific theory; the telling of the story involved time-honored strategies of delay, favored initiates, secrets, controlled leaks, and strategies for ensuring priority. It began with in winter of 1655-1656 when Christiaan and his older brother Constantijn first uncovered Saturn's secret. Occupied with the pendulum clock, however, Huygens delayed three years before finally publishing his Systema Saturnium in July 1659. In the interim, he attempted to ensure his priority with a strategy common to mathematicians - he substituted publication with an anagram. Encoded in the cipher - much like the mathematical theory embodied in his pendulum clock - lay the secret of Saturn.

But it was not a perfect secret, nor, for that matter, a perfect theory. Two years before it was made public, Huygens shared his secret with Boulliau. The formula for a good secret is well known. First, the secret should involve a benefit for each member; second, the confidant should be trusted to hold the secret in proportion to changing circumstances; third, the secret - if it is to ensure against rival claims - is best placed with an acknowledged authority, someone who adds credibility to the claim. Finally, assuming that the friend has sufficient authority to ensure a fair hearing, he might also assist in converting skeptics and mollifying critics.

16. Huygens' letter of dedication to Leopold is dated 5 July 1659.

[p. 109]

On all counts Boulliau qualified. But Huygens' secret produced additional effects. To be sure, Boulliau represented an established authority; but he could also keep a secret. While using the delay to make modifications to his theory, Huygens extended the drama as speculation, rumor, and gossip that heightened public anticipation. But if the logic of the secret was that Huygens would not tell, Boulliau, as bearer of the secret, became the focus of interest. He may have taken the confidence too seriously.

In spring of the next year Huygens shared his secret with Jean Chapelain. A tertiary poet with little reputation in science, Chapelain became a central figure in the emergence of state-sponsored science. With the death of Gassendi, whom he championed, Chapelain encouraged Huygens to publish his results with all due speed; he also made it clear that he would assist Huygens' career in any way possible. A highly visible member of the Montmor group, Chapelain was one a handful asked to identify potential candidates for inclusion in the nascent Académie des Sciences. In spring 1658, Huygens authorized Chapelain to read a letter to the Montmor group explaining his ring hypothesis. Chapelain soon emerged as Huygens' chief Parisian contact.

Following publication of the Systema, Boulliau found himself dealing with charges from a different direction, from his friend Johannes Hevelius. Having met 25 years earlier in Paris, Boulliau and Hevelius were longtime friends and frequent correspondents. The son of a wealthy brewer, the Danzig astronomer enjoyed an international reputation, and like many of his generation - Gassendi, Boulliau, Riccioli, and Roberval - Hevelius had observed Saturn systematically for some time. From at least 1642 Hevelius followed Saturn's strange appearances but had withheld publication in order to observe a representative phase of Saturn's ‘solitary’ appearance. Hevelius' Dissertatio de nativa Saturni facie finally appeared in June 1656. Here he provided, with typical clarity and practical mindedness, comprehensive tables and illustrations of Saturn's changing form.

As is clear from a long letter of protest from Hevelius to Boulliau, Huygens was not the only person - certainly not the first - to study Saturn.^17. Although he failed to identify Titan as a moon, Hevelius had observed and plotted its position years before Huygens, and as for the ring hypothesis, Hevelius queried, how could Huygens defend his hypothesis regarding the thickness of the ring? At the heart of Hevelius' fury, however, was Huygens' claim that his telescopes were superior to all others. Though Boulliau was successful in pacifying his anger, Hevelius recognized that Huygens' claim could not go unchallenged. If the claim were taken seriously, if superior instruments implied better observations and stronger theories, then the astronomer with the best instrument was the best judge. Huygens, of course, was not without reason, particularly in light of rival hypotheses of the 1650s and 1660s. Comparison of printed illustrations - not to mention hand drawings - suggests a mangle of guesswork and speculation.

When he sought Boulliau's opinion concerning the ring hypothesis, however, Huygens was offered the following advice; it foreshadowed an ensuing debate:

‘You establish your hypothesis very well, and it proceeds regularly, provided you can persuade how this ring can become invisible however small its consistent thickness. I know that nature has been able to make a ring around this said body, and that by [the same] reason that the earth is suspended; in the open air, a ring can also be suspended:

17. The letter is found in the Collection Boulliau, Hevelius to Boulliau, 9 December 1659, BN Paris, f. fr. 13043, f. 87r-92v; see esp. f. 89v-90r.

[p. 110]

nevertheless, you still need some experiments in order to demonstrate absolutely that which you propose.’^18.

The thickness of Saturn's ring - and the angle of inclination - would become continuing issues. It is important to recall that Huygens' hypothesis held that the system of Saturn involved a substantial ring - a thick, solid, permanent structure - that remained parallel to itself throughout its 30-year solar orbit. And the ring had an invisible outer edge. The reason for the thickness of the ring, Huygens argued, was to account for the broad shadow cast on Saturn's central body. A thin ring, he maintained, would not do. The difficulty that remained was to explain how a thick ring could pass unobserved, particularly when viewed ‘on-edge’. Here Huygens speculated that the outer edge was covered with an non-reflective material or, perhaps was so smooth that it reflected like a point surface.

Although he was supportive of Huygens' hypothesis, Boulliau's main concern was that the value assigned to Saturn's ‘equatorial’ ring-plane - 23.5 degrees - was optimistically close to that of Earth. As Boulliau well understood, the supposed symmetry was unfounded. Having observed Saturn for nearly two decades, Boulliau knew the angle of inclination would have to be modified. His second reservation concerned the thickness of the ring itself. Boulliau's own theory held the ring to be extremely thin and elliptical, possibly joining the body of Saturn in two places.^19. What remained was to conduct experiments ‘in order to demonstrate absolutely that which you propose.’^20. Experiments? While he was no stranger to mathematical analogies - and in possession of a good telescope from the Grand Duc^21. - Boulliau's best advice was to construct a working model of Saturn's ring. To demonstrate the hypothesis absolutely, appearances of the ring would have to be reproduced by experiment.^22.

Happily, beginning in summer 1660, members of the Cimento would began a brilliant series of tests in an attempt to reproduce the appearances of Saturn's rings.^23. In succeeding months the Cimento developed a number of physical models to represent the appearances of rival theories. The motives seem clear enough. If Huygens' hypothesis proved correct, it was necessary to demonstrate the difficulties of the problem or, more delicately, to show how inadequate instruments might account for inconsistencies in Galileo's pioneering efforts.

In the meantime, the pendulum clock had became less of an issue. Through Boulliau as intermediary,^24. Leopold slowly confided his opinion that Huygens was clearly capable of producing the pendulum clock - indeed, now seeing the ‘eminence of his Genius’ Leopold expected ‘even greater things’. For his part, Huygens had presented his Systema Saturnium with an elaborate dedication to the Prince. Assuming that the printed epistle within the volume would speak for itself, Huygens sent it without a cover letter, and inexplicably received no reply. Although he suffered a year of anxiety, Huygens knew from other sources that the Prince had not only received the volume but highly approved.

Throughout summer 1660 Saturn became the cause célèbre of the Cimento. Following Borelli's lead, members constructed and tested three-dimensional models of Saturn's form based on Huygens' propositions in the Systema Saturnium. Placing the model at the end of a long hallway illuminated with torches, they then observed the apparatus with telescopes of varying quality. Viewed at different distances

18. ‘Vous establissez fort bien vostre hypothese, & elle procede regulierement, pourveu que vous puissiez persuader que ce cercle puisse devenire invisible a cause du peu de consistance en espesseur qu'il a en soymesme. Je scay que la nature a pu faire un cercle autour de ce corps la, & que par la raison qui fait que la terre est suspendu; en aëre libero, un anneau peut aussi y estre suspendu; neantmoins il vous faut encore quelques experiences pour demonstrere absolument ce que vous posez.’ Boulliau to Huygens, 21 Nov 1659, O.C., vol. 2, p. 510. In this letter Boulliau goes on to express doubts concerning Huygens' figure for the angle of obliquity of Saturn's ring.

19. Boulliau to Huygens, 21 Nov 1659, O.C., vol. 2, pp. 510-511.

20. ‘... neantmoins il vous faut encores quelques experiences pour demonstrer absolument ce que vous posez.’ Boulliau to Huygens, 21 November 1659. O.C., vol. 2, p. 510.

21. Boulliau had received a nine-foot telescope from the Grand Duc of Tuscany nine years earlier. To Huygens' chagrin, Boulliau was initially unable to confirm the discovery of Titan. Although the telescope was a prestigious gift, we can only speculate about its quality. It seems clear that it was not the worst instrument in Paris in 1659. If theoretical elegance and telescopic observation failed to persuade, experiment was an obvious alternative.

22. Despite his extraordinary skill with clocks and working planetaria, there appears to be no evidence that Huygens constructed a mechanical model of Saturn's ring. As an observer, there is evidence that Huygens participated in the ‘Société de Lunetterie de Paris’, which in January 1661 included Auzout and Petit, who were later joined by Boulliau, Thévenot, and Huygens. In general, Huygens showed little interest in systematic observation.

23. This discussion owes much to conversations with Al Van Helden, and his superb article, ‘The Accademia del Cimento and Saturn's Ring’. In: Physis 15 (1973), pp. 237-259. See also, Middleton, The Experimenters (n. 10), esp. pp. 256-262.

24. At about this time Huygens began to correspond directly with Leopold, no longer depending on intermediaries, chief among them Boulliau, Nicolaas Heinsius, and Carol Dati.

[p. 111]

under various lighting conditions, they also ingeniously included outside observers. Acknowledging that variations in skill are sometimes accompanied by varying investments and expectations, the Cimento invited passers-by to report what they saw.

In the end, the Cimento concluded not only that a ring hypothesis was consistent with the model's reported shape (viewed with a superior instrument) but that Galileo's observations were consistent with the model's reported appearance viewed with an inferior instrument. As for Huygens' specific model, while the Cimento failed to reproduce the exact appearances, the elegance of the theory prevailed. But the jury was not entirely satisfied. The thick ring assumed in Huygens' model, despite application of various coatings to its outer surface, remained visible.

Despite this criticism, Huygens remained adamant regarding the ring's thickness. In time, however, he modified his view of the inclination of the ring, increasing it to about 31 degrees from the analogical value of 23.5 degrees.^25. Although he never changed his mind on the question of thickness, the best measure of Huygens' success is that such details counted little. As with the pendulum clock and the spring-balance watch, Huygens' general solutions - brilliant, elegant, workable - won the day.

25. A. Van Helden, ‘“Annulo Cingitur”. The solution to the problem of Saturn.’ In: Journal for the History of Astronomy 5 (1974), pp. 155-174, p. 166.

Calculation & Clocks

‘I grant that the calculations rest on a slippery basis since, to be sure, I have taken the magnitude of the Earth intermediate between those of Mars and Venus on no other ground than that of verisimilitude.’

Systema Saturnium (1659)^26.

When he first met Boulliau in Paris in 1655, Huygens was beginning work on the pendulum clock and attending to the very problems that would eventually dominate the agenda of the nascent Académie des Sciences.^27. Central to both careers were issues associated with planetary motion and, concomitantly, the equation of time,^28. the height of the pole, obliquity of the ecliptic, and, not least, solar parallax.^29. These were key concerns for early members of the Académie, Huygens in particular.^30. They also offer insight into the relationship between Huygens and Boulliau and the authority of science. The core problem stems from the work of Johannes Kepler. Like Huygens and Boulliau, Kepler considered nature to be simple, uniform, and harmonious. For all of that, the problem bearing Kepler's name - which occupied both Boulliau and Huygens - had no direct solution. Anything but simple and uniform, the chief difficulty in understanding planetary motion - embodied in the so-called ‘Kepler-Problem’ - was to determine a planet's position for any given time in its orbit. This problem occupied Boulliau throughout his career, and his reputation, then as now, depended in large measure on his justification for his widely cited ‘elliptical hypothesis.’ Huygens also had a great deal invested in the problem. If the pendulum clock was to be applied to astronomical research, the issue of determining - not necessarily calculating - the equation of time was critical.

Briefly stated, the equation of time refers to the constantly changing relation

26. A. Van Helden, Measuring the universe: cosmic dimensions from Aristarchus to Halley. Chicago, 1985, p. 123. O.C., vol. 15, pp. 348-349.

27. See, for example, O.C., vol. 19, pp. 255-257.

28. The equation of time involves determining the constantly changing relation of solar time (evident in the daily changes of the length of the day) to mean time (as measured uniformly by a clock). To illustrate the problem, the solar time (sun time) can move in advance of a clock (meantime) by up to sixteen minutes, and contrarily, solar time can lag behind the clock by as much at fourteen minutes. To account for this, Huygens eventually developed tables for the equation of time which he began to circulate in Spring 1662. See O.C., vol. 4, pp. 138-142.

29. Obtaining an accurate figure for solar parallax was critical; the assigned value affects other calculational elements. Historically, figures for solar parallax were too high, in concert with the belief in a relative small cosmos. By the 17th century, traditional figures for solar parallax gave way to lower values resulting in a corresponding increase in the size of the planetary system. The modern value for solar parallax is 8.8″. Ptolemy, Copernicus, and Tycho accepted a value of 3′, Boulliau, 2′21″, Huygens, 8.2″.

30. See C. Wilson, ‘Predictive Astronomy in the century after Kepler.’ In: Planetary astronomy from the Renaissance to the rise of astrophysics, part A, Tycho Brahe to Newton. Cambridge, 1989, pp. 161-206, citation on p. 176.

[p. 112]

between solar time and mean time. While the inequality of the solar day was well known to the ancients, the daily inequality was so small that it could not be tested. In the absence of accurate clocks, Ptolemy approached the problem mathematically focusing on long-term cumulative inequalities^31. which in turn included figures for solar parallax, solar eccentricity, and obliquity of the ecliptic. Huygens - as well as Auzout, Picard, and Cassini - would continue to re-determine these critical constants.

For centuries astronomers, including Copernicus, accepted Ptolemy's assumptions and followed similar calculational procedures.^32. Kepler, however, broke with tradition regarding the equation of time; Kepler argued, as did several followers - including Boulliau, Thomas Streete, Vincent Wing and others - that the Earth's rate of diurnal rotation is not uniform but increases as it approaches the sun.^33. Employing the pendulum clock to determine right ascension directly (without assumptions or measurement of refraction), Huygens was persuaded that the Earth rotates uniformly. But how is the calculation to be made? Here the disagreement began to unfold between Huygens and Boulliau. In the course of their correspondence, Boulliau found himself defending Kepler against Huygens and the ‘universal measure.’^34. Unfortunately, there is no record of subsequent conversations between Boulliau and Huygens on this matter, though we can assume that they discussed the matter when Huygens later visited Paris. There is, however, a long letter from Huygens to Pierre Petit in May 1662 detailing Huygens' views. This letter leaves no doubt that Huygens had small regard for traditional calculational procedures.^35. In the end, the dispute over the equation of time is not mentioned again after the 1662 exchange. More curiously, and within the next five years, Huygens broke off correspondence with Boulliau, refusing to respond to his requests.^36.

By mid-1666 Huygens was of course situated at Paris.^37. To be sure, during the four-year interval their exchange of letters was interrupted by various trips, notably in 1661 when Huygens visited London and Boulliau traveled to Poland to visit Hevelius. The exchange during this period - which deals with the new academy and the long-awaited transit of Mercury - is suggestive if not telling. In his letters from Danzig Boulliau showed great enthusiasm for Hevelius' industry, not to mention his personal satisfaction (as he later learned from Hevelius) that the much awaited transit accorded well with his Philolaic Tables - indeed, better than the Rudolphine.^38. Although he had spent the previous month assisting Hevelius with his observations, on the day of the transit Boulliau was on the road between Danzig to Warsaw; he had been called to court to be honored by the Queen.^39. Boulliau lamented having missed such a rare spectacle. In London, for his part, Huygens took every precaution to witness the passage. In the aftermath of the Great Fire, London was rebuilding and would soon crown a new king - indeed, 3 May 1661, a day of conjunction, presented two spectacles, a transit and a Coronation. Much to his father's chagrin, Huygens attended the former. Assisted by a little-known astronomer, one Mr Streete, Huygens' established his vigil at the shop of Richard Reeves, the telescope-maker at Longacre.^40. Later that year, Huygens' assistant published his Astronomia Carolina in honor of Charles II.

At best symbolic, the exchange of letters concerning the transit of Mercury signals a shift. Thereafter, the question of the clock and the equation of time are never

31. See Ptolemy's Almagest, Chapter 9, Book 3. For the discussion between Boulliau and Huygens on this problem, see Huygens to Boulliau, 29 January 1660 (O.C., vol. 3, p. 29), and Boulliau 's treatment of 26 March 1660 (Ibid., pp. 51-55). In his letter of 22 April 1660, Huygens suggests the discussion be delayed until his forthcoming visit. The topic does not appear in Huygens' correspondence until 25 April 1662 when he wrote Petit (O.C., vol. 4, pp. 138-142).

32. Both Ptolemy and Copernicus assumed a uniform daily motion. Regarding solar parallax, see A. Van Helden, ‘Solar Parallax and Refraction from Riccioli to Richer’ (Unpublished).

33. Wilson, ‘Predictive Astronomy’ (n. 30), p. 197.

34. An accurate clock allowed Huygens to determine right ascensions directly without recourse to traditional observations and tables of refraction. Some 17th-century planetary tables involved multiple refraction tables showing slight variations between seasons. Tycho, for example, employed separate tables for the sun, moon, and for the planets. Huygens published tables for the equation of time only in 1665. See Huygens to Pierre Petit, [25 May 1662], O.C., vol. 4, pp. 138-142, ‘A Monsieur Petit, Sur l'Aequation des jours.’

35. See Huygens to Pierre Petit, [25 May 1662], O.C., vol. 4, pp. 138-142.

36. See Boulliau to Huygens, 19 March 1666 (O.C., vol. 6, p. 20), and particularly, Boulliau to Huygens, 11 April 1667 (Ibid., p. 125).

37. Huygens returned to The Hague in 1670-1671 and 1676-1678, finally leaving Paris permanently in 1682.

38. Boulliau to Huygens, 11 July 1661. O.C., vol. 3, p. 290.

39. Boulliau arrived in Danzig in mid-March 1661 and stayed for six weeks. During that time he observed the solar eclipse of 29 March but failed to witness the transit on 3 May. En route to Warsaw, Boulliau received 1,000 livres from Queen Marie-Louise de Gonzague. See Correspondance Politique, vol. 14, f. 463r, Archive du Ministère des Affaires Etrangères, Paris.

40. See Huygens to Boulliau, 13 June 1661. O.C., vol. 3, pp. 278-281.

[p. 113]

again mentioned, nor are Boulliau's planetary tables. But clearly these were continuing concerns. Planetary tables were a critical issue for early members of the Académie. In particular, Huygens and Picard repeatedly claimed that Kepler's tables, though in need of revision, were the best planetary tables available. To be sure, other tables vied for allegiance, most notably those of Thomas Streete - and justly so. Although he followed Kepler and Boulliau in certain matters, Streete employed an extraordinarily good figure for solar parallax. In his Astronomia Carolina he followed Huygens' harmonic argument.

And clearly, one of Huygens' chief contributions to planetary theory was devising a new figure for solar parallax. As described in his Systema Saturnium (1659), Huygens rightly rejected a number of traditional methods for determining the value, and finally invoked a method based on the principle of harmony. In retrospect, the figure Huygens selected for solar parallax was critical to his success. In the end, Huygens settled on a value of 8.2″, which is very close to the modern figure.

Conclusion

Previous commentators have noted that Huygens and Boulliau were ‘friends’, ‘good friends’, and ‘intimate friends’, but of all of Huygens' ‘anciens amis’, none, perhaps, provides a better counterpoint to Huygens' career. As Boulliau remarked, when the Académie des Sciences selected its members, Christiaan Huygens was unquestionably ‘first among them’, and if the ‘Triumph of Huygens’ was crowned by his appointment to the Académie, we cannot ignore his authority in questions of problem selection and standards of evidence. From his apartments in the Bibliothèque du Roi on rue Vivienne, Huygens represents a clear generational shift. And if friendship can illustrate transformation, it is difficult to imagine two more likely figures - Huygens and Boulliau - to mark the path of the Scientific Revolution.