Newton · 1684
Halley's question
In August 1684 the astronomer Edmond Halley rode up to Cambridge on a question that had been arguing the Royal Society into a circle for eighteen months. If the planets are pulled toward the Sun by a force that diminishes with the square of the distance, what shape would their orbits take? Robert Hooke had said an ellipse and could not prove it. Christopher Wren had offered Halley a forty-shilling prize for the proof. Halley took the question to Newton, who had spent the years since Woolsthorpe in retreat from the world. Newton answered him at once. He had calculated it. He could not, on the spot, find the paper. He sent it down to London three months later as a nine-page treatise, *De Motu Corporum in Gyrum*, and Halley, reading it on a bench at the Society in November, sat very still for ten minutes before going to find the President.
It is the early afternoon of a Wednesday in August, 1684, in the Master's Lodge of Trinity College, Cambridge. The room smells of beeswax and the old smoke of the previous winter's fires. The window is open onto Great Court. Edmond Halley is sitting on a wooden bench by the fireplace, twenty-eight years old, the youngest fellow of the Royal Society, just back from St Helena where he has been mapping the southern stars. He has ridden from London since the Friday. The horse is in the college stables, lame.
Isaac Newton is standing at the table. He is forty-one years old. He is the Lucasian Professor of Mathematics. He has not been to a meeting of the Royal Society in seven years. He has not published anything since the 1672 paper on light and colour, which Hooke savaged in print. He is the only man in Europe who knows that he has a private branch of mathematics no one else has ever seen, called by him fluxions, and at the moment, none of this is on his face. His face is what it always is, which is closed.
Halley has put the question to him in twelve words. If the force be reciprocal to the square of the distance, what curve?
Newton says, without pause: an ellipse.
Halley sits up.
Newton says: I have calculated it.
Halley says: show me.
Newton goes to the cabinet by the window. He opens the upper drawer. He goes through it. He goes through the lower drawer. He looks at Halley. He says: I cannot find the paper. I will send it after you.
Halley rides back to London on a hired horse the next morning. For three months he hears nothing. In November a parcel arrives at his house in Islington, nine folio sheets in Newton's hand, in a Latin so compressed that Halley has to read the first proof three times. The treatise is called De Motu Corporum in Gyrum, On the Motion of Bodies in Orbit. He goes through it sitting on a bench at the Royal Society on a winter afternoon. When he has finished he goes upstairs and asks the President for an immediate appointment with Newton. He spends, by his own account, the next eighteen months riding back and forth from London to Cambridge talking the Lucasian Professor into expanding the nine pages into a book.
The book was published in July 1687, three years after the question, financed at Halley's personal cost when the Royal Society's funds had gone on a treatise on fishes. Philosophiae Naturalis Principia Mathematica. Three books, the laws of motion, the law of universal gravitation, the system of the world. Halley wrote the preface. Newton dedicated nothing to him. By the modern judgement of historians of science it is the most consequential single book published in the English language. It exists because, on a hot August afternoon in 1684, a young astronomer who could not get his Society to agree on anything walked into a college room and asked the right man the right question, and the right man, who had had the answer in a drawer for fifteen years, said yes, I have calculated it, and turned to look for it.