IF YOU o select t convivial scientific field trip of all time, you could certainlydo ion of 1735. Led by a named Pierre Bouguer and a soldier-matician named C y of scientists and adventurers o Peru riangulating distances the Andes.

    At time people ely become infected o understand to determine  y’s goal o tle tion of t by measuring tance aroundt) along a line reaco, to just beyond Cuenca in ance of about two hundred miles.

    1Almost at once to go imes spectacularly so. In Quito, torssome of toones. Soonafter, tion’s doctor anding over a anist became deranged. Ot senior member ofty, a man named Pierre Godin, ran off een-year-old girl and could not beinduced to return.

    At one point to suspend o sort out a problem s. Eventually opped speakingand refused to ogety  it   suspicions from officials  to believe t a group of Frencists ravel o measure t made no sense atall. ter it still seems a reasonable question.  ts in France and save t of ture?

    tly  t eigury scientists, ticular,seldom did ternative ly ical problem t  arisen ronomer Edmond o South America,much less had a reason for doing so.

    * triangulation, tecric fact t if you knoriangle and t all its otleaving your c you and I decided o triangulation, t t do is put some distance bets say for argumentt you stay in Paris and I go to Mosco t time. Noing t is, you and I and t forms a triangle. Measuret can be simplycalculated. (Because terior angles of a triangle alo 180 degrees, if you knoantly calculate triangle and tells you t tronomer,o  tance from Eart ground level, triangulation are t t triangles dont reaco space but rato side on amap. In measuring a degree of meridian, te a sort of criangles marche landscape.

    ional figure. In tive career, ain, a cartograpry at ty of Oxford, deputycontroller of t, astronomer royal, and inventor of te autatively on magnetism, tides, and tions of ts, and fondly on ts of opium. ed tuarial table, proposed met ts distance from ticalmet of season. t do, interestingly enoug t bears  t   didn’tbecome  until 1758, some sixteen years after h.

    For all s, est contribution to o take part in a modest scientific hies of his day:

    Robert  remembered no person to describe a cell, andt and stately Sir Copually an astronomer first and arcectsecond, t is not often generally remembered nourned to tions of celestial objects.

    It  planets o orbit in a particular kind of oval knoo quote Ric it understood o a coupleof o wion.

    aking credit for ideas t  necessarily   declined noo s on terestingand inventive grounds t it isfaction of discovering tead “conceal it for some time, t ot kno.” If  any more on tter,  no evidence of it. o t t traveled toCambridge and boldly called upon ty’s Lucasian Professor of Matics, IsaacNe he could help.

    Ne beyond measure, but solitary, joyless, pricklyto t of paranoia, famously distracted (upon s of bed in tedly sometimes sit for s to riveting strangeness.  ory, tat Cambridge, but t bizarre experiments. Once ed a bodkin—a long needle of t used for seo  and rubbed it around“bet my eye and to [t to see  noting. Onanotared at to determine  ito spend somedays in a darkened room before his eyes forgave him.

    Set atop traits, ional cen sendency topeculiarity. As a student, frustrated by tations of conventional matics, ed an entirely ne told no one about it for ty-sevenyears. In like manner, ics t transformed our understanding of ligion for troscopy, and again c to ss forthree decades.

    For all ed for only a part of erests. At least o alcs. t meredabblings but ions.  ad of a dangerously icalsect called Arianism,   trinity(sligon’s college at Cambridge rinity).  endless udying t temple of King Solomon in Jerusalem (teacter to scan original texts) in t it icalclues to tes of t and ttac toalc. In 1936, t Jo a trunk ofNe auction and discovered onis t t ics or planetary motions, but  to turn basemetals into precious ones. An analysis of a strand of Neained mercury—an element of interest to alcs, ters, and ter-makersbut almost no one else—at a concentration some forty times tural level. It is pertle  rouble remembering to rise in the morning.

    Quite o get from  in August1684  to ter account of a Ne, Abra oric encounters:

    In 1684 Dro visit at Cambridge [and] after timetoget  t s supposing ttraction too bereciprocal to tance from it.

    to a piece of matics kno t of tion, t sure exactly how.

    SrIsaac replied immediately t it or, struck , asked . ‘edit,’  fart could not find it.

    tounding—like someone saying  couldn’tremember on agreed to redo tions and produce a paper.  tired fortensive reflection and scribbling, and at lengteruralis Principia Matica or Matical Principles of NaturalPter knohe Principia .

    Once in a great e and unexpected t people can’t quite decide . Principia s. It made Neantly famous. Fort of s and  person in Britain knigific ac. Even t Germanmatician Gottfried von Leibniz, on ter figyfor tion of t ributions to matics equal to all ted  al may approaceiment t herssince.

    Alt inaccessible books ever ten”

    (Neentionally made it difficult so t  be pestered by matical“smatterers,” as  o t. It not onlyexplained matically ts of  also identified ttractive forcet got t place—gravity. Suddenly every motion in the universe madesense.

    At Principia ’s  on’s tion (e, very baldly, t ation in  raigil some ots to slo it; and t every action e andequal reaction) and ation. tates t every object in ts a tug on every ot may not seem like it, but as you sit  cat—totle(indeed, very little) gravitational field. And t on s is, to quote Feynman again,“proportional to tance bet anotance bets, ttractionbetimes  most of us could make practical use of, but atleast e t it is elegantly compact. A couple of brief multiplications, a simpledivision, and, bingo, you knoational position really universal laure ever propounded by a on isregarded eem.

    Principia’s production   drama. to  as ion Nee over ty for ton refused to release t tle sense. Only ic stle diplomacy and t liberalapplications of flattery did o extract tic professor.

    raumas  yet quite over. ty o publis no, citing financial embarrassment. ty ly flop called tory of Fised t t fora book on matical principles  great, paid for tion out of . Neributed noto make matters ime  accepted a positionas ty’s clerk, and  ty could no longer afford to provideo be paid instead in copies of tory of Fishes .

    Neides, tions ofplanets, icular trajectory before to Eart flung into space as t spins beneat  ittook a o seep in. But one revelation became almostimmediately controversial.

    tion t t quite round. According to Nerifugal force of t in a sligtening at t tor,  meant t t be taly as it land. Specifically, ten as you moved a good nes of tion t tsphere, which was everyone.

    For ury people rying to  tly bymaking very exacting measurements. One of t suctempts o Bermudaending to make a fortune scooping pearlsfrom t  Nor one to e an experience. In teentury Bermuda e. t tional tools for dealingy e. t even yet an agreed lengtical mile. Over t miscalculations  sen missed Bermuda-sized targets by dismaying margins. Norrigonometry and to bring a little matical rigorto navigation and to t end ermined to calculate th of a degree.

    Starting  to ted yearsmarco York, repeatedly stretc, all t meticulous adjustments for tep o measure t York attime of day and on t measurement inLondon. From termine te tance around t  ludicrouslyambitious undertaking—a mistake of test fraction of a degree  by miles—but in fact, as Noro “ling”—or, more precisely, to  six ric terms,  at 110.72 kilometers per degree of arc.

    In 1637, Norerion, tice ,   teen editions and ill in printty-five years after urned to Bermuda  you are spinning depends on or to 0 at the poles.

    successful planter and devoting o  love, trigonometry. y-eig o report t ion. In fact, . On te, and someraumatized t ed muc of o persecutingNorwood in any small way hink of.

    Norional pain by making poor marriages.

    One of ted by tinually laid small cNor, causing ion and necessitating repeated trips acrossBermuda to defend crials came to Bermuda and Nor  rigonometry, aken as communications  reated to adreadful execution. So little is kno it may in fact be t  is certainly true is t  them.

    Meanermining to France.

    tronomer Jean Picard devised an impressively complicated metriangulation involving quadrants, pendulum clocks, zenitors, and telescopes (forobserving tions of ter). After trundling and triangulatinge measure of 110.46 kilometersfor one degree of arc. t source of pride for t it ed ontion t t spon no .

    to complicate matters, after Picard’s deateam of Giovanni andJacques Cassini repeated Picard’s experiments over a larger area and came up s tsuggested t tter not at tor but at t Nely   prompted to dispatco Souto take nes.

    to measure near tor, to determine ifty t mountainslines. In fact, tains of Peru antly lost incloud t team often o  , ted one of t nearly impossible terrains on Earto tado —“muced”—and t most certainly is. t only to scale some of t cains—mountainst defeated even t to reacains to ford , nearly all of it unced andfar from any source of supplies. But Bouguer and La Condamine tenacious, and tuck to task for nine and a ered years.

    Sly before concluding t, t a second Frenceam, takingmeasurements in nortable discomforts of to dangerous ice floes),  a degree  longer near ton y-ters stouter op to bottom around the poles.

    Bouguer and La Condamine t nearly a decade o t o learn no t even t to find it. Listlessly, ted t t Frenceam . till notspeaking, turned to t and took separate ships home.

    Sometured by Ne a plumb bob ain ain, affected by tain’sgravitational mass as . If youmeasured tion accurately and  tain, you couldcalculate tational constant—t is, ty, kno th.

    Bouguer and La Condamine ried t C ed by botecies and tion laydormant for anoty years until resurrected in England by Nevil Maskelyne, tronomer royal. In Dava Sobel’s popular book Longitude, Maskelyne is presented as a ninnyand villain for failing to appreciate t ed to  mentioned in  least foro ain of sufficiently regular so judge its mass.

    At y agreed to engage a reliable figure to tour tiso see if sucain could be found. Maskelyne kne sucronomer and surveyor C to measure an astronomical event of great importance:

    t Venus across tireless Edmond ed years before t if you measured one of ted points on triangulation to  tance to t calibrate tances to all tem.

    Unfortunately, transits of Venus, as t years apart, but t for a century or more, and time.

    3But t transit came due in 1761,nearly ter ific  ronomical event before.

    itinct for ordeal t cerized tists set off for more tions around to Siberia, Ccy-taineigill ot out from Saly, Germany, Ireland, andelsewhere.

    It  cooperative international scientific venture, and almost everyo problems. Many observers ions but opened tes to find equipment broken or ropical .

    Once again ted to provide t memorably unlucky participants.

    Jean C montraveling to Siberia by coac, and sleigeinstruments over every perilous bump, only to find t vital stretc transit ietury.

    rivers, t of unusually  to blame on er ting strange instruments at to escape  s.

    Unluckier still il, il set off from France a yearaime to observe transit from India, but various setbacks left ill at sea on transit—just about t place to be since steady measurements ching ship.

    Undaunted, Le Gentil continued on to India to a t transit in 1769. ityears to prepare, ed a first-rate vieation, tested and retested ruments,and ate of perfect readiness. On transit, June4, 1769, o a fine day, but, just as Venus began its pass, a cloud slid in front of t exactly tion of transit: teenminutes, and seven seconds.

    Stoically, Le Gentil packed up ruments and set off for t port, but en routeracted dysentery and ill o a s  er setting off, and  ives ically plundered ate.

    In comparison, tments experienced by Britain’s eigtered observers along ing partnersructions o travel to Sumatra and c transit t after just one nig sea ttacked by a Frence. (Altists ernationally cooperativemood, nations .) Mason and Dixon sent a note to ty observing t itseemed an’t to be called off. In reply t and cing t t tion and scientific community ing on tto proceed  in trievable loss of tations. Cened,t en route ra o transit inconclusively from topped on tlantic outcrop of St.  Maskelyne, idalflows.

    Soon afterurned to England ly more seasoned—set off for four long and often perilousyears surveying to settle aboundary dispute betates of illiam Penn and Lord Baltimore and tive colonies of Pennsylvania and Maryland. t er took on symbolic importance as tates. (Altask, tributed severalastronomical surveys, including one of tury’s most accurate measurements of a degreeof meridian—an ac t brougtlingof a boundary dispute betocrats.)Back in Europe, Maskelyne and erparts in Germany and France o t transit measurements of 1761 ially a failure. One of t too many observations, en proved contradictory and impossible to resolve. ting of aVenusian transit fell instead to a little-kno from a sunny op in tai, and t on to c andclaim Australia for tisurn tion fortronomer Josepo calculate t tance from tottle over 150 million kilometers. (transits in teentury alloronomers to put t 149.59 million kilometers, ers.) t last ion in space.

    As for Mason and Dixon, turned to England as scientific nersurn up atseminal events in eigury science, remarkably little is kno eit and feten references. Of Dixon tionary of National Biograpes intriguingly t o  t to tion to supply a plausible explanatory circumstance, and adds t Dur from ion hing more isknown.

    Mason is only slig in 1772, at Maskelyne’s be, ed to find a suitable mountain for tational deflectionexperiment, at lengting back t tain tral Scottis above Locay, and . urned to tkno eriously, urned up in P cly on titution.  been backto America since completing een years earlier and rons to greet er he was dead.

    ito survey tain, to Maskelyne. So for four montent in a remote Scottis ing a team of surveyors, ion. to find tain from all t deal oftedious calculating, for on ion at some pointon or around tain. It ially just a confusing mass of numbers, but tonnoticed t if o connect points of equal , it all became mucantly get a sense of tain.

    ed contour lines.

    Extrapolating from s, ton calculated t 5,000 million million tons, from  s and tcontour lines into t bad for a summer’s work.

    Not everyone isfied s, coming of t  it  possible to get a truly accurate figure  knoual density of tain. For convenience, ton  tain y as ordinary stone, about 2.5 times t of er, but ttle more ted guess.

    One improbable-seeming person ter ry parsonnamed Joe e and comparatively uation, Mic scientific teentury and muceemed for it.

    Among a great deal else, ure of earted muco magnetism and gravity, and, quite extraordinarily, envisioned ty of black ive deductiont not even Ne in life ronomy, it ruction in making telescopes, a kindness for wary science ever since.

    4But of all t Micer impactt for measuring tunately,  ts and boto a brilliant but magnificently retiring London scientist named henryCavendish.

    Cavendiso a life of sumptuous privilege—ively, of Devons— gifted Englisistof  also trangest. o a “degree bordering on disease.” Any act .

    Once o find an Austrian admirer, fres step. Excitedly trian began to babble out praise. For a fes Cavendiss as if t object and to takeany more, fled do te, leaving t door  y. Even edter.

    Altimes venture into society—icularly devoted to tific soirées of t naturalist Sir Josep o ts t Cavendis to be approac. t o o y as if by accident and to “talk as4In 1781  person in to discover a planet. ed to call it George,after tis ead it became Uranus.

    it o vacancy.” If tifically  receive amumbled reply, but more often t to curn to find an actual vacancy and t of Cavendishfleeing for a more peaceful corner.

    ary inclinations allourn o a largelaboratory ricity, , gravity, gases, anyto do ion of matter. teentury ime  greenselyinterested in ties of fundamental tricity inparticular—and began seeing en e in an electricalstorm. In France, a c named Pilatre de Rozier tested ty of  a stroke t ible and t eyebro necessarily a permanent feature ofone’s face. Cavendis, conducted experiments in ed jolts of electrical current, diligently noting til imes his consciousness, no longer.

    In tring of signal discoveries—among muc person to isolate  to combine o form er—but almost notirely divorced from strangeness. to tinuing exasperation of ists, en alluded in publiso ts of contingent experiments t  told anyone about. In iveness  merely resemble Ne actively exceeded s ricalconductivity ury aime, but unfortunately remained undiscovereduntil t century er part of il te nineteentury ook on taskof editing Cavendisime credit o others.

    Among muc telling anyone, Cavendisicipated tion of energy, Oon’s Laial Pressures, Ricions, Cricalconductivity. t’s just some of it. According to torian J. G. Croidal friction on sloation of t of localatmospures, and some of terogeneous equilibria.” Finally,  clues t led directly to ts kno t of t found until 1962. But our interest kno  ty-seven, urned tention to tes of equipment t  to ly out of simplescientific respect—by John Michell.

    us looked like noteentury version of a Nautilus ed orsion  t of tational deflection of t measurement of tational constant, and fromrictly speaking, th could be deduced.

    Because gravity s in orbit and makes falling objects land endto t as a po it is not really. It is only poivesense, o anot, like t an elemental level gravity is extraordinarily unrobust. Eacime you pick up a bookfrom a table or a dime from tlessly overcome tationalexertion of an entire planet.  Cavendisrying to do y at tremely feat level.

    Delicacy  a o taining tus, so Cavendisook up a position in an adjoining room and made ions elescope aimed tingand involved seventeen delicate, interconnected measurements, ook nearly ayear to complete.  last ions, Cavendis ttle over 13,000,000,000,000,000,000,000 pounds, or six billion trillionmetric tons, to use tric ton is 1,000 kilograms or 2,205 pounds.)today, scientists  tect t of asingle bacterium and so sensitive t readings can be disturbed by someone yay-five feet a t significantly improved on Cavendiss of1797. t best estimate for Eart is 5.9725 billion trillion metric tons, adifference of only about 1 percent from Cavendiserestingly, all of timates made by Nealevidence at all.

    So, by te eigury scientists knes distance from ts; and no determining tively straiger all, terials erally att. But no.  tom and invent television, nylon, and instantcoffee before t t.

    to understand ravel norto Scotland and begin  and genialman, of ed a new science called geology.

    5to a p, mass and e different tays tyour  like a planet.

    travel to ter but no less massive. On Eartical purposes, massand reated as synonymous. at least outside the classroom.