Kelvin, Perry and the Age of the Earth

Had scientists better appreciated one of Kelvin's contemporary critics,the theory of continental drift might have been accepted decades earlier

Philip C. England, Peter Moinar and Frank M. Richter

The 19th-century scientific communitygrappled at length with the question of the

age of the Earth, a subject for which a defini-tive answer did not arrive until the refinementof radiometric dating in the mid-20th century.The most famous—and famously wrong—estimation of the Victorian era came from therenowned physicist William Thomson (1824-1907), known from 1892 as Lord Kelvin.

The story of Kelvin and the age of the Earthis often told as a David-and-Goliath struggle,with geologists playing the role of underdog,armed only with the slender sword of geo-logical reasoning, while Lord Kelvin blud-geoned them with the full force and prestigeof mathematical physics. Kelvin's eventualcomeuppance is often taken as evidence tliatsimple physics ought not to be applied to com-plex geological problems. But there are manysimple physical models that have had greatexplanatory power in geology.

Many people believe that Kelvin's calcula-tion failed through his ignorance of radioac-tivity. Here, we examine Kelvin's approachand show that this was not where his errorlay. The flaw in Kelvin's thinking was di-vined by one of his own assistants, a scholar,educator and inventor named John Perry,who attempted and failed to convince theestablishment of the day that enhanced heattransfer in the Earth's interior—by convec-tion or some other means—could reconcilethe geological and the physical arguments.Today it is possible to see how Perry's ideascould have advanced the study of the Earthconsiderably, had geologists understood andappreciated them.

Philip C. England received

a doctorate in geopln/sics in

1976 from Ute University of

Oxford. He carried out research

md teaching at Cjimbridge

and Harvard before moving

in 1986 to Oxford, where he is

now a professor in the Depart-

matt ofGeolog}/. Most of his

work centers on tlieoretical and

observational aspects of the

deformation of the continents.

Peter Moliujr earned a Ph.D. in

1970 after studying seismology

at Columbia University. He

taiighl ami did research at tlte

Scripps Institution of Ocean-

ography, at tlw Massachusetts

Institute ofTechnologif and at

Oxford (among other places)

before joining the Department

of Geological Sciences at the

Uniivrsity of Colorado. Boulder,

in 2001. His current research

there focuses on the interactions

between geodynamics, geomor-

phology and long-tertti clinwte

change. Frank M. Richter re-

ceived a Ph.D. in 1972 from the

Universiti/ of Chicago, where he

is currently Sen<e! L Avery Dis-

tingitislied Sen-ice Professor in

the Departme>it of Geophysical

Sciences. Tliis article is adapted

with permission of the (^logi-

cal Society of America from a

paper by Englami, Moinar and

Richter, "John Perry's neglected

critique of Kelvin's age for the

Earth: A missed opportunity

in geodynamics." which ap-

peared in the January 2(X)7 issue

o/GSA Today. AddressprEngland: Departmetit of Earth

Sciences, University of Oxford,

Parks Road, Oxford 0X1 3PR.

Internet: philip.england®earth.

ox.ac.iik

On the Cooling of Planets and TurkeysThe French mathematician Joseph Fourier(1768-1830) laid the quantitative groundwork forKelvin's estimation of the age of the Earth in an1822 treatise titled Tlu'Otie Anali/tique de la Chaleur(Analytic Theory of Heat). Kelvin began writingon this subject when he was 16, clarifying someof Fourier's mathematics, and he first addressedthe age of the Earth in 1844, when he showed

that measurement of tlie rate of heat loss faim theplanet's surface could place limits on its age.

Kelvin imagined the Earth to have solidifiedfrom an originally molten state, such tiiat its ini-tial condition was of uniformly high temperaturethroughout, with its surface maintained at somecoastant temperature thereafter. Under these as-sumptiotis, temperature depends on the depthbelow the Earth's surface and on the time tiiathas elapsed since the initial state existed.

To get a feel for the physics at hand, onecan carry out a simple thought experiment.Imagine what would happen if you took aThanksgiving turkey piping hot from theoven and immediately placed it in a freezer.(Consider a perfect freezer—one that can re-move heat instantly and always stay at its settemperature.) Initially, the turkey would be atthe same temperature throughout (assumingthat you had roasted it for sufficiently long).Only a very thin skin would immediately takeon the temperature of the freezer. But soon,the outer layers of turkey meat would cool asheat diffused outward, even though tho cen-ter retained its initial oven-tike temperature.Eventually, of course, everything including thestuffing would cool off; that is, the tempera-ture inside your turkey would depend both onthe distance from the surface and on the timeelapsed since you placed it in the freezer.

Kelvin's analysis allows one to put num-bers to this thought experiment. The rate offlow of heat through a surface is proportionalto the gradient (or spatial derivative) of thetemperature. Fourier had shown that tempera-ture changes within a solid obey the diffusionequation, in which the rate of change of tem-perature at a point Is proportional to the sec-ond spatial derivative of the temperature (thecurvature of the line on a temperature-distanceplot), with the constant of proportionality be-ing a property of the material called thermaldiffusivity. The essential feature of all solutionsto the diffusion equation is that the length oftime required for heat to travel a given dis-tance is proportional to the square of that dis-tance divided by the thermal diffusivity. For

342 American Scientist, Volume 95

Figure 1. When observed over a human lifetime, the mantle of the Earth is as rigid as steel, but over thousands and millions of yeare it acts as a highlyviscous fluid, which carries heat from the interior to the surface. The details of that motion remain to be determined, but the computer model illustrat-ed here su^ests that plumes of hot rock rise from the bottom of the mantle and that colder material sinks toward the hot liquid-iron core (rcil). Theplate-tectonic revolution in the late 1960B led to the understanding that the Earth's surface drifts around in response to such convection airrents in themantle. As the authors describe, John Perry, an erstwhile assistant of Lord Kelvin, proposed in 1895 that the same phenomenon could account for thedifference between Kelvin's estimate for the age of the Earth and that of the geologists, (image courtesy of Shuo Wang, University of Minnesota.)

For the sake of having concrete numbers touse in this thought experiment, assume a tem-perature difference of 2(X) degrees Celsius be-tween the interior of the oven and tlie interiorof the freezer; 180 degrees is a pretty good tem-perature for roasting turkeys, and -20 degrees isa pretty good temperature" for freezing ice cream.Five minutes after the start of the experiment,the outer 1 centimeter of turkey has ctxiled, andthe gradient in temperature with depth is 20 de-grees per millimeter of turkey. After 20 minutes,2 centimeters have cooled, and the gradient is 10degrees p>er millimeter of turkey. Another wayof putting this relation is to say that tlie thermal

, 5 minutes after you place the bird inyour freezer, only a thin layer of meat, about 1centimeter thick, will have felt any effect of thecold surroundings; anything deeper than thiswill still be at the roasting temperature. Butwhile it takes about 5 minutes to conduct awaythe heat from the top 1 centimeter of a turkey,it takes 20 minutes to mine the heat from theoutermost 2 centimeters. (This simple physicalprinciple underlies the advice given in manycookbooks that one should take the turkey outof the oven as much as an hour before carvingit, because its interior will continue to cook,without the exterior's drying out,)

www.americanscientist.org 2007 July-August 343

100-

200 -

300

0 1,000 2,000 3,000

temperature (degrees Celsius)

Figure 2. Mathematical physicist William Thomson, better known as Lord Kelvin, reasoned that the geothermal gradient—the rate at whichtemperature rises with depth in the Earth—must depend on the time elapsed since the planet was o uniformly hot ball of molten rock. Ac-cording to Kelvin's view, soon after the Earth solidified, the outermost rind began to cool, giving rise to a large geothermal gradient near thesurface. As time elapsed, heat diffused outward, and the geothermai gradient gradually diminished (graph). Thus, according to Kelvin's model,measurements of the near-surface geothermal gradient (brown wedge) can be used to ascertain the age of the Earth. Kelvin initially calculatedthat tbe mean geothermal gradient (black line in wedge) corresponds to an age close to 100 million years. He later lowered his estimate to about20 million years. (Photograph from Bumdy Library, courtesy of AIP Emilio Segre Visual Archives.)

gradient is inversely proportional to the squareroot of the time since the turkey was put in thefreezer.

By inverting—or turning inside out—Fourier's diffusion calculation, Kelvin couldsolve for the age of the Earth in terms of thegeothermal gradient at the surface. To pursuethe analogy, if you found that a Thanksgivingturkey mysteriously appeared in your freezer,you could determine how long ago someonehad put it there by measuring the temperaturegradient at its surface. A temperature gradientof 5 degrees per millimeter would, for exam-ple, imply an "age" of 80 minutes. (There is aparallel here, familiar to devotees of detectivefiction, with the measurement of a corpse'stemperature to determine the time of death.)

When Kelvin first made these arguments(though more formally) in 1844 and 1846, hehad no reliable measurements of geothermalgradient, but by the time he returned to theproblem 15 years later, geothermal gradientshad been measured in several parts of theworld. Kelvin quoted temperature increasesof between l/llOth and l/15th of a degreeFahrenheit for each foot of depth in the Earth.He chose the mean gradient in his calculationto be l/50th of a degree Fahrenheit per foot(or about 36 degrees Celsius per kilometer).He estimated Earth's initial temperature (7,000degrees Fahrenheit, or 3,900 degrees C) frommelting experiments on rocks, and laboratorymeasurements gave him values for the thermaldiffusivity of typical crustal materials. Insert-

ing the observed quajitities into his calculationsgave Kelvin an age for the Earth of betu'een 24million and 400 million years, with the rangereflecting the uncertainties in the values of thegeothermal gradient and thermal conductivity.

Scientists derive an extra measure of confi-dence in a conclusion if they can arri\'e at it bymore than one independent route, and this wasno doubt true for Keh-in, who looked also atthe age of the Sun. Given what was known atthe time, the only plausible source for the en-ergy radiated by the Sun was internal, derivedfrom the gravitational potential energy releast'dduring its accretion. Kelvin had calculated theamount of this energy and concluded that theSun could sustain its present rate of radiationfor no more than 100 million years. The agav-ment with his mdependently derived age of theEarth undoubtedly sb'engthonod Kelvin's confi-dence in his result, and though he Niter reducedhis estimate to about 20 million years, he neverswerved from his conviction that the Earth'sage was a few tens or hundreds of millions ofyears, no more.

Geologists now know that the Earth is some4.5 billion years old. Where did Kelvin gowrong? Did he use erroneous values for thegeothermal gradient, for the thermal diffu-sivity of rocks or for the initial temperatureof Earth? None of these. If one were to takeadvantage of today's best understanding ofthese parameters, repeating Kelvin's calcula-tion would still give an age between 24 millionand 96 million years.

344 American Scientist, Volume 95

liefore dissecting Kelvin's arguments, it isworth dfscribinj^ the vvorldview that he was op-posing. Eiirly 19th-century geologists largely ac-cepted the doctrine that the Earth was of unlimit-ed age, reflecting an aphorism of the 18th-centuryScottish geologist Jamos Hutton: that the geologi-cal record showt-d "no vestige of a beginning, noprospect of an end." This doctrine allowed geolo-gists to explain any phenomenon not by the lawsof physics, but by what tbe American get:ilogistand educator Thomas Chrowder Chamberlin in1899 referred to as "reckless drafts on tlie bank oftime." For Kelvin, this game without rules wassimply not scientific. Indeed, it was forbiddenby the laws of themnKiynamics, which he hadpla}'ed a large part in de\'eloping.

In 1867, Kelvin had a telling exchange withthe Scottish geologist Andrew Ramsay after alecture on the geological history of Scotland.Kelvin relates:

I asked Ramsay how long a time he al-lowed for that history, He answered thathe could suggest no limit to it. I said "Youdon't suppose geological history bas runthrough l,(K)n,00(),000 years?" "CertainlyI do." "10,(XX),000,000 years?" "Yes." "Thesun is a finite body. You can tell how manytons it is, Do you think it bas been shiningfor a million million years?" "I am as inca-pable of estimating and understanding tbereasons which you physicists have for lim-iting geological time as you are incapableof undtTstanding the geological reasons forour unlimited estimates." I answered, "Youcan understand the physicists' reasoningperfectly if you give your mind to it."

It is easy to overlook the enormous gains togeology that came simply from ha\'ing to fightthe battle with Kelvin about the age of the Earth.By the end of the 19tli century, the doctrine of asteady-state Earth of indefinite age had gi\ en wayto a more sophisticated \'iew: Geologists had cometo accept that tlie age of the Earth was finite andthat estimating its v alue by quantitative reasoningwas a crucial part of getilogical endeavor. Whatnobody did until 1895, however, was to put tlieirmind, as Kelvin had suggested, to his reasoning.

A single principle underlies all Kelvin's argu-ments about the age of tbe Eartli—tbat energyis conser\'ed. To carry out his analyses, Kelvinadded tbree assumptions, two of whicli appliedonly to bis arguments about the Earth: that theplanet is rigid and that its physical properties arehomogeneous. Tiie tliird assumption, tbat therewas no undiscovered source of energy, appliedboth to the Earth and to the Sun. We now knowthat the third assumption explains Kelvin's errorabout tbe age of the Sun; tbe energy radiated bythe Sun is generated by tbe fusion of bydrogeninto belium in its interior, altbougb quantitativedemonstration that this is so had to await thedetection of tbe "missing neutrinos" in 2001.

Tbe conventional story bas it tbat Kelvin'sthird assumption was also his undoing in cal-culating the age of tbe Earth. Although it is truetbat the decay of radioactive elements insidethe Earth provides a long-lived source of heat,ignorance of this energy source was not respon-sible for Kelvin's incorrect estimate for tbe ageof the Earth. Tbe real mistake in his argumentwas pointed out by one of his former assistants,John Perry, almost a decade before radioactivitybecame recognized as a source of heat.

'You canunderstandthe physicists'reasoningperfectly ifyou give yourmind to it/'

10 20 50 100 200 500 1,000 2,000predicted age (millions of years)

rigure 3. John Perry, a professor of engineering who had at one time served as Kelvin's assistant, was able to reconcile measurements of thegpothcrmal gradient with the Earth being billions of years old by considering the planet to have a convecting, fluid mantle overlain by arelatively thin lid of solid rock. Calculations using Perry's model with a 50-kiIometer-thick lid, along with modem estimates for the thermaldiffusivity and freezing point of mantle rock, show that the range of estimates for the mean geothermal gradient (bnmm Immi on graph) iscompatible with ages as great as 2 billion or 3 billion years (green line). With Kelvin's model of uniform thermal conductivity, the geothennalgradient is compatible only with ages between about 20 million and 100 million years ibliie line).

www.americanscientist.org 2007 July-August 345

\ . .asl came tothe importantpoint, I sawthe old bird situp, open aneye and cock abaleful glanceat me!"

Perry, a northern Irishman, attended Queen'sUniversity in Belfast, where he received lec-tures in engineering from Kelvin's hrotherJames, who was also a notable scientist. Aftergraduating. Perry spent four years as a school-teacher before going to work as Kelvin's assis-tant in Glasgow, He remembered Kelvin withaffection and respect all his life, not least—itseems likely—because Kelvin transformed theyoung Perry's career. Within a year, the school-teacher had become a professor of engineeringin Tokyo, where he contributed greatly to thebirth of Japanese industry, before returning toa professorship in London.

In botii Tokyo and London, Perry was a tire-less educator in engineering and mathematics,insisting that mathematics should be presentedto scientists in a clear and concrete fashion. Gen-erations of schoolchildren, all unknowing, wereinfluenced by him because he recognized theenormous power of graph paper in the plottingof functions and data and, by dri\ ing down itsprice of production, ensured that it entered intoctimmon use. He ended his career as Pmfessorof Engineering at the Royal College of Science(the present Imperial College London).

Perry discovered the flaw in Kelvin's argu-ment in 1894 but, reluctant to embarrass his pa-tron, tried first to convince Kelvin face to faceand hy private correspondence. He was brushedoff, either because Kelvin did not understandPerry's approach or because he was not interest-ed. In 1895, therefore. Perry decided to go public,and he wrote to the journal Nature: "I have some-times been asked by friends interested in geol-ogy to criticize Lord Kelvin's calculation of theprobable age of the earth. 1 have usually said thatit is hopeless to expect that Lord Kelvin shouldhave made an error in calculation." Instead offcxnjsing cm Kelvin's math, Perry suggested thatone should examine his assumptions.

In Kelvin's model, the thermal gradient nearthe surface of the Earth (or, in the thought ex-periment given above, of the turkey) drops asthe cooled outer skin thickens with age. If theEarth were much older than about 100 mil-lion years, this skin would be so thick that tliethermal gradient would be much lower than isobserved. Perry realized that there is a simpleway to stop the skin from thickening: He pro-posed that heat might he transferred muchmore efficiently in the interior of the Earththan at the surface. If this were so, the deepinterior could provide a large store of heat,which would keep the surface temperaturegradient high for a long time, and Kelvin'sestimate of the age of the Earth would be toolow, potentially by a large multiple.

Perry had various suggestions as to howthis might happen, but, for our purposes,his most important argument was that con-vection in the fluid, or partly fluid, interiorof the Earth could transfer heat much more

effectively than does diffusion. He pointedout that if only a thin outer skin of the planetis solid and if the rest of the Earth is a con-vecting fluid, then the interior would be wellmixed and at the same temperature through-out. Perry's model thus replaces the thought-experiment turkey with a turkey-sized bottleof, say, hot cider. Only the outer few millime-ters of this object are solid (the glass of thebottle), and convection churns the interior.Thus the temperature gradient Lit the surfacecan stay high for a very long time.

Perry's calculation shows that if the Earth hasa conducting lid of 50 kilometers' thickness, witha perfectly convectijig fluid undomcath, then themeasured tliermal gradients near tiie surface areconsistent with any age up to 2 billion or 3 bil-lion years. Recognizing that heat transfer in themantle cannot be perfectly efficient. Perry sub-sequently modeled the deep interior as a solidwitli high "quasi-diffusivity." His results agreedwith the original simple calculation in suggest-ing that the Earth could be se\'erai billions ofyears old. Full calcLilations of convection in themantle (which were impossible until the adventof computers) confirm that Perry's reasoningwas sound.

in other words. Perry was able to reconcile aphysical calculation of Earth's thermal evolutionwith the great age that geologists required. Perryneeded nothing more than to intrcxiuce the ideathat heat moved in the deep interior of the Earthmore readily tlian it moved in the outermost lay-ers. Yet to this day, most geologists believe thatKelvin's (understandable) mistake was not tohave known about Earth's internal radioactivity.

The Radioactive Red Herring\n 1903, Pierre Curie and his assistant AlbertLaborde determined that the newly discoveredprocess of radioactive decay releases heat, andseveral people soon argued that this sourcewas great enough to overturn Kelvin's conclu-sion about the age of the Earth. In particular,Ernest Rutherford, who is considered the fa-ther of nuclear theory, spoke on the matter at ameeting at the Royal Institution in 1904:

1 came into the room, which was half dark,and presently spotted Lord Kelvin in theaudience and realized that I was in fortrouble at the last part of the speech dealingwith the age of the eartli, where my viewsconflicted with his. To my relief he fell fastasleep but as 1 came to the important point,I saw the old bird sit up, open an eye andcix:k a baleful glance at me! Tlien suddeninspiration came, and I said Lord Kelvinhad limited the age of the earth, provideduo new source of heat was discovered. Thatprophetic utterance refers to what we arenow considering tonight, radium! Behold!The old boy beamed at me.

346 American Scientist, Volume 95

100 200 500 1.000

predicted age {millions of years)

2,000 5.000

Figure 4. In remarks made during a 1904 meeting at the Royal Institution, physicist Ernest Rutherford suggested that Kelvin's estimates forthe age of the Earth were too low because he had not known about radioactive heating, a process discovered years later. In fact, modem knowl-edge about the amount of radioactive heating that takes place in the mantle changes the prediction of Kelvin's model (blue line on griiph) onlyslightly (green line): Ages greater than 100 million years remain incompatible with measured geothermai gradients (brown band). (Photographby Ramsay and Muspratt, courtesy of AIP Emilio Segre Visual Archives, Brittle Books Collection.)

Perhaps the fame of this anecdote ex-plains the still-common statement that thediscovery of radioactive heat underminedboth an assumption behind Kelvin's calcu-lation and its conclusion. But that assertionis logically incorrect. Kelvin's conclusionwould have been invalidated by the discov-ery of radioactive heat only if incorpora-tion of that heat into his calculation wereto produce a substantially different age forthe Earth.

The modern estimate for the total rateof radioactive heat generation within theEarth is about 2 x 10'-̂ watts, equivalent toabout half the total amount of heat flowingout of the planet at present. It might, there-fore, seem that Earth's internal heat pro-duction can make a sizable contribution totemperature gradients at the surface. Onemust recall, however, that this heat pro-duction is distributed through the wholevolume of the 2,900-kilometer-thick mantleand that Kelvin's calculation showed thatdiffusion can mine the heat from only theouter 100 kilometers of the Earth in 100million years. One should correspondinglyexpect that if Kelvin's calculation were re-run with the inclusion of radioactivity, onlythe heat generated in the outermost 100kilometers of the Earth (ahout 5 percent ofthe volume of the mantle) would contributeto the temperature gradient at the surface.Hence, even if Kelvin had included radio-active heat in his calculation, his estimateof the age of the Earth would have beenvirtually unaffected. A careful calculationthat takes account of the details of the dis-tribution of radioactive heating validatesthis simple argument.

Perry's Prescient Picture of the MantlePerry's analysis of the age of the Earth fol-lowed Kelvin's lead, in that he insisted onanalysis of a simple physical system—butthe system he chose to analyze was differentfrom Kelvin's. A fluid mantle was widelyunderstood as the necessary condition forisostasif. the idea (worked out earlier in the19th century) that crustal features such asmountain ranges must float on the densermantle, in the same way that icebergs floaton water. Yet Kelvin felt that he was on firmground in rejecting the notion of a fluid inte-rior: He knew from the study of Earth tidesthat at least the outer 1,500 kilometers of themantle are as rigid as steel. Perry tried hardto change Kelvin's mind on this point, usinglanguage specifically addressed to Kelvin'sway of thinking. He wrote:

... the real basis of your calculation is yourassumption that a solid earth cannot alterits shape ... even in 1000 million years,under the action of forces constantly tend-ing to alter its shape, and yet we see thegradual closing up of passages in a mine,and we know that wrinkling and faultsand other changes of shape are always go-ing on in the solid earth under the actionof long-continued forces. I know that solidrock is not like cobbler's wax, but lO** yearsis a long time, and the forces are great!

Perry's reference to cobbler's wax was de-liberate and requires some explanation. Kel-vin, like many physicists at the time, thoughtthat light could not travel in a vacuum butrequired a physical medium, the "ether," forpropagation. That medium had to possesselastic properties at very short times to allow

7 know thatsolid rock is notlike cobbler'swax, but 10^years is a longtime, andthe forces aregreat!"

www.americanscieiitist.org 2007 July-August 347

age of oceanic crust(millions of years)

high

100

low

0 50 100 150distance from spreading ridge (kilometers)

Figure 5. Geologists tended to dismiss Kelvin's attempt to estimate the age of the Earth as being too simplistic, but the model Kelvin used—thaiof a cooling "half-space"—has in fact proved very useful in geology. In particular, it accounts well for the overall character of oceanic plates asthey move away from the volcanic ridges where they form. A slice of the North Atlantic crust fleft) illustrates the general configuration, withrelatively shallow ocean above the young, hot rock of the ridge {red). Older seafloor to either side (blue) has had time to cool and contract andhas thus sunk farther beiow sea level. Departures from the cooling-half-space model, such as the tendency for geothermal gradients (solidpoints on graph) near mid-ocean ridges to be less than this model predicts (blue line), help to reveal other phenomena, in this case the circula-tion of seawater through young oceanic crust (Graph adapted from Sclater et al. 1980.)

light waves to propagate, but it needed to beweak at longer time scales so that the Earthcould move freely through it.

Although he could not find a satisfactorymathematical formulaticm for tlie ether, Kelvinwas fond of a physical demonstration tliat illus-trated its required physical properties. He placedwater in a glass cylinder, floated a number of5mall corks on the surface, covered them witha layer of Scottish shoemaker's wax and finallyplaced bullets on the top. CK'er a short period ofobser\-aHon, nothing visible happened, but aftersix montlis the corks and the bullets had embed-ded themselves within tlie wax. After a year, thecorks could be found on the top and the bulletson the bottom. The wax exhibits strength ui tlieshort term but is weak on long time scales.

These properties, qualitatively, were exactlythose that Kelvin required of the ether. Perrywas arguing that the disagreement betweenKelvin and the geologists could be resolved ifit were accepted that the mantle of the Earth isrigid at short times but fluid over longer timescales. Kelvin completely missed the point,and so, it seems, did everyone else.

Perry published his arguments in the pagesof Nature, which was as prominent an organ ofscientific discourse in 1895 as it is today. Othersconcerned with tiie debate about the age of theEarth certainly knew of Perry's challenge toKelvin's conclusions. So why was Perry's rec-ognition of convection in the Earth's interior notaccepted in the decade before radioactive heatbecame established—or indeed, thereafter?

Personal factors were probably important.Most modem scientists, if they were as con\'inced

as Perry was about a major topic of debate, wouldha\'e pushed harder. Perry re\'ered KeK'in aiid,although he felt strongly that an alternative physi-cal argument should be put forward, be was notthe sort of person to indulge in egtitistical disputa-tion. He seems not to have pursued tliis topic btitto have spent another 25 years researching andteachiiig on tlie wide I'ange of subjtxrts that inter-ested liim, eventually succumbing to scur\'y con-tracted on a long sea voyage taken for his health.

Perry was not alone in deferring tti figuresof authority in a way that is uncommon today.Perhaps a similar atmosphere of deference al-lowed Kelvin's assessment of the situation to besupplanted by Rutherford's after 1904.

The neglect of Perry's argument may alsobe explained by the fact that it was not under-stood by most people who cared about the ageof the Earth. Biologists seized on Perry's con-clusion that Kelvin's estimate could be wrong,while at the same time freely admitting tbattbey couldn't understand his argument. Thegeological community was happy to take thedemonstration that Kelvin was wrong as evi-dence that geological intuition trumps simplephysical analysis as far as the "real" Earth isconcerned. (One should not forget, though,that the geologists of the time produced esti-mates for the age of the Earth which were justas wrong as Kelvin's—often more so.)

Many geologists felt, as Andrew Ramsay'start conversation with Kelvin suggested, thatphysicists were incapable of Linderstandinggeological reasoning and that geology is toocomplex to be encapsulated in a mathemati-cal model. Perry's analysis shows, however.

348 American Scientist, Volume 95

that Kelvin's failure lay not in the use of simplephysics, but in using the wrong simple physics.

Ik t̂h Kelvin and Perry knew that simple mod-els—the purpose of which is to allow analysis ofthe major features of phenomena, not slavishlyto reproduce all their details—are indispensablet(xils in science. Many of the most useful modelsare underlain by a principle Einstein famouslyexpressed: "Everything should be made as sim-ple as possible, but not simpler."

It is worth illustrating the explanatorypower of simple models in geology with a rel-evant modern example. Suppose one wishedto explain the thermal evolution of the oceantloor. A model that accounted accurately formajor, obvious variables (different thermalproperties and thicknesses of the various geo-logical layers, the heat-driven circulation ofwater through the shallower portions of thisrock, seafloor volcanism and so forth) wouldstill have at least a dozen parameters, manyof them poorly known, and would requiremillions of calculations simply to explorethe many possibilities. Consequently, the re-sults of such a model would be impossibleto grasp.

In contrast, treating the ocean floor as a ho-mogeneous slab of rocky material yields Kel-vin's simple analytical solution for a cooling"half-space," which captures the main featuresof oceanic plates as they move away from thevolcanic ridges where they form. And by in-cluding the thermal contraction that takes placeas the slab cools, such a mtxiel neatly explainsthe measured deptli of most of the seafloor.

What Kelvin did not allow for is that, tovarying degrees, all simple models are boundto break down, and scientists may learn asmuch by their failures as by their success-es. The cooling-half-space model fails foryoung ocean floor because heat is also car-ried through oceanic ridges by the circulationof hot water. However, the degree to whichthermal gradients depart from the predictionof the simple model allows geophysicists toestimate the amount of heat transferred bythat circulation and hence to determine theflux of water through the ridges. The modelalso fails for ocean floor older than about 80million or 90 million years, but in doing soit reveals a second scale of convection in themantle and allows geophysicists to estimatethe thickness of tectonic plates.

In a parallel way. Perry's analysis showedthat the failure of a conductive model for theEarth could be explained if the mantle wereto convect. If the scientific community of theday had absorbed Perry's message, the first ra-diometric ages for the Earth would have comeas confirmation of the convective explanationfor the Earth's observed geothermal gradient.The realization that convection takes placewithin the Earth's apparently solid interior

would have made it hard to sustain the "fix-ist" view of the Earth—which held that it wasphysically impossible for continents to movehorizontally. That perception of fixity exerteda powerful brake on geological progress inthe first half of the 20th century: Proponentsof continental drift needed repeatedly to makearguments that the solid Earth could flow overlong time scales—against considerable skepti-cism. It took until the 1960s for their views toprevail.

One is left with the question of why manyscientists (professional geologists included)continue to believe that the discovery of radio-activity simultaneously proved Kelvin wrongand provided the explanation for his error.Part of the answer, perhaps, is that it makes fora good story. Arthur Eve, one of Rutherford'searly biographers, reported that this influentialphysicist repeated on many tKcasions his taleof thinking on his feet in front of the "old bird"Kelvin. It is entirely possible that the pleasingform of the anecdote, and the eminence of itsauthor, led to the uncritical acceptance of themyth. It is hard to dissuade aging scientists,as they slip into their anecdotage, from repeat-ing stories that they find amusing. But theiryounger colleagues must be careful not to mis-take such accounts for history.

Bibliography

Biurhfield, J. D. 1975. Lmi Kelvin mni the Age of the Earth.New York: Science History Publications.

Chamberlin, T. C. 1899. Lord Kelvin's address on the age

of the earth as an abL>de fitted for life. Science 9:899-901.

Curie, I'., and A. Labordc. 1903. Siir la chaleur degageespontanemeiit par les sels de radium. Campte^ Rnidtifde rAauleinie des Sciences 136:673-673.

England, P C, P Molnar and F. M. Richter. 2(X)7. John Peny'siieglecteii crilique of Kelvin's age for tlie B.irth: A missedopportunity' in geodyn.imics. GSA Tainii 17(1 ):4~9.

Eve, A, S. 1939. Rulhcrford. New York: MacmiUan.Fourier, J. B. J. 1822. Tlworit' Anali/tiqiw de In Chalcjir. Paris:

Fimiin Didot.Kelvin, W. T. 1863. On tlie secular axiiiiig of the earth.

Transactions of the Royiil SiKiehfofEdinliw'^h 23:157-170.Kelvin, W. T. 1895. On the age of the earth. Nature

51:438-440.

Lindley, D. 2004. Degrees Kelvin. Washington, D.C: JosephHenry Press.

Perry, J. 1895. On the age of the eartii. Nature 51:224-227.Perry, J. 1895. On the age of the earth. Nature 51:341-342.Perry, J. 1895. On the age of the earth. Nature 51:582-585.Richter, F. M, 1986. Kelvin and the age of the earth, jounxal

:395-401.Sclater, j . G., C. Jaupart .ind D- Gatson. 1980. Heat flow

through oceanic and continental crust and the heatloss of the earth. Reinews of Geophysics and Space Phys-ics 18:269-312.

Shipley, B. 2001. "Had Lord Kelvin a right?": John Perry,natural selection and the age of the Earth, 1894-1895.In The Age of the Earth: from 4004 BC to AD 2002. ed.C. L. E. Lewis and S. J. Knell, London: The Geologi-cal Society.

Stacey, F. D. 2000. Keh'in's age of the earth paradoxiled. jourual of Geophifsicat Ri-search 105:13155-13158

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