Between Friends:  Huygens & Boulliau
Robert A. Hatch - University of Florida

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

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

In 1655 Ismaël Boulliau (1605-1694) was widely regarded as the foremost mathematical astronomer in France. 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 'intelligencer' he played a major role in the Republic of Letters. When the son of Constantijn Huygens visited Paris in 1655, Boulliau was at the height of his career.  Boulliau was fifty years old, Christiaan barely half that at age twenty six. 

But the decade brought dramatic change. As the 'Young Archimedes' became the acknowledged Ornament of Europe, the centerpiece 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 pivotal point in the Scientific Revolution. The relationship between Huygens and Boulliau, a counterpoint in individual careers, reflects similar shifts in authority. 

While a number of studies focus on Huygens' dramatic decade--several citing his friendship with Boulliau--the relationship has been largely overlooked.  This essay explores that relationship, not to highlight Huygens' success or Boulliau's decline, but to illustrate dramatic shifts in scientific 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.

Making Time:  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 the extraordinary outcome of his career, it is well to recall the difficulties Huygens faced at the outset. In the course of the decade, the ambitious son of Constantijn Huygens would be accused of plagiarism by no less than Prince Leopold de Medici, Galileo's patron; Vincenzio Viviani, Galileo's devoted disciple; most members of the Accademia del Cimento; and from other quarters, by Hooke, Wallis, Roberval, Hevelius, and a coterie of clockmakers preferring to avoid patent royalties.  It was an inauspicious beginning. 

The most disturbing yet fruitful part of Huygens' first controversy began shortly after the publication of the Horologium of 1658. Since the basic outlines of the dispute are well known, I focus on the challenge of Prince Leopold, an accusation sent to Boulliau. A longtime friend, correspondent, 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. 

As widely noted, Boulliau defended Huygens' honor and exercised tact and sound judgment.  Here we dwell on the obvious. The accusation was unwanted; Boulliau was caught between two worthy 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. 

Though the pendulum clock promised significant scientific, practical, and perhaps monetary rewards, the dispute left young Huygens feeling smitten.  The sensation would linger.  Yet 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 design. To avoid being taken as a 'rascal plagiarizer,' as he put it to Boulliau, Huygens needed information. 

But Huygens was young, unknown, and doubtless represented a threat to Galileo's legacy. Protocol required a proper introduction, and here Boulliau, interceding on Huygens' behalf, requested that Leopold provide diagrams of Galileo's pendulum clock as well as evidence of the model that was said to be constructed by Galileo's son. In response, in addition to drawings, Leopold added further weight to the Florentine's claim by including an historical account of the clock composed by Viviani. 

Here again Boulliau mediated in an attempt to act in Huygens' best interests. Upon receiving Leopold's large parcel, Boulliau made copies for himself and sent the two drawings to Huygens. But here, a point of some contention, Boulliau exercised his judgment and took advantage of his position as intermediary. Judging Viviani's history as a complicating factor, he did not forward the document to Huygens, nor did he raise the issue again with the Prince of Tuscany. The evidence (or lack thereof), of Boulliau's failure to forward the document to Huygens, and his silence on the matter with Leopold, suggest this was not a secretarial error but a strategic gesture based on years of diplomatic experience. In retaining Viviani's history, Boulliau withheld fuel from the fire. And as luck would have it, attention soon shifted to a new problem, Saturn's rings. As Huygens' theory fixed attention on another Galilean legacy, Viviani's effort was soon forgotten.

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.  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 he was no plagiarist or usurper but an ally. By substituting Saturn for the pendulum clock, uygens was no longer the enemy but the legitimate heir to his Italian hero. Far from threatening or contradicting the master, Huygens' work would now recall and extend Galileo's pioneering efforts, the Medici name would grow with Galileo's--and Huygens'--reputation. 

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, secrets, favored initiates, controlled leaks, and strategies for ensuring priority. It began with in winter of 1655-1656 when Christiaan and his younger brother Constantine first uncovered Saturn's secret. Occupied with the pendulum clock, however, Huygens delayed three years before finally publishing his Systema Saturnium ( July 1659). In the interim, Huygens 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 clock. Two years before it was made public, Huygens shared his secret with Boulliau. The formula for a good secret has longstanding ingredients. First, the secret should involve a benefit for each member; second, the confidant is trusted to hold the secret in proportion to circumstances; third, the secret--if it is to ensure against later claims--is best placed with an acknowledged authority, someone who adds credibility to the claim. Finally, the friend and authority should be selected not only to ensure against rival claims, but to exercise influence in ensuring a fair hearing. If possible the confidant should be converted early to assist in persuading or at least mollifying the most powerful critics. 

On all counts Boulliau was qualified. But the secret also produced residual effects. To be sure, Huygens had 'high regard' for the astronomical skills of the older Boulliau, and doubtless, Huygens appreciated his skilled intervention in the affair with Leopold. But Boulliau could keep a secret.  In stretching the drama--using the delay to make modifications to his theory--rumor, gossip, and speculation heightened anticipation of its public debut. The logic of the secret was that Huygens would not tell, and as holder of the secret, Boulliau became the envy of Paris. 

The second person to join in Huygens' secret was Jean Chapelain. A tertiary poet with little reputation in science, Chapelain would nevertheless become a central figure in the emergence of state-sponsored science. With the death of Gassendi, whom he championed, Chapelain made it clear he would assist Huygens' career in any way possible. A visible mainstay of the Montmor group, Chapelain was one a handful asked to identify potential candidates and forward names for inclusion in the nascent Académie des Sciences. In spring 1658, Huygens authorized Chapelain to read a letter to the Montmor group explaining his hypothesis. Chapelain was honored to deliver the message. Thereafter he became Huygens' chief source on Parisian society and politics. 

In the meantime, Boulliau continued to represent Huygens in his pursuit of a just gloire. Skilled in controversy, Boulliau now represented Huygens in charges from a different direction, this time from Boulliau's longtime friend, Johannes Hevelius. The Danzig astronomer had earned an international reputation, and like many of his generation--Gassendi, Boulliau, Riccioli, and Roberval--Hevelius had observed Saturn for a number of years. Systematically observing Saturn's appearances since at least 1642, Hevelius patiently withheld publication for nearly fifteen years in order to observe a representative phase from one 'solitary' appearance of Saturn to the next. Finally, in June 1656 Hevelius published his Dissertatio de nativa Saturni facie, where he provided, with his usual clarity and practical mindedness, tables and illustrations of Saturn's period and changing form. Huygens was certainly aware that Boulliau and Hevelius were longstanding friends. 

Happily for Huygens, Boulliau was able to fulfill a key function of the confidant. As it turned out, Huygens had offended Hevelius (among others) with certain of his claims. 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. Although he had mistaken it for a fixed star, Hevelius had observed and plotted the position of Titan years before, and as for the ring hypothesis, what evidence could Huygens produce? Here Hevelius focused his harshest criticism on Huygens' insistence on Saturn's thick solid ring. But the heart of the matter was Huygens' claim that his telescopes were superior to all others. Having vented his spleen, Hevelius soon forgot the matter, but he recognized that Huygens' claim should not go unchallenged. If the claim was taken seriously, superior instruments implied better observations and stronger theories. If rival theories were based on questionable observations--which Huygens suggested might account for disagreements surrounding the triple-bodied appearance of Saturn--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 interpretation and guesswork. With Hevelius quelled, Huygens again profited from Boulliau's friendship. 

When he sought Boulliau's opinion concerning the ring hypothesis, however, Huygens received 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: nevertheless, you still need some experiments in order to demonstrate absolutely that which you propose. 

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 the course of its 30-year solar orbit. The solid ring, moreover, had an invisible outer edge. One of the functions of this ring, Huygens argued, was to account for the broad shadow cast on Saturn's central body. A thin ring, Huygens' maintained, would not do. On the assumption of a thick ring, the difficulty that remained was to explain how it could pass unobserved, particularly when viewed 'on-edge.' Here Huygens speculated that the outer edge of the ring was covered with an non-reflective material or, perhaps, was so smooth that it reflected like a point surface. 

When Huygens sought his opinion, Boulliau offered several reservations but was clearly supportive of his general hypothesis. His main concern was that Huygens reconsider the value that he had assigned to Saturn's 'equatorial' ring-plane--23.5 degrees--which was suspiciously close to that of the Earth. As Boulliau well understood, the supposed symmetry was not consistent with observation. Having observed Saturn for nearly two decades, the older Boulliau knew the angle of inclination would have to be modified. Boulliau's second reservation concerned the thickness and function 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.  What remained, Boulliau suggested, was to conduct experiments 'in order to demonstrate absolutely that which you propose.'   Experiments--with Saturn's ring? Although he would be the first to accept mathematical analogies, and while he had received a relatively good telescope from the Grand Duc, Boulliau was clearly suggesting that Huygens construct a working physical model. To demonstrate his hypothesis absolutely, Huygens would have to account for the appearances by means of repeatable experiment. 

But happily, back in Florence, Huygens was about to be vindicated. Beginning in summer 1660, members of the Cimento began a brilliant series of tests in an attempt to reproduce the appearances of Saturn's rings.  In the course of the next year they developed physical models representing alternative hypotheses that claimed to account for the appearances of Saturn's rings. At about this time Huygens began to correspond directly with Leopold, no longer depending on Boulliau or intermediaries such as Nicolaas Heinsius and Carlo Dati. 

The impetus behind the Cimento's research obviously cannot be known with certainty, though the results clearly moved Huygens' reputation beyond vindication to celebrity. In all likelihood, the Cimento was more concerned to clear the name of Galileo than to promote the young man from Holland. If Huygens' hypothesis proved correct, it was necessary to demonstrate with deliberate speed the difficulties of the problem or, more delicately, to show how inadequate instruments might account for inconsistencies in Galileo's pioneering efforts. 

As an interlude, the question of the pendulum clock was still at issue. Through Boulliau as intermediary, Leopold had amply expressed that he had no doubt of Huygens' ability to produce the pendulum clock. Indeed, now knowing the 'eminence of his Genius,' Leopold had come to expect 'even greater things.' For his part, Huygens would now present his Systema Saturnium, complete with an elaborate dedication to the Prince. Since the printed epistle within the volume seemed to speak for itself, Huygens sent it without a personal cover letter, and consequently (but inexplicably) received no personal reply. For all of that, it was clear from other sources that the Prince had received the dedicated volume and he highly approved. 

In the meantime, during summer 1660, Saturn became the cause célèbre for the Cimento. Following Borelli's lead, members constructed and tested a number of 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, at different distances, and under various lighting conditions. They also ingeniously included outside observers. Acknowledging that variations in skill are sometimes accompanied by different investments and expectations, the Cimento invited passers-by to report what they saw, to add their weight as witnesses to that of the Prince. 

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

Given the final verdict, which affirmed the superiority of Huygens' model over cruder multi-body models, Huygens nonetheless remained steadfast on the issue of the ring's thickness. With time he modified some of his opinions. One of the easiest to change was his view on the inclination of Saturn's ring, which he increased to about 31 degrees from the strongly analogical value of 23.5 degrees.  Although he never changed his mind concerning the question of thickness, Huygens best measure of success was that such details counted little. As with the pendulum clock and the spring-balance watch, Huygens' general solutions--brilliant, elegant, workable--won the day.

Calculations & Clocks

I grant 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. -- Chr. Huygens,  Systema Saturnium (1669) 

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 Académie des Sciences.  Central to the careers of both Boulliau and Huygens were issues concerning planetary motion and, concomitantly, the equation of time, the height of the pole, the obliquity of the ecliptic and, not least, solar parallax.  These were key concerns for early members of the Académie, Huygens in particular.  These mutual concerns also offer insight into the relationship between Huygens and Boulliau on issues of authority.

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 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 which in turn included figures for solar parallax, solar eccentricity, and obliquity of the ecliptic. Huygens--as well as Auzout, Picard, and Cassini--would attempt to re-determine these critical constants. 

For centuries astronomers, including Copernicus, accepted Ptolemy's assumptions and followed similar calculational procedures.  Kepler, however, broke with tradition. 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.  Employing the pendulum clock to determine right ascension directly (without assumptions or measurements concerning refraction), Huygens was persuaded that the Earth rotated uniformly. But how was the calculation to be made? With what assumptions? Here a disagreement began to unfold between the two friends. In the course of their correspondence, Boulliau soon found himself defending Kepler against Huygens and the 'universal measure.' 

Unfortunately, there is no record of subsequent conversation between Boulliau and Huygens on this matter, though Huygens clearly indicated that discussion was best deferred until his forthcoming visit to Paris. Although Huygens never wrote Boulliau again on this matter, there is a long letter from Huygens to Pierre Petit in May 1662 detailing Huygens' views. This letter leaves no doubt that Huygens had little regard for the calculational procedures of Boulliau--or anyone else. 

It should now be noted that some five years later, in spring 1667, Huygens broke off correspondence with Boulliau and inexplicably refused to respond to two of Boulliau's requests.  The reasons are not at all clear. By mid-1666 Huygens was of course situated at Paris, and there is no evidence of significant contact thereafter. 

One factor in the failed friendship can be traced to the dispute over the equation of time. It is not mentioned following their 1662 exchange. To be sure, their exchange of letters was interrupted by Huygens' various trips, among them to London, as well as Boulliau's extended visit with Hevelius. In his letters from Danzig Boulliau showed great enthusiasm at Hevelius' industry, not to mention his findings for the transit of Mercury in 1661, which seemed to accord so well with his Philolaic Tables. For his part, Huygens politely inquired after Hevelius and his observational efforts, his instruments, and their doubtless magnificence and beauty. From London, Huygens informed Boulliau of his observations of the transit, which he made with the telescope-maker Reeves and a little-known astronomer, one Mr Thomas Streete. 

Thereafter, the number and character of letters exchanged between Huygens and Boulliau suggests their close relationship had ended. The question of the clock and the equation of time, two critical concerns for Huygens, are never mention nor are Boulliau's planetary tables. The apparent change of heart merits further investigation. 

Elsewhere, however, one finds information about Huygens' views on the equation of time. Here it becomes clear that his solution was to employ the clock in concert with conversion tables. Published in 1665, these tables allowed the user to convert between mean time and solar time. More generally, planetary tables were a constant topic of discussion between early members of the Académie. Most notably, Huygens and Picard repeatedly claimed that Kepler's tables, though in need of revision, were the best available. To be sure, other tables vied for allegiance, most notably those of Thomas Streete. And justly so. Although Streete followed Kepler and Boulliau on certain matters, he employed an extraordinarily good figure for solar parallax. 

And clearly, Huygens' chief contribution 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 this figure but finally settled on a method based on the principle of harmony. In retrospect, the figure seized upon by Huygens for solar parallax, which largely determines the accuracy of other elements in planetary theories, was critical to his final success. In the end, Huygens chose a value of 8.2', which is extremely close to the modern figure.


Previous scholars have judged Huygens and Boulliau 'friends,' 'good friends,' and as 'intimate friends' with Boulliau acting as 'agent,' 'advisor,' and 'confidant.'  But of all of Huygens' 'anciens amis,' Boulliau is perhaps the best counterpoint to Huygens' career.  As Boulliau remarked, when the Académie des Sciences was founded, Christiaan Huygens was unquestionably 'first among them,' and if the 'Triumph of Huygens' was crowned by his appointment to the Académie des Sciences, we cannot overlook the authority he brought to problem selection and standards of evidence. From his apartments beneath the Bibliothèque du Roi on rue Vivienne, Huygens represents a generational and institutional shift.  At this critical juncture of the Scientific Revolution, it is difficult to imagine two friends with two more telling careers.

Delivered 8 July 1995, Academy Building, Leiden University
The final version of the paper presented above has been published as an article, with full citations, in the conference proceedings De zeventiende eeuw: Cultuur in de Nederlanden in interdisciplnair perspectief, 12 (1996), nummer 1: 106-116.