Halley's question

Some answers wait. They sit folded in a drawer through the changes of a decade, while the men who would need them argue themselves hoarse in coffee-houses two days' ride away. The work is done. The world does not know it is done. What is needed is not a new calculation but a visitor: someone willing to climb the stairs, put the question plainly, and accept the plain reply.

THE QUESTION IN LONDON

For eighteen months the gentlemen of the Royal Society had circled the same problem and could not close it. If the Sun draws the planets by a force diminishing as the square of their distance, what figure must their paths describe? Robert Hooke claimed the answer was an ellipse and claimed, further, to possess the demonstration; pressed, he would not produce it. Sir Christopher Wren, who had built St Paul's still rising over the river, had set a forty-shilling book as the prize for whoever could deliver the proof in two months. Two months passed. The prize lay on the table. Edmond Halley, twenty-eight years old, lately returned from St Helena where he had charted three hundred and forty-one southern stars, decided the question had to be carried out of London. He knew where to carry it. There was a man at Cambridge who had not attended a meeting of the Society in seven years, who had published nothing since Hooke had savaged his paper on light and colours in 1672, and who was reputed, by those few who corresponded with him, to be the most formidable mathematician in England. Halley hired a horse.

THE RIDE TO CAMBRIDGE

He set out from London on the Friday and came up the Cambridge road through the hot dust of August, 1684. The barley was already cut in the fields east of Royston. By the time he turned in under the gate of Trinity the horse was lame and the rider stiff in the saddle. He was shown across Great Court to the Master's Lodge. The casement stood open on the warm afternoon. The room smelt of beeswax and the cold soot of the previous winter's fires. Isaac Newton came down to him in a plain coat, forty-one years old, Lucasian Professor of Mathematics, his hair already greying at the temples and his face composed in the closed expression by which his pupils knew him. Halley had rehearsed the question all the way from Ware. He put it in twelve words. What, he asked, would be the curve described by the planets, supposing the force of attraction towards the Sun to be reciprocal to the square of their distance from it?

A SECOND OF TIME IN A COLLEGE ROOM

Newton answered immediately. An ellipse. Halley, in the joy and amazement of it (so he afterwards told Abraham De Moivre, who set the meeting down in writing), asked him how he knew it. The Professor replied that he had calculated it. There it is, the second on which the next two centuries of natural philosophy turned: not a discovery made in that room but a discovery acknowledged. For fifteen years, since the plague years at Woolsthorpe when he had been a young fellow turned out of Cambridge by the pestilence, Newton had carried the demonstration in his papers and in his head, and had spoken of it to no one. He had built a private branch of mathematics for it, which he called the method of fluxions, and which no other man in Europe had seen. He had been content to let it lie. What another man would have rushed into print to claim, he had set down in a drawer and walked away from. The world's argument had not reached him; or, having reached him through Hooke's voice, had reached him in a form he despised. Now the question stood before him in a young astronomer's mouth, civilly, without rivalry, asking only for the answer. He went to the cabinet by the window. He opened the upper drawer and went through it. He opened the lower drawer. He turned, with that same closed face, and said he could not at the moment lay his hand on the paper, but he would search for it and send it after. Halley accepted this. He did not press. He rode back to London the next morning on a fresh hired horse and waited.

NOVEMBER, ISLINGTON

Three months passed in silence. Halley went about his business at the Society. He kept watch on the post. In November a parcel was delivered to his house in Islington, nine folio sheets in Newton's tight hand, the Latin so compressed that he had to read the first proposition through three times before the geometry opened to him. The treatise was titled De Motu Corporum in Gyrum, On the Motion of Bodies in Orbit. He carried it down to Crane Court and sat with it on a bench in the Society's rooms on a winter afternoon, the light failing through the high windows. He read it once through without stopping. Then he sat for some minutes without moving. He had ridden up to Cambridge for the answer to a single problem in conic sections. He had been sent back the seed of a system of the world. He rose and went upstairs to ask the President for an appointment with Mr Newton at the earliest convenience.

THE LONG PERSUASION

From the winter of 1684 through to the spring of 1686 Halley rode the Cambridge road as often as the term allowed. He was, in his own phrase, the midwife. Newton, once roused, worked at a rate that frightened his servants: he forgot to eat, slept in his clothes, and walked out into the garden to stand staring at the gravel until a proposition came clear and he turned back to write. The nine sheets expanded into a book, the book into three. When Hooke, hearing of the work, claimed at the Society that the inverse-square law had been his own first, Newton in a cold fury struck every reference to Hooke from the manuscript and threatened to suppress the third book altogether. Halley wrote to him by return, in the careful flattering register of a man holding a powder magazine open with one hand. He soothed. He coaxed. He undertook, when the Society's treasury proved to have been spent on Francis Willughby's Historia Piscium, to pay for the printing himself, out of his own pocket, though he had a young family and the salary of a clerk. The book came off the press in July 1687.

THE BOOK

Philosophiae Naturalis Principia Mathematica. Three books in Latin: the laws of motion, the law of universal gravitation, the system of the world. Halley wrote the preface, in verses that compared the author to a god. Newton dedicated nothing to him. The first edition ran to perhaps four hundred copies. Within a generation it had remade the practice of natural philosophy across Europe; within two, no educated man could speak of the heavens without speaking through it. The historians of science have since called it the most consequential single book published in the English language, and it exists because on a hot afternoon in August 1684 a young astronomer, unable to get his learned Society to agree on a question of curves, rode up to Cambridge and asked the right man the right question, and the right man, who had had the answer folded in a drawer for fifteen years, said I have calculated it, and turned to the cabinet to look.

THE RETURN

Newton lived another forty years. He was made Warden, then Master of the Mint; he was knighted; he buried Hooke and burnt his correspondence with him. He never thanked Halley by name in print. Halley went on, charted the trade winds, predicted the return of the comet that bears his name, became Astronomer Royal in his sixty-fourth year, and died in his observatory at Greenwich in 1742, having lived just long enough to know the comet was due back. The drawer in the Master's Lodge at Trinity has been emptied for three hundred years; the paper Newton looked for that afternoon and did not find has never been recovered, and may have been, as some of his biographers suspect, not yet quite written. It does not matter. The hinge had turned. In the small library at Woolsthorpe Manor, on the table by the window through which the apple tree can still be seen, lies a first edition of the Principia, opened to the dedication page. The dedication is to the Royal Society. Halley's name is not on it. His question is on every page that follows.