belief that there had been no Holy Trinity (slightly ironic since Newton’s college at Cambridge was Trinity). He spent endless hours studying the floor plan of the lost Temple of King Solomon in Jerusalem (teaching himself Hebrew in the process, the better to scan original texts) in the belief that it held mathematical clues to the dates of the second coming of Christ and the end of the world. His attachment to alchemy was no less ardent. In 1936, the economist John Maynard Keynes bought a trunk of Newton’s papers at auction and discovered with astonishment that they were overwhelmingly preoccupied not with optics or planetary motions, but with a single-minded quest to turn base metals into precious ones. An analysis of a strand of Newton’s hair in the 1970s found it contained mercury-an element of interest to alchemists, hatters, and thermometer-makers but almost no one else-at a concentration some forty times the natural level. It is perhaps little wonder that he had trouble remembering to rise in the morning.
Quite what Halley expected to get from him when he made his unannounced visit in August 1684 we can only guess. But thanks to the later account of a Newton confidant, Abraham DeMoivre, we do have a record of one of science’s most historic encounters:
In 1684 Dr Halley came to visit at Cambridge [and] after they had some time together the Dr asked him what he thought the curve would be that would be described by the Planets supposing the force of attraction toward the Sun to be reciprocal to the square of their distance from it.
This was a reference to a piece of mathematics known as the inverse square law, which Halley was convinced lay at the heart of the explanation, though he wasn’t sure exactly how.
Sr Isaac replied immediately that it would be an [ellipse]. The Doctor, struck with joy amp; amazement, asked him how he knew it. ‘Why,’ saith he, ‘I have calculated it,’ whereupon Dr Halley asked him for his calculation without farther delay, Sr Isaac looked among his papers but could not find it.
This was astounding-like someone saying he had found a cure for cancer but couldn’t remember where he had put the formula. Pressed by Halley, Newton agreed to redo the calculations and produce a paper. He did as promised, but then did much more. He retired for two years of intensive reflection and scribbling, and at length produced his masterwork: the
Once in a great while, a few times in history, a human mind produces an observation so acute and unexpected that people can’t quite decide which is the more amazing-the fact or the thinking of it.
Although the
At
which is of course way beyond anything that most of us could make practical use of, but at least we can appreciate that it is elegantly compact. A couple of brief multiplications, a simple division, and, bingo, you know your gravitational position wherever you go. It was the first really universal law of nature ever propounded by a human mind, which is why Newton is regarded with such universal esteem.
Halley’s traumas were not yet quite over. The Royal Society had promised to publish the work, but now pulled out, citing financial embarrassment. The year before the society had backed a costly flop called
Newton’s laws explained so many things-the slosh and roll of ocean tides, the motions of planets, why cannonballs trace a particular trajectory before thudding back to Earth, why we aren’t flung into space as the planet spins beneath us at hundreds of miles an hour [4]-that it took a while for all their implications to seep in. But one revelation became almost immediately controversial.
This was the suggestion that the Earth is not quite round. According to Newton’s theory, the centrifugal force of the Earth’s spin should result in a slight flattening at the poles and a bulging at the equator, which would make the planet slightly oblate. That meant that the length of a degree wouldn’t be the same in Italy as it was in Scotland. Specifically, the length would shorten as you moved away from the poles. This was not good news for those people whose measurements of the Earth were based on the assumption that the Earth was a perfect sphere, which was everyone.
For half a century people had been trying to work out the size of the Earth, mostly by making very exacting measurements. One of the first such attempts was by an English mathematician named Richard Norwood. As a young man Norwood had traveled to Bermuda with a diving bell modeled on Halley’s device, intending to make a fortune scooping pearls from the seabed. The scheme failed because there were no pearls and anyway Norwood’s bell didn’t work, but Norwood was not one to waste an experience. In the early seventeenth century Bermuda was well known among ships’ captains for being hard to locate. The problem was that the ocean was big, Bermuda small, and the navigational tools for dealing with this disparity hopelessly inadequate. There wasn’t even yet an agreed length for a nautical mile. Over the breadth of an ocean the smallest miscalculations would become magnified so that ships often missed Bermuda-sized targets by dismaying margins. Norwood, whose first love was trigonometry and thus angles, decided to bring a little mathematical rigor to navigation and to that end he determined to calculate the length of a degree.
Starting with his back against the Tower of London, Norwood spent two devoted years marching 208 miles north to York, repeatedly stretching and measuring a length of chain as he went, all the while making the most meticulous adjustments for the rise and fall of the land and the meanderings of the road. The final step was to measure the angle of the Sun at York at the same time of day and on the same day of the year as he had made his first measurement in London. From this, he reasoned he could determine the length of one degree of the Earth’s meridian and thus calculate the distance around the whole. It was an almost ludicrously ambitious undertaking-a mistake of the slightest fraction of a degree would throw the whole thing out by miles-but in fact, as Norwood