ion） and his universal law of gravitation。 this states that every object in theuniverse exerts a tug on every other。 it may not seem like it； but as you sit here now you arepulling everything around you鈥攚alls； ceiling； lamp； pet cat鈥攖oward you with your own little（indeed； very little） gravitational field。 and these things are also pulling on you。 it wasnewton who realized that the pull of any two objects is； to quote feynman again；鈥減roportional to the mass of each and varies inversely as the square of the distance betweenthem。鈥潯ut another way； if you double the distance between two objects； the attractionbetween them bees four times weaker。 this can be expressed with the formulaf = gmmr2which is of course way beyond anything that most of us could make practical use of； but atleast we can appreciate that it is elegantly pact。 a couple of brief multiplications； a simpledivision； and； bingo； you know your gravitational position wherever you go。 it was the firstreally universal law of nature ever propounded by a human mind； which is why newton isregarded with such universal esteem。
principia鈥檚 production was not without drama。 to halley鈥檚 horror； just as work wasnearing pletion newton and hooke fell into dispute over the priority for the inversesquare law and newton refused to release the crucial third volume； without which the firsttwo made little sense。 only with some frantic shuttle diplomacy and the most liberalapplications of flattery did halley manage finally to extract the concluding volume from theerratic professor。
halley鈥檚 traumas were not yet quite over。 the royal society had promised to publish thework； but now pulled out； citing financial embarrassment。 the year before the society hadbacked a costly flop called the history of fishes ； and they now suspected that the market fora book on mathematical principles would be less than clamorous。 halley； whose means werenot great； paid for the book鈥檚 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 positionas the society鈥檚 clerk； and he was informed that the society could no longer afford to provide him with a promised salary of 锟�50 per annum。 he was to be paid instead in copies of thehistory of fishes 。
newton鈥檚 laws explained so many things鈥攖he slosh and roll of ocean tides； the motions ofplanets； why cannonballs trace a particular trajectory before thudding back to earth； why wearen鈥檛 flung into space as the planet spins beneath us at hundreds of miles an hour2鈥攖hat ittook a while for all their implications to seep in。 but one revelation became almostimmediately controversial。
this was the suggestion that the earth is not quite round。 according to newton鈥檚 theory；the centrifugal force of the earth鈥檚 spin should result in a slight flattening at the poles and abulging at the equator； which would make the planet slightly oblate。 that meant that thelength of a degree wouldn鈥檛 be the same in italy as it was in scotland。 specifically； the lengthwould shorten as you moved away from the poles。 this was not good news for those peoplewhose measurements of the earth were based on the assumption that the earth was a perfectsphere； which was everyone。
for half a century people had been trying to work out the size of the earth； mostly bymaking very exacting measurements。 one of the first such attempts was by an englishmathematician named richard norwood。 as a young man norwood had traveled to bermudawith a diving bell modeled on halley鈥檚 device； intending to make a fortune scooping pearlsfrom the seabed。 the scheme failed because there were no pearls and anyway norwood鈥檚 belldidn鈥檛 work； but norwood was not one to waste an experience。 in the early seventeenthcentury bermuda was well known among ships鈥櫋aptains for being hard to locate。 theproblem was that the ocean was big； bermuda small； and the navigational tools for dealingwith this disparity hopelessly inadequate。 there wasn鈥檛 even yet an agreed length for anautical mile。 over the breadth of an ocean the smallest miscalculations would beemagnified 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 rigorto 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 yearsmarching 208 miles north to york； repeatedly stretching and measuring a length of chain ashe went； all the while making the most meticulous adjustments for the rise and fall of the landand the meanderings of the road。 the final step was to measure the angle of the sun at york atthe same time of day and on the same day of the year as he had made his first measurement inlondon。 from this； he reasoned he could determine the length of one degree of the earth鈥檚meridian and thus calculate the distance around the whole。 it was an almost ludicrouslyambitious undertaking鈥攁 mistake of the slightest fraction of a degree would throw the wholething out by miles鈥攂ut in fact； as norwood proudly declaimed； he was accurate to 鈥渨ithin ascantling鈥濃�攐r； more precisely； to within about six hundred yards。 in metric terms； his figureworked out at 110。72 kilometers per degree of arc。
in 1637； norwood鈥檚 masterwork of navigation； the seaman鈥檚 practice ； was published andfound an immediate following。 it went through seventeen editions and was still in printtwenty…five years after his death。 norwood returned to bermuda with his family； being a2how fast you are spinning depends on where you are。 the speed of the earth鈥檚 spin varies from a little over1；000 miles an hour at the equator to 0 at the poles。
successful planter and devoting his leisure hours to his first love； trigonometry。 he survivedthere for thirty…eight years and it would be pleasing to report that he passed this span inhappiness and adulation。 in fact； he didn鈥檛。 on the crossing from england； his two young sonswere placed in a cabin with the reverend nathaniel white； and somehow so successfullytraumatized the young vicar that he devoted much of the rest of his career to persecutingnorwood in any small way he could think of。
norwood鈥檚 two daughters brought their father additional pain by making poor marriages。
one of the husbands； possibly incited by the vicar； continually laid small charges againstnorwood in court； causing him much exasperation and necessitating repeated trips acrossbermuda to defend himself。 finally in the 1650s witch trials came to bermuda and norwoodspent his final years in severe unease that his papers on trigonometry； with their arcanesymbols； would be taken as munications with the devil and that he would be treated to adreadful execution。 so little is known of norwood that it may in fact be that he deserved hisunhappy declining years。 what is certainly true is that he got them。
meanwhile； the momentum for determining the earth鈥檚 circumference passed to france。
there； the astronomer jean picard devised an impressively plicated method oftriangulation involving quadrants； pendulum clocks； zenith sectors； and telescopes （forobserving the motions of the moons of jupiter）。 after two years of trundling and triangulatinghis way across france； in 1669 he announced a more accurate measure of 110。46 kilometersfor one degree of arc。 this was a great source of pride for the french； but it was predicated onthe assumption that the earth was a perfect sphere鈥攚hich newton now said it was not。
to plicate matters； after picard鈥檚 death the father…and…son team of giovanni andjacques cassini repeated picard鈥檚 experiments over a larger area and came up with results thatsuggested that the earth was fatter not at the equator but at the poles鈥攖hat newton； in otherwords； was exactly wrong。 it was this that prompted the academy of sciences to dispatchbouguer and la condamine to south america to take new measurements。
they chose the andes because they needed to measure near the equator； to determine ifthere really was a difference in sphericity there； and because they reasoned that mountainswould give them good sightlines。 in