The Clockwork Universe: Isaac Newton, the Royal Society, and the Birth of the Modern World - Edward Dolnick (2011)

Part III. Into the Light

Chapter 46. A Visit to Cambridge

Newton’s moon calculation had buttressed his faith in simple laws, but he still had an immense distance to cover before he could prove his case. The moon was not the universe. What of Kepler’s laws, for instance? The great astronomer had devoted his life to proving that the planets traveled around the sun in ellipses. How did ellipses fit in God’s cosmic architecture?

Stymied by the difficulty of sorting out gravity, or perhaps tempted more by questions in other fields, Newton had put gravity aside after his miracle years. He had made his apple-and-moon calculation when he was in his twenties. For the next twenty years he gave most of his attention to optics, alchemy, and theology instead.

Late on a January afternoon in 1684, Robert Hooke, Christopher Wren, and Edmond Halley left a meeting of the Royal Society and wandered into a coffeehouse to pick up a conversation they had been carrying on all day. Coffee had reached England only a generation before, but coffeehouses had spread everywhere.49 Hooke in particular seemed to thrive in the rowdy atmosphere. In crowded rooms thick with the hubbub of voices and the smells of coffee, chocolate, and tobacco, men sat for hours debating business, politics, and, lately, science. (Rumors and “false news” spread so quickly, as with the Internet today, that the king tried, unsuccessfully, to shut coffeehouses down.)

With steaming mugs in hand, the three men resumed talking of astronomy. All three had already guessed, or convinced themselves by the same argument Newton had made using Kepler’s third law, that gravity obeyed an inverse-square law. Now they wanted the answer to a related question—if the planets did follow an inverse-square law, what did that tell you about their orbits? This question—in effect, where do Kepler’s laws come from?—was one of the central riddles confronting all the era’s scientists.

Halley, a skilled mathematician, admitted to his companions that he had tried to find an answer and failed. Wren, still more skilled, confessed that his failures had stretched over the course of several years. Hooke, who was sometimes derided as the “universal claimant” for his habit of insisting that every new idea that came along had occurred to him long before, said that he’d solved this problem, too. For the time being, he said coyly, he preferred to keep the answer to himself. “Mr. Hook said that he had it,” Halley recalled later, “but that he would conceale it for some time, that others trying and failing might know how to value it, when he should make it publick.”

Wren, dubious, offered a forty-shilling prize—roughly four hundred dollars today—to anyone who could find an answer within two months. No one did. In August 1684, Halley took the question to Isaac Newton. Halley, one of the few great men of the Royal Society who was charming as well as brilliant, scarcely knew Newton, though he knew his mathematical reputation. But Halley could get along with everyone, and he made a perfect ambassador. Though still only twenty-eight, he had already made his mark in mathematics and astronomy. Just as important, he was game for anything. In years to come he would stumble through London’s taverns with Peter the Great, on the czar’s visit to London; he would invent a diving bell (in the hope of salvaging treasure from shipwrecks) and would descend deep underwater to test it himself; he would tramp up and down mountains to compare the barometric pressure at the summit and the base; in an era of wooden ships he would survey vast swaths of the world’s oceans, from the tropics to “islands of ice.”

Now his task was to win over Isaac Newton. “After they had been some time together,” as Newton later told the story to a colleague, Halley explained the reason for his visit. He needed Newton’s help. The young astronomer spelled out the question that had stumped him, Wren, and Hooke. If the sun attracted the planets with a force that obeyed an inverse-square law, what shape would the planets’ orbits be?

“Sir Isaac replied immediately that it would be an Ellipsis.” Halley was astonished. “The Doctor struck with joy & amazement asked him how he knew it. Why saith he I have calculated it.”

Halley asked if he could see the calculation. Newton rummaged through his papers. Lost. Halley extracted a promise from Newton to work through the mathematics again, and to send him the results.