“Yes, a notice to other scholars that I intend to translate this book. There was the most fearful uproar after three translations of the same book on steelmaking came out within months of each other, all three scholars working unbeknownst to each other. After that, the library agreed to keep records, so that everyone can know which books are already being attended to.”
“And what will you teach now? This probability? Would I understand it?”
“You would, but I won’t teach it until it’s published at least in English so that every student can obtain a copy. I intend to give regular lectures on complex variables at first, since that follows directly after calculus, which is already taught here? Yes? And also an introductory course in physics, which they teach in Grantville at the same time as calculus, so there are many here such as your good self who could follow it. There will be laboratory demonstrations to illustrate the principles and give evidence of their truth.”
“Oh, so? You follow our own Francis Bacon in this, that the nature of the world cannot be known by reasoning alone?”
“To be sure, and Master of Arts Charnock Fielder of Grantville High School as well, who I’ve heard to say in two sentences what the learned Bacon required entire books to convey.”
“And that is?”
“ ‘In science there is no authority. There is only experiment.’ ”
* * *
Richard wasn’t accustomed to being awakened by Doctor Comber. But then, the distinguished Thomas Comber—Doctor of Divinity, Master of Trinity College, past Vice Chancellor of the university, and Dean of Carlisle besides—wasn’t known to make a practice of waking mere lecturers, or even to take the trouble of ascending to a third-floor room.
“Good morrow, Leamington. The dean of the chapel has informed me that Master Ramsey just now went to practice at the organ, and encountered a student of yours asleep beside a guttering candle, by which he was fortunately able to see a large cannon ball on a cord swinging from the ceiling. Would you care to explain that? To the dean? And arrange to have it removed before the morning lectures?”
“Uff? Asleep? At once. My apologies, Dr. Comber.” He scrabbled for his clothing. Under his breath he muttered, “I hope he got the data.”
“And, Leamington? Attend me in my rooms after the second lecture. There are matters we must discuss.”
* * *
Richard knocked on John Rant’s door. In moments there was a stirring within, and the door opened to reveal a very disheveled and confused-looking B.A.
“Richard? There’s light in the sky! I wasn’t called.”
“Indeed. I’ve just now been told that Tom fell asleep during the experiment instead of calling you at midnight to take your turn recording the data. We are required to remove the apparatus at once. Dress and join me in the chapel, if you will. If we’re quick about it, we may even have time for some breakfast.”
“Yes, of course. I’ll be but a moment.”
Richard left at as rapid a walk as the dignity of a lecturer allowed.
* * *
During the first hour Richard attended a lecture. By ironic chance it was on musical scales, and the lecturer was Master Robert Ramsey, the chapel organist. He made no remarks beyond his recent inquiries into the startling notion of an equally tempered scale, in light of the ancient Greek modes, but his displeasure was clear enough by his posture and the dark glances he periodically cast toward Richard. Still, Richard managed to keep his mind on the subject at hand. Mostly.
The second hour went to giving a private lecture on vector calculus to several post-graduate students, who had made considerable inroads into the fragments of new mathematics that had reached the university during Richard’s absence. It was somewhat easier for Richard to keep his mind on that.
And then it was time to call on Dr. Comber in the master’s lodging at the north side of the Great Court. Richard knocked, then entered to see him seated at his writing table, by the big windows.
“Take a seat, Richard. I just want to capture one thought before it escapes...There.” Dr. Comber put down his pen and straightened in his chair. “Richard, you’ve annoyed two fellow members of this college for no good reason. The dean was most upset that you and your students hung that heavy ball in the chapel and set it swinging without saying anything to him first, or indeed to anyone who had reason to go into the chapel and could have walked into its path unaware. He’s responsible for keeping the place in good order and fit for services, lectures, and everything else that takes place there. He needs to know what goes on in his domain. As for Master Ramsey, he had a moment of fright, seeing that thing rush toward his ankles in the gloom.”
“I’m sorry for that, Dr. Comber. Still, no harm was done.”
“No, no harm, except to your own reputation. And that’s concern enough. You’re no longer some raw undergraduate, whose inevitable transgressions are to be corrected with stern admonishments and suitable penalties, and then forgotten. You’re well known throughout the university now, and there are those who look up to you. Your actions have real consequences—some mistakes may not be so easily undone. I had to assure the dean and the organist that you and your students were conducting some serious lesson, and not a midnight jape. I was correct, wasn’t I?”
“Yes, of course. It was a teaching experiment in physics, demonstrating the validity of certain mathematical predictions.”
“Good, as I expected. What, exactly, was this demonstration?”
“It was the Foucault pendulum. It’s one of the two classic demonstrations of the rotation of the Earth.”
Dr. Comber dropped his hand to the writing table in front of him and stared wide-eyed at Richard for a heartbeat or two.
“A demonstration of the rotation of the Earth? A classic demonstration?”
“Yes, first performed in public by the French physicist Léon Foucault in the other history, in 1851.”
Dr. Comber leaned forward with his hands flat on the table and gave a distinct impression of a bulldog. “Do I understand you correctly? Is this a tangible demonstration that apparently settles the controversy between the Aristotelian and Copernican world models at one stroke? And you did this without telling me, or any other officer or senior fellow of this college? Which will now circulate by rumor, because we don’t tell students not to talk about their studies? And cause all manner of upset to scholars who’ve spent their lives studying this very question?”
Richard froze.
“Exactly. You didn’t think. You considered only the mathematics and natural philosophy, and how to present it to your students. Not altogether a bad thing. But now you need to think about your colleagues as well. You’ve told me and the fellows of your hopes to bring whole new fields of learning here. You wish others to take up these studies, and make the university greater in consequence? For that, you need not merely the acquiescence of your fellows, you need their wholehearted support. You won’t get it by discourtesy.”
Dr. Comber sat back, thinking furiously.
“What must be done now is to present this in a proper and respectful scholarly manner to the whole university, and quickly. But before any announcement, I need to fully understand it myself. I would like you to explain it to me. Completely. Now, I understand your time tonight is to be taken up preparing a lesson?”
“Yes, Dr. Comber.”
“And I’m heavily occupied for the next two days. Can you come here after Hall on Friday?”
“Yes, certainly.”
“Good. Come then with your notes and whatever else is needful to make this clear. I think I may ask Thorndike to join us; he’s spent a good deal more time on this new mathematics than I’ve been able to.”
* * *
Richard’s right hand trembled slightly. He told himself it wasn’t from nervousness; after all, he was a seasoned teacher long since. He sat up straighter and looked around the chapel. Nearly time. The seats were filling rapidly with fellows and undergraduates from all over the university. There were at le
ast three heads of colleges. Well, the pendulum was rigged and secured at the start of its arc ready to release, and it wasn’t as if he’d never presented this material before.
The bell overhead rang the hour. Dr. Comber rose and walked to the lectern.
“Masters and presidents, fellows, and scholars, there has been considerable talk of late concerning the knowledge conveyed here from Grantville, in particular a demonstration that took place in this chapel a few nights ago. I’ve asked Scholar Richard Leamington to repeat that demonstration today as a university lecture. I believe this will be of great interest to many of you. Scholar Leamington, if you will.”
Richard went to the lectern, where his notes already rested. He was glad to grasp the side with one hand and steady himself; this was no time to look shaky, insidious malady or no. He straightened, faced the audience with level gaze, took a full breath, and began.
“Thank you, Dr. Comber. Thank you all for coming. As you’ve heard, this will be a demonstration of the Earth’s rotation, by means of mathematics and modern physics used together. Since many of you are able to stay only for the hour allotted to the lecture, we’ll start the physical demonstration first and let it run. I will explain the reasoning while you observe what occurs.” Richard turned slightly and gestured toward the pendulum. “You see before you a weight, suspended by a cord from as high up as the hall allows. As you can see, it’s free to swing in any direction. Notice the sewing needle attached to the bottom of the iron ball with sealing wax, the degree circle marked on the large sheet of paper lying directly beneath the point of suspension, and the narrow ring of sand on the paper. Each time the needle crosses the ring, it will sweep aside a few grains of sand to mark the place where it crossed. The whole apparatus together is called the Foucault pendulum.
“As you can see, we have a clock already running. This is a very accurate laboratory instrument, made in Grantville. Scholar Crosfield will start the pendulum for us now.”
Thomas Crosfield was awake enough today, and blessed with steady hands as well. He stepped forward shielding a lighted candle behind his hand, and gingerly knelt by the pendulum, taking care not to breathe upon it.
Richard fastened his eye on the clock as it came up to the minute. He called out, “Five. Four. Three. Two. One. Loose.”
On that word, Tom brought up the candle and burned through the thread holding back the pendulum. The ball swung away in a stately arc toward the sand ring, while Tom stepped back and blew out the candle. There was the faintest of sounds as the needle flicked through the sand. He returned to his seat and took up a lead pencil and paper.
“Scholar Crosfield has written down the time the pendulum started, and the angle where it first crossed the degree circle. He will continue to do this periodically. By this we will be able to measure the rate at which the plane of oscillation rotates.
“As the pendulum moves, it’s acted upon by the forces imparted by the motion and gravity of the Earth. Starting with the Newtonian equations for these forces and the resulting acceleration of the moving ball, we can show by mathematical proof that at the latitude of Cambridge the plane in which the ball swings must rotate by two hundred and eighty-four degrees per day relative to the stars, or two hundred and eighty-five relative to the sun, just under twelve degrees per hour.” He turned to the movable blackboard standing near the lectern, already filled with the first part of the accompanying derivation. “We begin with the equation for the force of gravity...”
* * *
Today Richard had no lectures to give or attend. John Rant had arranged to call later on, to ask his advice regarding the best way to present a seminar on proof by infinite series. For now, though, it was a perfect time to immerse himself in correcting the latest sheaf of typeset proofs for the English edition of the probability textbook. It wasn’t a large batch today; there should be plenty of time to make progress on the translation work as well. In truth, he was happy to be able to spend most of the day seated. Well, perhaps he’d feel more like visiting one of the taverns tomorrow, or just walking by the river. He glanced out the window at a few students hurrying past the great fountain in the court below—it was just as well to be inside in any case. He took up his pen and set to working steadily through the stack by the watery light from the late autumn sky.
Shortly before the midday meal Richard finished the proofreading and set it aside. He was the picture of an absentminded professor as he hurried across the court toward the dining hall, in spite of being far below that exalted rank. He didn’t seek company at dinner today, being occupied in considering the practicality of constructing the apparatus for the measurement of the universal gravitation constant—without sending to the piano makers in Grantville for a length of fine-gauge music wire. Could it be done with a common lute string? Perhaps some testing might reveal the answer.
He returned still deep in thought to his room, and settled in to rendering probability theory clearly and concisely in Latin, a satisfying challenge. The tingling in two fingers of his right hand faded from his notice. He wrote in the spare up-time style, with no classical allusions, metaphors, or digressions beyond the bounds of mathematics itself. Richard wrote, crossed out, wrote again, made editing marks, wrote again. After a time the weather became typically English. Rain, sun, overcast, wind, at twenty-minute intervals. The sky abruptly turned fair with an unseasonably warm breeze, and Richard thought to air out his room while he had the chance. He opened the windows and the door to the staircase.
He went back to his translation. Hmm, what would be the best way to express the concept of expectation?
There was a soft caress against his ankle. He looked down at orange fur and blue eyes. Nan was looking up at him. He reached down to stroke her side. She leaped to his lap, and from there to the table. She sniffed at the inkwell and brushed her upraised tail against his nose. Richard lifted her aside, off his rough draft, and began scratching her behind the ears to tempt her to stay where she was. She settled down with one paw draped limply over the edge, purring and swishing her tail from side to side. Richard was a little too distracted at the moment to remember whose cat she was, but it hardly seemed to matter to her anyway. His hand continued moving, back and forth, as his mind returned to pondering the problem. Perhaps...He weighed alternative constructions, as they took shape in his mind. After a time footsteps sounded on the staircase. Richard listened with half an ear for a moment, but he didn’t recognize the step, and it was early for John. He wrote another sentence.
There was a knock on the door frame. Richard looked up. “Oh, Dr. Comber.” He started to rise.
Dr. Comber waved him back down. “Do you have a few moments, Richard? I have some questions.”
“Certainly.” Richard waved his hand toward the second chair.
As Dr. Comber drew it up to the other side of the writing table and settled down, Nan opened her eyes. He reached out his hand and she leaned into it, while he gathered his words. His gaze swept across the stacked page proofs and the scattered manuscript sheets on the table. “How does it go, then?” Nan rose to her feet at the broken silence, jumped off the table, and sauntered off to parts unknown.
“Very well. There should be only one more batch of page proofs after these, before the English edition can go to press and I can think of offering a course of lectures. There are already inquiries for copies. As to the Latin manuscript, it’s nearing the halfway mark. The Latin lexicographers helped me greatly in devising suitable terms for the new principles before I left Grantville, and they’ve added them to their technical dictionary.”
“Excellent. But I was asking after your health, more than the work.”
“Not too bad.” He reached for the cane leaning against the bookcase and held it up. “I have this, but seldom need it. The special candle lamp with the focusing lens and mirror that I brought for the microprint viewer helps me work after dark.”
“You didn’t need that cane at all, earlier. Perhaps we’d better find you quarters downst
airs for next term. I’ll say a word to the bursar and see what might be done. More difficulties seeing, too? You have my sympathy. I’m thankful to have spectacles, these days. But you’re able to continue teaching? I know how greatly you wish it.”
“Yes, and it gives me greater satisfaction to aid others in taking up the work. I could never bring such a body of new knowledge to Cambridge by myself. No man could, alone.”
“Indeed. And so we come to my reason for calling on you today.”
John Rant appeared in the doorway. “Oh, Dr. Comber, I didn’t know you were with Richard. Should I come back later?”
“No, stay, you might have some thoughts to illuminate the discussion, with all the time you’ve spent together in study and inquiry.”
Both chairs being occupied, John leaned against the wall beside the door and folded his arms, an expectant expression on his face.
“Richard, I’ve been much occupied with many matters, but you’ve spoken before of what new learning this university might offer to our students. I would like a more thorough understanding of what it consists, and how large a body of knowledge it might be.”
“You’re giving consideration to this, then?”
“It’s far too soon to say that. Before I can consider anything, or usefully speak of such things with the fellows and officers, I must understand the meaning of these subjects you say are studied now in the Germanies, and as well the numbers of those to do the instructing. Particularly the latter. Do you know, this university has been trying for years to get an endowed chair of mathematics?”
“No, I didn’t.”
“Well, it has. With no success. But it seems you made a deep impression on your merchant friend Jeremiah Brantley, who is well known in commercial circles and among other notables of the town. He and the mayor unexpectedly called on me yesterday. He’s apparently made inquiries overseas and consulted with others, and is now engaged in raising subscriptions all over the shire to found such a post. From merchants and town officials! With relations between the university and the town always in a delicate state, this is to be marveled at. It’s also to be approached with great caution, so as not to upset matters.”