The Book Nobody Read

by Owen Gingerich

  Did this single, crucial word give Kepler the clue for his greatest discovery? And was Copernicus himself on the scent of the planetary ellipses? The fact that we can definitively answer the second question with a resounding "No!" comes as a considerable surprise to many of my colleagues.

  I N 1985 A Louisville Seminary theologian named Harold Nebelsick published a fascinating but wrongheaded book entitled Circles of God. He made the provocative claim that the requirement of using circles and only circles to explain celestial motions was a theological invention of the ancient Greeks and a bad idea that had held astronomy in thrall for two millennia. Included in his contention was the insinuation that Copernicus had failed because he stuck with circles, not noticing that the orbits of the planets were really ellipses. But there was no way Copernicus could have found the ellipse, because the observations he had weren't nearly accurate enough.

  That there is a problem becomes very clear if you draw an ellipse corresponding to the orbit of Mars. Take an ordinary piece of letter paper, put two tacks in about an inch and a half apart to represent the foci of the ellipse, then loop a string around them to guide the pencil using the page to its fullest, and you will get an ellipse. If you then draw the corresponding circle (with a radius of nearly four inches), you will be hard put to tell which is the ellipse and which is the circle, because the difference is about the width of the pencil line. Naturally astronomy textbooks don't show it this way, because they can't make the point about ellipses unless they enormously exaggerate the eccentricity of the ellipse. So for centuries, beginning with Kepler himself, a false impression has been created about the elliptical shape of planetary orbits. The eccentricity of planetary orbits (that is, their off-centeredness) is quite noticeable—even Ptolemy had to cope with that—but the ellipticity (the degree the figure bows in at the sides) is very subtle indeed. Observations of Mars must be accurate to a few minutes of arc for this tiny ellipticity to reveal itself. This is near to the limit of naked-eye acuity, and such observations simply weren't available to Copernicus or any of his predecessors. Not until Tycho Brahe's massive and precise observational campaign was the requisite data bank available, and within fifteen years of that availability, Kepler, with Tycho's record books in hand, found the elliptical compression of the orbit.

  What about that passage in De revolutionibus, the place where Schreiber had written ellipsis in the margin? Could Copernicus have been on the trail of the ellipse? The Polish astronomer realized that when he replaced the Ptolemaic equant with a small epicyclet, the resulting path would not be exactly circular. In fact, though he never said so explicitly, the combination of deferent and epicyclet produced an ellipse. But it's a wrong ellipse, one that bowed out where the correct ellipse bows in. Copernicus' curve was an artifact of his model and had nothing to do with the true trajectory of the planet. Still, it's very romantic to speculate that the Greek word Schreiber penned in the margin had some subliminal power of suggestion on Kepler.

  Copernicus, like Ptolemy centuries earlier, used very few observations to establish the parameters of the planet's orbit. He was no doubt blissfully unaware that for a brief period every seventeen years both his and Ptolemy's predictions for Mars went horribly wrong. For Ptolemy, Mars lagged behind the predictions by five degrees; for Copernicus, the ruddy planet went ahead by about four degrees. Apparently Kepler was the first person to comment on this, and he probably noticed it only after he had corrected the orbit of Mars for other reasons.

  When I first became aware of this anomaly, I assumed it was caused by some erroneously chosen constant that entered into the calculations. Eventually I tried tweaking the numbers used in the model. The results proved very disconcerting. While I could make the error go away in one place, it always popped up somewhere else. Clearly there was a fundamental defect in the model itself, and it couldn't just be the lack of an ellipse.

  Copernicus failed in this matter not because he hadn't caught on about the ellipse but because he wasn't Copernican enough. It was Kepler who remarked, in a slightly different context, that Copernicus was unaware of his own riches. If Copernicus had really believed that the Earth was just one of several planets, he should have treated them all the same. That would have been the "Copernican" thing to do. But Ptolemy hadn't used an equant for the Sun, and therefore Copernicus didn't use his equant substitute for the Earth. (The Earth and the Sun are the two celestial objects at opposite ends of the connecting line, and the mathematics works the same way regardless of which end of the stick is considered the stationary reference point.) The bottom line: In the Ptolemaic system the Sun moved around its circle at a constant speed—it just looked as if it moved at different speeds because that circle was eccentric to the earth. Likewise in the Copernican system the Earth moved around its circle at a constant speed—the Sun just looked as if it moved at different speeds because it wasn't at the center of the Earth's circle.

  And this, Kepler believed, had to be wrong. If Mercury, the planet closest to the Sun, moved fastest, and Saturn, the most distant planet, moved slowest, then this was because Mercury, being closer, soaked up more of the Sun's motive power and thus naturally moved faster. But in winter the Earth was closer to the Sun than in summer, and Kepler reasoned that it should actually be going faster in its orbit in winter. That was physics, and Kepler, as the world's first astro-physicist, worked out the consequences. Maestlin rapped his student on the knuckles for that. He wrote to Kepler, "I think that one should leave physical causes out of the account, and should explain astronomical matters only according to the astronomical method with the aid of astronomical, not physical, causes and hypotheses. That is, the calculation demands astronomical bases in the field of geometry and arithmetic."

  But Kepler persisted. He had to adjust the position of the Earth's orbit to make it work, and when he did, the periodic five-degree error in the Mars predictions just melted away. That was the biggest single correction that Kepler made in predicting the positions of the planets, and he doesn't get much credit for it because the astronomers who later selected three of Kepler's discoveries and numbered them as three laws (perhaps to match Newton's three laws) simply passed over this one as being too obvious.

  Even before he made this discovery, Kepler found a tricky way to calculate, quite accurately, the longitude of Mars as it went in orbit around the Sun. But when he tried to locate Mars as seen from the Earth, he ran into trouble. The calculation that worked so well in tracking the east-west motion of Mars around the sky simply wouldn't work for Mars's north-south deviations in latitude. When he fixed that, he ended up with a maximum error of around half a degree. This was already ten times better than Ptolemy or Copernicus had achieved, but it wasn't good enough for Kepler because it didn't match Tycho's excellent observations. He could have used a jury-rigged, physically inconsistent scheme to get the longitudes almost five times better (or fifty times better than Copernicus' maximum error), but to Kepler that lacked reality because it didn't give correct latitudes, and unlike his teacher, he was a thoroughgoing realist. Kepler tried an ellipse, not quite the right one, as an approximating curve. And then came a moment of truth. "Oh ridiculous me!" he wrote. "I could not find out why the planet would rather go on an elliptical orbit. . . . With reasons agreeing with experience, there is no figure left for the orbit of the planet except a perfect ellipse."

  Had he got the clue from that little marginal note in his De revolutionibus? I doubt it, but who knows what pathway triggered his imagination?

  The ellipse would have been hard for Copernicus to accept because he was so thoroughly committed to the principle that celestial motions should be explained in terms of uniform, circular motion, but in the end he surely would have approved the quest for a physically real system.

  * Ever since reading that, I've wished I could read Latin well enough to make such a judgment. Considering that its author misled a great many readers into supposing that the introduction was by Copernicus himself, I have to assume that it takes a parti
cularly astute and perceptive critic to detect such nuances.

  * In the Tubingen grade reports, a capital A was an A, and a lowercase a was an A.

  * Edition Leipzig agreed to print a repair kit for the Astronomicum Caesareum, but abandoned the project when so few buyers caught on that something of this sort was needed. Since then I have used the color proofs of its aborted repair project to correct more than a dozen copies—typically requiring nearly eight hours of work on each one—and I have distributed repair kits to about a dozen other owners.

  * ln fairness to full disclosure, I have to say that two of Germany's leading experts on Kepler's hand are fully convinced that I'm wrong, but their opinion does not come to terms with the fact that such a similar annotation also appears in Maestlin's De revolutionibus. Clearly there is a close connection between the two notes, which both begin with the identical words Quae de hac quaestione . . . possunf, it would be exceedingly odd if Kepler copied just part of the annotations and nothing else from his teacher's book. The most distinctive handwriting feature of the short nore is the way the tall s and t are joined in the word quaestione. I searched many pages of Kepler's manuscripts and found that he used such a combination only very occasionally. For Maestlin the conjoined letters are frequent, including in his own name, with a closely matching appearance.

  Chapter 11

  THE INVISIBLE COLLEGE

  IT WAS DUMB luck that Miriam and I missed the flight out of Oklahoma City on a Sunday in February 1993. The airline counter was suspiciously empty, and we should have had an instant foreboding that something was wrong. "You're quite early for the flight," the attendant cheerfully informed us. But then she examined our tickets. "Woops—your plane left half an hour ago! But don't worry. You can get to Boston via Chicago instead of Dallas, and neither segment is full."

  The nature of my blunder dawned on me after a few moments. At that hour our connection in Dallas was boarding, not the link from Oklahoma City, which had long since departed. We had showed up at the right time, but in the wrong state! But if I hadn't made that stupid mistake, I might never have learned where Jofrancus Offusius was born nor unscrambled his connection with De revolutionibus, and I might even still think that his name was an erudite Greek pseudonym based on the celestial constellation Ophiuchus, the Serpent Bearer.

  We had come to Oklahoma to attend a conference at the university in Norman, and while there I intended to take advantage of its outstanding collection of rare books in the history of science. I had inspected its copy of Copernicus' book early on in my search, in fact, so near the beginning that I hadn't been very savvy about what to look for in the annotations.

  My colleague Bob Westman had come to the conference too, and when I learned that after the conference the library was being opened specially for him Sunday morning, I decided to come along to have a fresh look at the De revolutionibus. Had I remembered when our plane was really scheduled to leave, I never would have taken the extra time to sit with the Copernicus book again, and to copy out some of the more interesting notes. And then I would have overlooked an important clue to a puzzle about the Copernicus books that had been baffling me for nearly a decade.

  Unfortunately, not every owner of De revolutionibus bothered to put his name in it, and in particular I had a cluster of copies with very similar annotations but no clearly defined original annotator. One potentially useful feature of Copernicus' book, for those readers who actually wished to calculate the position of a planet, was the so-called mean motion tables, the first step in locating a planet. But to use the tables, it was necessary to have a starting position, or radix, something that Copernicus unfortunately buried in the text where it was a nuisance to find, so this group of annotators had written in a starting position for 1550 at the bottom of each relevant table. Thus I called whoever started the sequence the "Master of the 1550 Radices," but his mysterious identity had eluded me.

  As I sat with the first-edition De revolutionibus at the University of Oklahoma that Sunday morning, one unusual detail caught my eye: three marginal references that attributed the original annotations to someone named Vesalius. Westman allowed that he had noticed the name earlier, but like me, the only Vesalius he had ever heard of was the famous medical doctor whose De humani corporis fabrica, published in 1543, the same year as De revolutionibus, had revolutionized the study of human anatomy. Did Andreas Vesalius also have a secret life as an astronomer? Strange things had turned up in the census, but nothing quite as astonishing as that.

  Thanks to the helpful clerk at American Airlines, we made it back to Cambridge only an hour after our originally scheduled plane. A few days later, in reviewing my notes, I suddenly noticed that the longest note I had transcribed, on folio 127, matched an annotation that had previously turned up in seven other copies of the book. What was really maddening was that each of the notes was written in the first person—"Ego reperi . . . (I have found . . .)—and yet they were written in eight different hands.

  A seemingly valuable clue to the elusive original annotator had come not from one of the books in the Master of the 1550 Radices series but from a quite different copy of De revolutionibus. It was in Yale's Beinecke Library, the copy that had exhilarated me so much years before when I had identified it as a long-lost one that had been owned by someone with at least an indirect connection to Paul Wittich. At the back of the Yale book an early owner had written that Thaddeus Hagecius—the personal physician to Emperor Rudolf II and a sometime astronomical author himself—had found out from Paul Wittich about three errors in Copernicus' book. These he listed in their stark triviality. The last two, minor arithmetic mistakes in the great cosmological chapter in Book I of De revolutionibus, were pretty inconsequential. But the first related to folio 127, the very place where the Master of the 1550 Radices copies had such a huge annotation.

  In at least one of the eight copies, in a De revolutionibus in Debrecen, Hungary, the same three errors were marked, in so precise a way that it couldn't be coincidence.* A slender clue indeed, but to me, it smelled of Central Europe and in particular of Georg Joachim Rheticus, the rebellious young man who had been Copernicus' only disciple and who had taken De revolutionibus to the press. Subsequently, he had been persuaded by a particularly high salary offer to leave Wittenberg for Leipzig, and had eventually settled in Cracow, from where he had later connections with both Hagecius and Paul Wittich's family.

  But why Rheticus? He had been the professor of mathematics at Wit­tenberg when Erasmus Reinhold was the professor of astronomy there. The census had turned up more than a dozen books with partial copies of Reinhold's annotations, but from Rheticus there were only a couple of presentation copies without any significant annotations. Surely the young man who made the trip to Poland, who first learned of the heliocentric system, and who brought the manuscript back to Germany for publication would have taught the details to a generation of students. Where was his teaching tradition? It was curiously absent from the annotated copies.

  Since finding Rheticus' annotations would be a major coup, I had a secret hope that these eight books might hold a precious record of his own master notes. Rheticus had carefully computed an ephemeris for 1551, that is, an almanac giving planetary positions for every day of the year, of course based on the tables in De revolutionibus. If anyone aimed to embark on such a task, probably the first step would be to calculate the mean position of each planet for some suitable starting date, such as 1 January 1550, and write that in a convenient place. And that is precisely what I had found in the tables of seven of these eight books, which helped me recognize their affiliation in the first place. Only the Oklahoma copy lacked these numbers, and that is why I hadn't caught on right away that it belonged to the set.

  Was the mysterious Master of the 1550 Radices, in fact, Rheticus? In 1992 my Polish colleague Jerzy Dobrzycki came to Cambridge for a research visit, and I put the suggestion to him. He lost little time in shooting it down. Though I had been collecting the materials and worrying about
the problem for some years, I had not yet made a definitive transcription and translation of the longest marginalium, the one on folio 127. Jerzy set to work on my preliminary notes and microfilms. "This is heavy criticism of what the annotator thinks are errors in this very technical passage," he pointed out, "but look here at the end. He says maybe Copernicus didn't do it but entrusted this part to a student. Since Rheticus was Copernicus' only student, he would hardly have written that."

  So it was back to the drawing board to find another candidate for the Master of the 1550 Radices. One of the eight copies, in the Bibliotheque Nationale in Paris, actually had inscribed on its title page the name of the student who had copied the notes: Jean Pierre de Mesmes, sometime astronomer of Paris, about whom very little is known except that he put out an elegant but rather derivative book entitled Les institutions astronomiques. In one marginal note, not found in any of the other copies of this family of annotations, he had added a value for the precessional motion "from my teacher Jofrancus for this current year 1557." And, near the end of the book, he wrote "Johannes Franciscus,* not your ordinary astronomer, made a wonderful Copernican instrument for Master Rousseau."