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 couldnt 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 Philosophiae Naturalis Principia Mathematica or Mathematical Principles of Natural Philosophy , better known as the Principia .
Once in a great while, a few times in history, a human mind produces an observation so acute and unexpected that people cant quite decide which is the more amazing-the fact or the thinking of it. Principia was one of those moments. It made Newton instantly famous. For the rest of his life he would be draped with plaudits and honors, becoming, among much else, the first person
in Britain knighted for scientific achievement. Even the great German mathematician Gottfried von Leibniz, with whom Newton had a long, bitter fight over priority for the invention of the calculus, thought his contributions to mathematics equal to all the accumulated work that had preceded him. Nearer the gods no mortal may approach, wrote Halley in a sentiment that was endlessly echoed by his contemporaries and by many others since.
Although the Principia has been called one of the most inaccessible books ever written (Newton intentionally made it difficult so that he wouldnt be pestered by mathematical smatterers, as he called them), it was a beacon to those who could follow it. It not only explained mathematically the orbits of heavenly bodies, but also identified the attractive force that got them moving in the first place-gravity. Suddenly every motion in the universe made sense.
At Principia s heart were Newtons three laws of motion (which state, very baldly, that a thing moves in the direction in which it is pushed; that it will keep moving in a straight line until some other force acts to slow or deflect it; and that every action has an opposite and equal reaction) and his universal law of gravitation. This states that every object in the universe exerts a tug on every other. It may not seem like it, but as you sit here now you are pulling everything around you-walls, ceiling, lamp, pet cat-toward you with your own little (indeed, very little) gravitational field. And these things are also pulling on you. It was Newton who realized that the pull of any two objects is, to quote Feynman again, proportional to the mass of each and varies inversely as the square of the distance between them. Put another way, if you double the distance between two objects, the attraction between them becomes four times weaker. This can be expressed with the formula
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.
Principia s production was not without drama. To Halleys horror, just as work was nearing completion Newton and Hooke fell into dispute over the priority for the inverse square law and Newton refused to release the crucial third volume, without which the first two made little sense. Only with some frantic shuttle diplomacy and the most liberal applications of flattery did Halley manage finally to extract the concluding volume from the erratic professor.
Halleys 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 The History of Fishes , and they now suspected that the market for a book on mathematical principles would be less than clamorous. Halley, whose means were not great, paid for the books publication out of his own pocket. Newton, as was his custom, contributed nothing. To make matters worse, Halley at this time had just accepted a position as the societys clerk, and he was informed that the society could no longer afford to provide him with a promised salary of £50 per annum. He was to be paid instead in copies of The History of Fishes .
Newtons 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 arent flung into space as the planet spins beneath us at hundreds of miles an hour -that it took a while for all their implications to seep in. But one revelation became almost immediately controversial.