by Stuart Clark
‘An ellipse,’ said Newton without hesitation.
Astonishment blossomed in Halley. ‘How, sir, do you know that so certainly?’
‘I have calculated it.’
‘Calculated?’
‘Yes, I calculated it some years ago. I have the paper here.’ Newton rose from his chair and began to rummage through the bookshelves.
Halley could not bear to stay in his seat, but sensed that any attempt to help would not be welcome. His heart quickened when Newton pulled a sheet of parchment from a book and examined it closely. The don then slid the page back into the book and replaced it on the shelf.
‘I cannot find it,’ he said, without looking round. ‘I will have to perform the calculation again and forward it to you.’
‘Can you remember the steps you took in the solution?’
‘Of course.’
Halley waited, expecting Newton to at least outline the stages, but Newton returned to his seat. ‘Who works on this problem in London?’
‘Sir Christopher, Mr Hooke and myself have all given it thought.’
‘Mr Hooke? How far has he got with the problem?’
‘He has ideas, as we all do, but he is no nearer a solution than the rest of us. I fear his algebra will let him down. Unlike yours.’
‘Of course, some say that algebra is the language of God.’
‘Then you must understand Him more than any man alive.’
‘I was born on Christmas Day. That must count for something.’
Halley laughed, but a sharp look from Newton silenced him.
‘Mr Halley, I will send you the calculation on one condition: that you keep it to yourself. You must not show it to anyone, especially not to Mr Hooke. I have found in the past that philosophy is a most litigious lady, with Mr Hooke her most bombastic admirer.’
‘I assure you that a proof of the elliptical orbits of the planets – if you did decide to make it public – would receive nothing but open-hearted praise. For my part, I’m content to receive such knowledge under any conditions that you see fit to impose. You can rest assured that I will follow them to the letter.’
Newton pursed his lips. ‘Then I will do this on account of our acquaintance. It will be my final gift to philosophy. But, I emphasise, it must remain strictly between the two of us.’
‘Granted.’
‘I am adamant.’
Halley met Newton’s cold gaze. ‘So am I.’
Newton’s fingers were still smarting from Halley’s parting handshake some minutes after the young man had bounded from the room. He was thankful that Halley had known better than to press him for a timetable. Even so, just agreeing to help rankled. He did not have the time.
Massaging his hand, he returned to the bookcase and drew out the sheet of paper again. Surrounded by his scribbled mathematics was his diagram of an ellipse, with intersecting lines cutting it into quarters. He had also drawn a couple of diagonal lines across the ellipse.
Unlike the first time he had contemplated the problem – sitting in the quiet of Woolsthorpe, having fled Cambridge during the plague summer – his breakthrough had come just a few years ago when he turned the problem around. Instead of asking what shape of orbit an inverse square force law created, he investigated what force law would create an ellipse.
Working the problem backwards like that had driven him further through the mathematics than before, as if he had just found a path through an overgrown coppice. But the path had been suddenly blocked: the equations had failed to simplify even though every sense within him told him they should work out. He had nearly confessed as much to Halley, but had stopped himself when he realised that to do so would place him on the same level as the London philosophers – the same level as Hooke.
He stared at the page; there must be an error on it somewhere. Perhaps he had confused some of the lines on the sketch. Loath as he was to admit it, drawing was not his strong point. He would check it all again, but not now. He turned the paper face-down and headed for the furnace.
This particular experiment had begun twelve days ago, when he and Humphrey had boarded up the windows and begun the ritual grinding of the limestone. They had lit the furnace and mixed the lime with sulphur and mercury, all in precise proportion. Then they began the continuous stirring that joined the alchemist to the alchemy itself.
Newton slid his hand along Humphrey’s lean forearm, feeling the life within him and gaining the precise motion of the stirring from the flexing of the young man’s muscles. His fingers found the wooden spatula and Humphrey slipped away, back into the main apartment.
The steely liquid should have been engrossing, urging Newton’s mind back to its former neutral state, but in that circulating fluid he saw nothing but orbits. Figures from the page on the bookcase crowded into his head, and symbols too. He began to imagine how the bulk of a planet might affect its motion. What about its distance from another object? And the size of that other object? All of these quantities must define how one body pulls on another. But how precisely did that happen?
Time and again Newton chased away the dancing symbols, only for them to flash back into his mind. He shook his head, then pinched the bridge of his nose so tightly that pain lanced across his cheeks. When he returned his attention to the furnace, he saw that the uniform circulation had broken into eddies.
The furnace transferred its fire into Newton. He stood up, raised his booted foot, and sent the ruined concoction cascading across the floor with a heavy clatter.
Humphrey rushed back into the shed, stammering, ‘I’ll get a bucket and mop.’
‘Leave it,’ growled Newton. ‘Fetch me quills and ink. I must calculate.’
19
London
Hooke fussed about, arranging chairs, yanking them into place and raising tiny puffs of dust from the faded rugs. He opened the folded screens that masked the messiest areas of his apartment and placed the Society’s mace on the table.
The Fellows began to arrive, including, Hooke was relieved to see, the Society’s new president, Samuel Pepys. Newly returned both to England and the heart of the monarchy, Pepys was as rotund as Halley was lean. Both men were chatting earnestly with Wren.
Curiosity burning, Hooke busied himself repositioning a few chairs, edging himself closer to his visitors. As he did so, Halley excused himself and disappeared deeper into the room. Hooke used this as cover and slid closer still.
‘I admire your fortitude,’ Wren was saying. ‘I’ve been hearing about the gale. You’re the talk of the coffee-shops.’
‘We just couldn’t get out of it. Went on for days. Howling, pitching. We took down all the sails and just let the sea have us. At one point I thought we were going to have to lash ourselves down. I still sometimes see the waves in my dreams, tall as mountains . . . Still, better those memories than ones of imprisonment.’
Hooke had heard the stories too. By all accounts, Pepys was something of a hero. He had evacuated the colony at Tangiers and supervised the blasting of the British fortifications into dust so that no enemy could occupy them. The service had finally erased the smears of Catholicism and accusations of leaking naval secrets to the French that had seen him briefly in the Tower.
‘Strange to think that destroying an English strategic asset could lead you back into favour,’ Wren chortled, but Pepys looked at him in all seriousness.
‘When royal whim is involved, one needs to do whatever it takes. Besides, the King couldn’t afford to defend it.’
‘You’re absolutely right. If someone doesn’t stop the counterfeiters, not only will the King go bankrupt, so will the country. But that’s a problem for the future, eh? Right now, congratulations on your new appointments, both here and at the Admiralty.’ Wren bowed his head.
Hooke glanced at the clock, wondering whether it was time to call the meeting to order. An icicle pierced his stomach: next to the tall case with its weights and pendulum, Grace was talking to Halley. She was punctuating her words with smiles and gla
nces through her eyelashes while he leaned against the wall, drinking in her flirtatious behaviour.
Hooke made for them at once.
‘Must all the Fellows be so old?’ Halley was asking her in conspiratorial tones.
Hooke cleared his throat.
‘Uncle,’ – Grace reached past Halley to where her latest creation was wrapped around a mannequin – ‘I was just collecting your coat to finish the alterations.’
She carried the woollen garment out of the room but took a final peep at Halley from the doorway. The gesture was not lost on Hooke, who glared up at the young astronomer.
‘Why do I sense a rebuke is about to be delivered?’ said his victim.
Hooke wagged a crooked finger. ‘I have warned you before.’
‘We were only talking.’
‘Do not bother Grace again. She’s out of your reach.’
‘Rest assured, I am reaching for nothing. Not that it is any of your business, but I’m to be a father. At least I hope so. Mary and I have decided that it’s time to start a family.’
Hooke looked away. ‘It would be best if you just sat down,’ said Halley.
‘Ah, there you are, Mr Halley!’ The new voice was not familiar to Hooke. A small man in a ridiculously large hat was coming towards them.
‘Mr Paget,’ Halley greeted him, ‘what brings you down from Cambridge?’
‘This meeting, of course.’ Paget turned his back on Hooke, who loitered. ‘I’m so relieved to find you, Mr Halley. I’m under instructions to give this to you, and to you alone. It’s from Mr Newton.’
Hooke peered round Paget’s shoulder, catching Halley’s sideways glance full-on. The astronomer took the proffered envelope, held it as if not quite sure what to do with it, then broke the wax seal.
Hooke strained to see inside, bumping into Paget in his excitement.
Halley abruptly stuffed the envelope into his jacket pocket. ‘Gentlemen, I regret that I must bid you farewell.’
Before Hooke could think of anything to say, Halley had left the room.
Hooke fixed Paget with a look. ‘What was in that envelope?’
‘I cannot tell you, because I don’t know.’
Deep down, however, Hooke already knew.
Gravity.
Once back in his Islington study, Halley excitedly scanned the manuscript. It had been months since his visit to Cambridge. He had almost given up hope.
De motu corporum in gyrum
On the motion of bodies in orbit. The title was in Newton’s tight handwriting. Just nine pages in all, but each one was a dense presentation of words, mathematics and diagrams. When Halley failed to find the simple answer as to why planets follow elliptical orbits, he stifled the twinge of impatience and returned to the first page. Reading from the beginning, he still found it difficult to follow the argument. He paused for breath and began again. This time he got a little further before losing the thread and having to retrace his steps.
He fumbled in his desk drawers for paper and copied out the mathematics and the diagrams, emulating the process Newton himself had gone through. Then in a flash he realised why the text was so impenetrable.
It was because he and all the others had been hopelessly naive. Not only had they lacked the skill to answer the question, they had not even known how to frame the question correctly. Newton’s paper gave no simple answer; it was an explanation of how to make the problem soluble.
This was no rough verbiage. Newton clearly stated principles and then tested the assumptions that could be built upon them, using mathematics and graphs, curves and caveats. It was intoxicating. Halley’s brain pulsed with energy and surrendered to the text, allowing his mind to be manipulated into thinking as Newton had done when writing the document.
As the planet drew away from the Sun, so the force dropped and the planet slowed down. Eventually, like a ball thrown into the air, the planet fell back towards the Sun, picking up speed as it went and whipping round the Sun to fly back out into space and start the orbit off again. What everyone had suspected, so Newton had proved. Double the distance, quarter the strength: an inverse square force of gravity.
How could he possibly keep this to himself?
20
Cambridge
Newton woke from a brief night’s sleep and was instantly bombarded with ideas for calculations and experiments. It was as if his brain had worked on through the darkness, waiting for him to revive so that it could force him into action.
Every morning since Halley’s visit had been the same. He hardly knew where to start. All his life he had relished questions and the way his mind drove him to investigate; now he was its slave.
The moving world had become nothing but curves. From the tumble of an orange in the market, to the oscillation of a cart as it rocked out of town. Every movement that Newton saw demanded his attention.
The sky was peachy with the dawn as he strode across the quad to rap on Humphrey’s door. The man appeared bleary-eyed, still in his night chemise.
‘Fetch the pendulum,’ said Newton.
‘But it’s freezing.’
‘Precisely! We will be the only ones about.’
Later that morning, Halley found Newton and Humphrey bundled up and hunched over the pendulum in the college cloisters, just as the urchin had described.
The frost was thick on the grass, and the flagstones were icy in places. Halley’s nose stung with the cold, and his fingers were numb despite being encased in leather gloves. He rounded the corner just as Newton began to stamp his foot. The sharp reports blended with Halley’s own footfalls.
Newton shot a look in his direction. ‘You’ve ruined the experiment.’
Halley came to a standstill. ‘My apologies, I had no idea.’
Newton peered. ‘Mr Halley?’
‘Yes, sir.’
‘Well, well. I fancied that I would see you again after sending my little paper.’
‘Nine pages of brilliant mathematical insight, if I may flatter you so.’ Halley reached into the satchel slung across his shoulder and waved the document. ‘I lost a night’s sleep reading and re-reading it.’
‘Only one?’ said Newton, bending back down to the apparatus.
De motu in hand, Halley addressed Newton’s back. ‘You have derived the planetary motions from first principles. It’s the perfection of astronomy, the–’
‘Not yet, it isn’t.’
‘You tease me, Mr Newton,’ said Halley.
‘Not at all.’ Newton shortened the length of the pendulum string.
‘I know that you wanted your ideas to remain secret, but I should like you to reconsider. They are too valuable to remain unseen.’
‘No!’ Newton whirled to face Halley. ‘Would you say that you have described the bird if all you had was a feather?’
Halley shook his head, discomfited by the intensity of the professor’s gaze.
‘Well, you hold before you the feather, not the bird.’
‘But you have derived Kepler’s three laws from an inverse square force. What else is there to do?’
‘What else indeed?’ said Newton, striding off.
Humphrey spoke quietly while pretending to be busy with the pendulum. ‘Mr Newton is upon this problem with every ounce of his being. I’ve found his meals untouched, and when I remind him he takes only a mouthful or two. If I succeed in urging him to the dining-hall, he is as likely to turn left instead of right and end up in the street. I lose him into the city, only for him to return later and continue working. He hardly sleeps. I have seen him jump from the gardens and run to his room to scribble frantically, breaking one pen after another in his haste to set down his thoughts. He’s lost all his students – he talks to the bare walls about his ideas – and he has me copy his manuscripts, but I can barely make any sense of them. I fear he is in the grip of some mania and is producing nothing but gibberish.’
‘Fifty-seven paces,’ Newton called from the end of the cloisters, startling both men.
Humphrey scribbled the figure down.
Newton walked towards them, talking. ‘So far, all I have done is show how the Sun pulls on the planets. But how does Jupiter pull on the Sun, or on Saturn? How does the Earth pull on the Moon, and does the Moon pull back? I have perfected nothing because I have understood nothing – I’ve barely glimpsed it.’
‘But it is a mighty first step, can we at least agree on that?’ ventured Halley. ‘There are many who–’
‘De motu is grossly incomplete – that is the end of it. You see this work as finished, but I know it is just the beginning.’
‘As you wish, but let me at least describe it at the next meeting of the Society. That way the discovery can be secured in your name.’
‘What about Hooke?’
‘What about him? He has had his opportunity. When I look at the mathematics required in your work, it is beyond Mr Hooke – beyond all of us.’
Newton’s lips narrowed in what might have been a smile. ‘Very well, you may describe our meeting, but not show the document. There are certain clarifications I wish to make, certain aspects of the present paper that could lead to discussion. And I am unwilling to enter into another challenge. I will fix those problems, and then you may publish it. And I will need the comet observations you made.’
‘You think you can do the comet’s paths as well? I will copy them out and send them as soon as I get home. When do you think the new De motu will be ready?’
Newton tutted. ‘Mr Halley, I must examine every aspect of what I propose. Hence today’s experiment to measure the speed of sound in air, so that I may understand how disturbances move through fluids. I tell you this because you are a friend. Now, quiet, please. I’m ready.’
Humphrey set the short pendulum swinging to and fro. Newton stamped his foot as the bob reversed direction. An instant later, the echo from the other end of the cloister returned, just as the pendulum reached the other side of its swing. Newton waited and stamped again. The echo fell in perfect time with the pendulum.
