Search for Hidden Chambersin the Pyramids

The structure of the Second Pyramid of Gizais determined by cosmic-ray absorption.

Luis W. Alvarez, Jared A. Anderson, F. El Bedwei,James Burkhard, Ahmed Fakhry, Adib Girgis, Amr Goneid,

Fikhry Hassan, Dennis Iverson, Gerald Lynch, Zenab Miligy,Ali Hilmy Moussa, Mohammed-Sharkawi, Lauren Yazolino

The three pyramids 6f Giza are situ-ated a few miles southwest of Cairo,Egypt. The two largest pyramids standwithin a few hundred meters of eachother. They were originally of almostexactly the same height (145 meters),but the Great Pyramid of Cheops hasa slightly larger square base (230 meterson a side) than the Second Pyramid ofChephren (215.5 meters on a side). Aphotograph of the pyramids at Gizais shown as Fig. 1. Figure 2 shows theelevation cross sections of the twopyramids and indicates the contrast inarchitectural design. The simplicity ofChephren's pyramid, compared withthe elaborate structure of his father'sGreat Pyramid, is explained by arche-ologists in terms of a "period of ex-perimentation," ending with the con-struction of Cheops's pyramid (1). (Thecomplexity of the internal architectureof the pyramids increased during theFourth Dynasty until the time ofCheops and then gave way to quitesimple designs after his time.)An alternative explanation for the

sudden decrease in internal complexityfrom the Great Pyramid to the SecondPyramid suggested itself to us: perhapsChephren's architects had been moresuccessful in hiding their upper cham-bers than were Cheops's. The interiorof the Great Pyramid was reached bythe tunneling laborers of Caliph Ma-

The authors are affiliated with the Joint Pyra-mid Project of the United Arab Republic and theUnited States of America. They reside either inCairo, United Arab Republic, or in Berkeley,California. The article is adapted from an ad-dress presented by Luis W. Alvarez at theWashington Meeting of the American PhysicalSociety, 30 April 1969.

832

mun in the 9th century A.D., almost3400 y'ears after its construction. Ofour group only Ahmed Fakhry (authorof The Pyramids, professor emeritus ofarcheology, University of Cairo, andmember of the Supreme Council ofArcheology, Cairo) was trained in ar-cheology. As laymen, we thought it notunlikely that unknown chambers mightstill be present in the limestone abovethe "Belzoni Chamber," which is nearthe center of the base of Chephren'sSecond Pyramid, and that these cham-bers had survived undetected for 4500years. [We learned later that such ideashad occurred to early 19th-century in-vestigators (2), who blasted holes in thepyramids with gunpowder in attemptsto locate new chambers.]

In 1965 a proposal to probe theSecond Pyramid with cosmic rays (3)was sent to a representative group ofcosmic-ray physicists and archeologistswith a request for comments concern-ing its technical feasibility and archeo-logical interest. The principal noveltyof the proposed cosmic-ray detectorsinvolved their ability to measure theangles of arrival of penetrating cosmic-ray muons with great precision, over alarge sensitive area. The properties ofthe penetrating cosmic rays have beensufficiently well known for 30 years tosuggest their use in a pyramid-probingexperiment, but it was not until theinvention of spark chambers with digi-tal read-out features (4) that such ause could be considered as a real pos-sibility. [Cosmic-ray detectors with lowangular resolution had been used in1955 to give an independent measure

of the thickness of rock overlying anunderground powerhouse in Australia'sSnowy Mountains Scheme (5)].The favorable response to the pro-

posal led to the establishment by theUnited Arab Republic and the UnitedStates of America of the Joint U.A.R.-U.S.A. Pyramid Project on 14 June1966. Cosmic-ray detectors were in-stalled in the Belzoni Chamber of theSecond Pyramid at Giza in the springof 1967 by physicists from the EinShams University and the Universityof California, in cooperation with ar-cheologists from the U.A.R. Depart-ment of Antiquities. Initial operationhad been scheduled for the middle ofJune 1967, but for reasons beyond ourcontrol the schedule was delayed forseveral months. In early 1968 cosmic-ray data began to be recorded on mag-netic tape in our laboratory building,a few hundred meters from the twolargest pyramids. Since that time wehave accumulated accurate angularmeasurements on more than a millioncosmic-ray muons that have penetratedan average of about 100 meters oflimestone on their way to the detectorsin the Belzoni Chamber.

Proof of the Method

Before any new technique is usedin an exploratory mode, it is essentialthat the capabilities of the techniquebe demonstrated on a known system.We gave serious consideration to aproposal that the cosmic-ray detectorsbe tested first in the Queen's Chamberof the Great Pyramid, to demonstratethat the King's Chamber and the GrandGallery could be detected. But thissuggestion was abandoned because theKing's Chamber is so close to theQueen's Chamber and because it sub-tends such a large solid angle that ear-lier (low resolution) cosmic-ray experi-ments had already shown that theupper chamber would give a largesignal. It was apparent that the onlyuntested feature of the new techniqueinvolved the magnitude of the scatter-ing of high energy muons in solid mat-ter. (An anomalously large scatteringwould nullify the high angular resolu-tion that had been built into the de-tectors, in the same way that frostedglass destroys our ability to see distantobjects.) We had no reason to doubtthe calculated scattering, but we wereanxious to be able to demonstrate toour colleagues in the U.A.R. Depart-

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Fig. 1 (top right). The pyramids at Giza.From left to right, the Third Pyramid ofMycerinus, the Second Pyramid of Che-phren, the Great Pyramid of Cheops.[L National Geographic Society]

ment of Antiquities in a convincingmanner that the techniquLe really workedas we had calculated. For this pturposewe required as our test objects notlarge features that were nearby but,instead, small featuLres separated fromthe detectors by the greatest possiblethickness of limestone. Fortunately,such features are available in the Sec-ond Pyramid; the four diagonal ridgesthat mark the intersections of neighbor-ing plane faces were farther from thedetectors than any other points on theindividual faces. (From now on, wewill refer to these ridges as the "cor-ners.")From the known geometry of the

Second Pyramid, the trajectories ofcosmic-ray muons that pass through apoint on a face 10 meters from a cornerand then down to the detectors can beshown to traverse 2.3 fewer metersof limestone than do muLons that strikethe corner. They shoulld therefore ar-rive with 5 percent greater intensitythan the muons from the corner. SuLchan increase in intensity, correspondingto suLch a decrease in path through thelimestone, is abouLt half of what wouldbe expected to result from the presenceof a chamber of "typical size" (5 me-ters high) in the pyramid. Since such achamber would necessarily be closer tothe detectors, it wotuld for these tworeasons be a muLch "easier object tosee" than the corner.The detection equipment was there-

fore installed in the southeast cornerof the Belzoni Chamber, with the ex-pectation that it would first show thecorners in a convincing manner, so thatthe presence or absence of unknownchambers could later be demonstratedto the satisfaction of all concerned. InSeptember 1968 the IBM-1130 com-puLter at the Ein Shams UniversityComputing Center produced the data

Fig. 2 (bottom right). Cross sections of (a)the Great Pyramid of Cheops and (b) thePyramid of Chephren, showing the knownchambers: (A) Smooth limestone cap. (B)the Belzoni Chamber, (C) Belzoni's en-trance, (D) Howard-Vyse's entrance, (E)descending passageway, (F) ascendingpassageway, (G) underground chamber,(fl) Grand Gallery, (1) King's Chamber,(J) QuLeen's Chamber, (K) center line ofthe pyramiid.

6 FEBRUARY 1970

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Fig. 3 (left). The initial measurement (with zenith angle of counts from 20 to 40 degrees) of the variation of cosmic-ray intensitywith azimuthal angle, as observed from the Belzoni Chamber underneath the Second Pyramid of Chephren. Fig. 4 (light).Detection of the northeast and southwest corners of the pyramid obtained by plotting the second differences of the countingrate on the planes tangent to the corners as a function of distance from the corners.

for Fig. 3, which shows the variationof cosmic-ray intensity with azimuthalangle (compass direction). The expectedrapid changes in cosmic-ray intensityin the vicinity of the corners wereclearly shown, and the capability of themethod could no longer be doubted.An analysis of more data was latermade on the Lawrence Radiation Labo-ratory's CDC-6600 computer and isshown in Fig. 4. Here the "second dif-ferences" of the counting rate withdistance from each corner are plottedon planes that are located symmetrical-ly with respect to adjacent faces andthat are tangent to the corner. Mathe-matically, we would expect to see asharp spike at the corner of a sharplydefined pyramid in the plot of thesecond derivative of counting rate withrespect to distance. The second deriva-tive becomes a second difference curvewhen we use bins of a finite size. Thesharpness of the peaks in the seconddifference curves shows that the effectof the scattering of muons in limestoneis somewhat smaller than the conserva-tive estimate made in the original pro-posal.We were at first surprised by the

large variations in maximum countingrate through the four faces of thepyramid. We knew that the BelzoniChamber was not at the exact center ofthe base of the pyramid, but we hadnot appreciated what large changes incounting rate would be occasioned bythe actual displacement of the detectorfrom the center of the base; the equip-ment is 15.5 meters east and 4 metersnorth of the center. There are two in-dependent ways to use cosmic-ray data

834

to determine the location of the detec-tor with respect to the exterior featuresof the pyramid.

1) The difference in the maximumcounting rate through the east and westfaces gives the displacement of thedetector toward the east, and similarmeasurements in the north-south di-rections give the displacement to thenorth.

2) The azimuthal angles of the dipscorresponding to the corners give asecond, quite independent, and moresensitive measure of the displacements.We can report that from cosmic-rayobservations alone, "looking through"100 meters of limestone, we can locatethe position of our detectors to within1 meter. To the best of our knowledge,no such measurement has ever beenmade before. Our cosmic-ray-derivedposition agrees to within less than 1meter in the north-south direction witha recently surveyed position obtainedby the U.A.R. Surveying Department,but it differs by 2 meters (that is, itindicates 13.5 rather than 15.6 meters)in the east-west direction.

Simulated X-ray Photographs

We have presented the cosmic-raydata in two different ways, one photo-graphic and the other numerical. Boththese methods involve the projectionof each recorded muon back along itstrajectory to its intersection with eithera horizontal plane or a sphere thattouches the peak of the pyramid. Figure5a is a diagram representing the Sec-ond Pyramid with the horizontal "film

plane" touching the peak of the pyra-mid and with a dashed line (represent-ing the path of a cosmic ray) passingfrom the detector through a hypotheti-cal chamber to the image of the cham-ber on the "film plane." (The mappingof the pyramid structure by this tech-nique is identical to what we wouldobtain by x-raying a small model ofthe pyramid, with an x-ray source inthe Belzoni Chamber and with an x-rayfilm touching the peak of the modelpyramid.) Figure Sb represents thespherical shell onto which cosmic rayswere projected for numerical analysis.

Figure 6 is a view of all the equip-ment, which occupied most of thesoutheastern part of the Belzoni Cham-ber. Figure 7 is a closer view of thedetector. The two spark chambers,each 6 feet (1.8 meters) square, areseparated vertically by a distance of1 foot (0.3 meter). Above and belowthe spark chambers and just above thefloor level were scintillation counters,which triggered the spark chamberswhen all three counters signaled thepassage of a penetrating muon. The4 feet (1.2 meters) of iron betweenthe bottom two scintillators was in-stalled to minimize the effects of muon-scattering in the limestone.The simulated x-ray photograph of

the pyramid shown in Fig. 13a is anuncorrected (raw data) scatter plot of700,000 recorded cosmic-ray muons asthey passed through the "film plane."The four corners of the pyramid arevery clearly indicated. If a Grand Gal-lery and a King's Chamber were locatedin the Second Pyramid as they are inthe Great Pyramid, the Grand Gallery

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Fig. 5. (a) Geometry of the bSecond Pyramid, showing theprojection technique used toproduLce a simulated x-ray photograph. The plane on the top of the pyramid can bethought of as the "film plane." (b) The spherical surface on which the events wereprojected for the ntumerical analysis of the data.

would have shown up clearly but theKing's Chamber would probably haverequLired some computer assistance tobe made visible. There is one unex-pected feature in Fig. 13a: on the northface, there appears to be a narrownorth-south-oriented region that hasa lower cosmic-ray intensity than isfound in surrounding areas. We wereat first hopeful that the north-southstreak indicated the presence of aGrand Gallery above and north of theBelzoni Chamber, just as the GrandGallery is above and north of theQueen's Chamber in the Great Pyra-mid. But we later found a satisfactoryexplanation of this feature in the pic-tuLre that did not involve any interiorstructure in the pyramid. The region oflower cosmic-ray intensity resultedfrom the construction of the sparkchambers. Since we could not transportsquare chambers 6 feet (1.8 meters)on a side through the small passage-

ways of the pyramid, each squarechamber comprised two chambers 3by 6 feet (0.9 by 1.8 meters) in area.Also, each of the large scintillationcounters was divided into sections. Theinactive areas between the two pairs ofspark chambers and between the sec-tions of the counters led in a predict-able way to the unexpected signalshown in Fig. 1 3a.

Numerical Analysis

We concluded from our study of thesimulated x-ray picture that no unex-pected features were discernible. Butsince we had been looking for an in-crease in intensity of approximately 10percent over a region larger than thatto which the eye responds easily, wethen turned to a more detailed numeri-cal analysis of the data. (The reason forexpecting a 10 percent increase in in-

tensity in the direction of a new cham-ber is simply that the integral rangespectrum of the muons is representedby a power law with an exponent equalto -2. Therefore, if the rock thicknessis changed by an amount AX, out ofan original thickness X, the relativechange in intensity is Al/I = -2AX/X.The four known chambers in the twolarge pyramids have an average heightof about 5 meters. Therefore AX/Xshould be -5 percent, and the corre-sponding value of AI/I should be +10percent.)

Since the counting equipment wassensitive out to approximately +45 de-grees from the vertical, our data wereplotted in a matrix with 900 entries,30 X 30 bins, each 3 by 3 degrees.Figure 5b illustrates this system ofbinning on a sphere that encirclesthe pyramid. We wrote a computerprogram to simulate the counting rateexpected in each of these bins. As thesimulation program became more so-phisticated with time, it took into ac-count the most detailed features of themeasured exterior surface of the pyra-mid, including the "cap" of originallimestone casing blocks near the top,the surveyed position of the detectorsin the Belzoni Chamber, the positionsof the walls and ceiling of the BelzoniChamber, and the sizes and positionsof each of the four spark chambersand the fourteen scintillation counters.An important control on the quality

of the experimental data being com-pared with the simulated data camefrom scatter plots showing the exactx and y coordinates of each riecorded

Fig. 6 (left). The equipment in place in the Belzoni Chamber under the pyramid.Fig. 7 (right). The detection apparatus containing the spark chambers.

6 FEBRUARY 19708 835

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muon as it passed through each of thefive planes containing scintillators or

spark chambers. Unsatisfactory opera-tion of the spark chambers showed upas small blank areas in the scatter plotsof muons passing through the cham-bers. Such unsatisfactory operation was

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Fig. 10 (bottom left). The differences be-tween the numbers of events measuredand predicted expressed in integral num-bers of standard deviations for the bestfit to the data for which the XI was 905.(The bins for which the predicted num-ber of events was less than 30 were notused in calculating the XI.)

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eliminated from the data base aboutone-third of the measured muons.The scatter plo-ts also served as a

check on the resolution and accuracyof the angle measurements. The edgesof the counters showed up on theseplots as sharp lines at positions thatagreed well with the direct measure-ments of the counter locations. Neitherthe direct measurements of the counterpositions nor the inferred positions ofthese counters as obtained from thedata themselves were good enough topermit the program to make sufficientlyaccurate calculations. In a typical 3-by 3-degree bin there are 1600 events.The statistical uncertainty in this numi-ber of events is 2.5 percent. It was

necessary to make calculations to atleast such an accuracy to make fulluse of the data. We first varied the as-sumed positions of the scintillat-ors bysmall amounts in an effort to fit theexpected counts to the measured counts.This approach was unsatisfactory. Cal-culations of the desired accuracy wereobtained only after we eliminated theevents that passed near the edge of atleast one of the counters. In effect, eachcounter was defined to be slightly small-er than it actually was, and only th--recorded muons that passed throughthese defined counter positions wereaccepted. This method eli-minated theproblems associated with small displace-ments of the counters during the ex-periment, with small-angle scattering ofmuons in the iron, and with decreasedsensitivity of the counters near theiredges. About 15 percent of the eventswere eliminated in this way. We believethat the 650,000 muons in the finalselected sample are free of importantbiases resulting from improper func-tioning of the equipment.

In the course of the computer anal-ysis, about 40 fits were made to mini-mize the difference between the ma-trices of actual and simulated counts.Although the matrices contain 30 x 30bins each, some of the bins at the edgescontain so few counts (or none at all)that the effective number of bins isclose to 750. If we knew all the physi-

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cal parameters of our detection equip-m-ient, if we were equally sure of thecquations describing the cosmic-rayspectrum, and if we were, in addition,sure that the pyramid was made of solidlimestone, then we would expect thex2 of the fit between the actual and thesimulated data to be about 750. Thecarliest fits had X2'S of close to 3000,but this important parameter droppedto approximately 1400 by the time thestereophotographically determined con-tours of the pyramid exterior were madeavailable to us through the courtesy ofthe U.A.R. Surveying Department.

Figure 8 is a -matrix showing thetotal number of real counts recordedin each of the 900 3- by 3-degreebins. Figure 9 is one of the finalsimulation runs, and Fig. 10 -is thedifference -between Figs. 8 and 9 ex-

pressed as the closest integral numberof standard deviations. [For a bin inwhich the number of counts was 2500,an entry for +2 standard deviationsmeans that the actual count exceededthe expected count by 2(2500)½2 = 100.1

If these deviations are only statisticalin nature, one expects about 87 percentof the bins to have contents of -1, 0,or ± 1, about 12 percent of the bins tohave ±-2, and 1 percent of the bins tohave ±-3. There is one chance in threeof finding one bin having ±14, onechance in 200 of finding one bin with-+-5, and only one chance in 3 X 104of finding one bin with ±t6, if the de-viations are due only to statistical fluc-tuations. Thus no single bin has a sig-nificant effect unless its contents are atleast ±+4. Figure 10 contains no binsshowing ±+4.

I)etection of the Cap

The most distinctive feature of theSecond Pyramid is the cap of originallimestone casing blocks near the top.All the casing was removed fro>m theGreat Pyramid in the Middle Ages, butthe builders of Cairo, who "quarried"the pyramids at that time, stopped be-fore completely stripping the SecondPyramid.

Before the simulation program in thecomputer took account of the presenceof the cap of limestone casing blockson. the pyramid, the difference plots(like the plot given in Fig. 11) alwayscontained a central region with a pre-ponderance of negative entries. Whenthe cap was properly allowed for in the6 FEBRUARY 1970

'A

N

0 2 u - L u 1 I- IL-1 0 -1 2 1 - 1 1 -2 2 2 0 -2 1 -1 -1 1 0 2

0 0 2- 1 1 0 -1 1 2 -1 1 0 0 1 -2 0 -2 0 -1 1- 0-1 01- 0-1 0 1 1- -2 1 0 0 0 1 1 1 0 1 -1 -1 0 1 0 0 -1 1o - 0-10 0 1 0 1 0- 2 -3 0 1 1 1 2 0 0 -2 -1 0 2 2 0 0 .2 -1 -1

1 1 1-1 2 0- 1 2 0 0 0 2 3 1 0 0 -1 2 -1 2 1 -2 0 -1 -11 - 1-1- -1 1 0 0 0- 0 -3 0 -2 -1 0 2 0 1 1 0 -2 0 1 0 1 -1 1 -1

2i 1 0 1- 1 0- 1 1-1 -1 0 1 1 -1 -1 2 0 -1 -1 0 0 0 -1 0-1 0 0 2-1- 2 0 0 0 1 0 -1 -1 -1 0 2 1 2 -1 0 0 -1 1

-2 1-1- 1- 2 0 0-2 0 -1 0 1 1 0 1 2 0 0 1 1 0 -1 -10 1- 1-1 1 0 2 - -1 - -1 - -1 -1 0 0 2 0 2 0 -1 1 1 -2 -1. 1 0 -2 1

g1 0 0- 1- 2 0-2 -2 1 0 2 0 -2 -1 1 0 0 1 1 0 0 0 E0-0119~,10 21 21 1102 0 112 00 1 0-1 1

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1- *1A1~.2~ 0 0-1 -2 1 1-11-2 30102313-121011 1 0-3 10 00 0 110 00 0

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12 0 2 2 0 0 0 0 1 0 0 1 1 -1 -1 -1 -1 0 0 0 1 2 1 -1 -10 1- 2-1 -1 1 -1 -1 -2 -1 -1 -2 -3 1 2 1 0 1 -1

- 3 1 21 1 1-1 0 0 0 1 0 1 -1 1 -1 0 -1 -2 -2 -1 -1 0 1 3 0 1 112 1 0 1 1 0 0 0 0 1 0 0 -1 -2 1 0 -1 0 -1 0 0 1 0 -1 0

1 1 03 0 2 0 0- 1 0 0 0 0 0 1 0 0 2 1 0 -1: -1 -1 0 0 1 0 -12 2 12- -1 0- 0 1-2 0 1 0 0 -1 0 3 0 -1 0 -1 0 -1 2 1 0 0 0

-1 1 3-1- 3 0- 1 0 1 2 0 -2 0 1 0 -2 0 0 0 -1 -1 -21 - 2-1 - -2 - -1 1 0 1 0 1 -2 1 1 1 0 0 -1- -1 -2 -1 -1

12- 2- 2 0 0 -1 -1 0 -1 0 1 0 1 0

45090

Fig. 11. The display of Fig. 10 as it would have appeared had there been a "King'sChamber" in the pyramid 40 meters above the apparatus. The group of numberslarger than 3 at the center-left (shaded area) indicates the chamber's position.

simulation, the actual counts in this re-

gion were no longer systematically lowerthan predicted by the computer, and,the value of x2 dropped accordingly.

Although the x2 of the fit betweenthe actual and simulated data was low-ere-d when the features of the cap wereintroduced into the simulation, thisdrop does not constitute the strongestproof that we were in fact detectingthe cap. Figure 12 compares the mea-sured and cosmic-ray-determined varia-tion in thickness of the limestone capin two 24-degree-wide strips that runover the top of the pyramid in thenorth-south and east-west directions.In the absence of a cap both on thereal pyramid and in the simulation, we

would expect the experimental pointsto lie along the zero lines of deviation.The smooth curved lines are obtainedfrom the simulation program by utiliz-ing the recently determined contoursof the pyramid. The generally goodagree-ment of the data points with theprediction (Fig. 12) shows clearly thatwe have detected the presence of thecap through more than 100 meters oflimestone.The detection of the cap was much

more difficult than detection of thecorners; together, these two "proofs ofthe -method" convinced us that we couldhave seen any previously unknownchamber that might exist in our "fieldof view."

T Fig. 12. This graph shows~North to South that the cap on the top

2 ~t Iof Chephren's Pyramid2 is observed in this ex-

Tperiment. The quantity

o plotted is the differenceI between the measured

distance from the detec--2 tor to the surface of the

I I pyramid and the distanceE calculated under the as-

sumption that the pyra-mid has no surface ir-

0 West to East regularities. The data0 onsrpeettedsponsrersn teds

.3 tances indicated by the'3) cosmic rays and are to0 0 i be compared with the

± solid line, which repre-

T2 sents the same distance-2 measured by the aerial

600 900 1200 survey. These distanceshave been averaged over

24-degree-wide bands centered on the middle of the pyramid, one running north-south,the other east-west.

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Se:arch for ('avities

A\s theIc Iil "Is pI o0cCerld ddiiiLInc-

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7t ( IC\ 1" siIo ic id has aIn inltexitrd1.-11IoC posse Ix~iwnrld\ ot1 2. .1 r)ilnrist ot th1Is t ImeIc xx Wxeie e'\cited bxthei pie-senlce of' t\\ o piosi tiI\ c rec-io,'

oIItent Iil iti"missit ilaIter- couxIIots )I(Itcot, thcse IcilitsppaIei-l\st i.ier thecpresecei ol i' IiI' abidiclx tinIerI theC ipx\ ot thl' px riilidtir .iboiit

() meiters abox c thc B3elzonii (haitibetl. BeCanse, rft theC displa"ICCletnet r)t theCBelzit C iabe to the no01ti~thann cist

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(ftthe ceniter of thc pvrIam id's baIse, thea)pparenlt chaIIImbe mlapped us1ontothe sonthic1n part ot' the s\\s,ici 0 laccot, the p\vrm iid I-lhe Ici atlI\ C nci C~casII LVnoJtjiIne ate 5\ as ab-out 11pi et'1'Cpecterd. The an colail- size ot thec

anomaix,1 ConIld bec elated to dis'tanlce()III bx) aCS~i- nc11( a ccrtila si/c tar1 thell(oli airca of, the habi7IxxesSLimCd tha~t theC anomals~tk came1 Ii om1 a(oni"lhe size ot, C~heopsx, k nc's (hanibei. it hadc to be abouh) It 3( meiters-,ixwxax aind its la poItion turneCd Ontto he almIos,t Ce\ar'lx cenItra,l.

L ntoi tona11~tel\V. thIsP In cc LinId pICI-sisentsiea.to-cetheir \\ itli at L1i-cci

IcnaltI ox 'I SIILCeratsnLIaller-anIcIilarac.d' ",isappea edaCIs x\x Cle 1-inedIImic evict]I

,IIl theC diMenions0, ot theC apartisadolf the pxramid that '\Cci e impoirtint InIthe s I nIaILt ion p rocr!lailntVC\chad niot

atcipatecd the nieed l'oi sutch aIccur-ate

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daIta. I Thec n11t itftcts 55 c obsci x ed tiremecinijone onlyv to sho\s thatItofa romiseeing, nothing'" thrloughIfont the tinal-sIs lpci-tor. xx\e hadtc thiree xcix\ e.\citinc

s11iunals that disa"~ppearedf nlxv Aimte the-eC~tca,et cai-c hadL beenl taken to ma1,ke

aectlv to thle 'e,omelllt\ bfoth the 'ip-

WAhen the sim rLilat(1ion pograml 5\Vas atscompleIte andI aPs coilCCi aIS 5\C couldImIake- it. thec fit bhtxx ce thec recoi ded

-) at 01 abhout 11)1. -1 he loiml-1

nnenIxIocalls thatIcl t1ts Ic af,I S

t cIsIIxc1istitico x.Bt a[ careu-l look0I\ it

the mati i\ otdiflicnce"s IsossedL thaItbeinc11.i,case inl " loserCl the eNpeCIedIaloeC 0ottabouIt 7 5 )) caLtmec pi- niai lx-1IIima-11tl t-itherI Lunit otlminlcrease inl dlittIteCe-IC Vx aLuIS root11 s,outh to nor1thl. II

C ISssIlleCd thtit the cosmic-rtiv m1ien-sitS1 saietilcfLs h ICOS 0. xv here Oi Isl90) decree-Cs Inl ti Vcitictillxv ot lentedl eas,t

est plane11. tindl O) degree f'or rtivs ap1-protarhing horizontalyIN riomi the nionI-i.the <\ drIoppedI to 90-5 xwhen di htid theN atloe of' 0. 15 (Fig. 101. Suich a \al Lic01' d1 would corres,pondl to ti smioothix rantiton in cosmic-ray inteolsity, fromn3(1 degrees niorth to 30) dlegrees sooth1.ot -_7 percenit. We do niot believe. ot'couirse, that the cosmic.--rtav inltensitschang1(es in suich ti maniner. but it is,qulite reasontible to a SII-,LiII thait oLi r'spark chamber sy sterns had SLuch asma ll a~nd systema-tic chlange in scnsit ix-

Ouri confidenice inl suich tim explmiiition1 " as inlcreased xx heni xx e fotindc th.itthec reqitit -ed x tiltie ot' the conistant I\5tis dAiftYcent sxhen xwe atdvzedl thecdffata In t\\0sctr.t Samples. one Olca1sLi edC bxe-ach parof 3- bx 6-too t111.9- bx 1 .8 meter) spark cha-mbi-ers,WAc knoss tha-lt thc spairk cha-mber-, \%i-cnot un11it orml1v sflsit IxeN oxVer theicIr \% holearctis. ticl 55 e d1cisea dec all diatatirourunlis inl xxilch thii- erexxcr ross chain cesill seC,1ivsitvitxI omi pioinit to point Ilin th:hinmbcr.s. 13tii %\e hI,-e n]o technirlueLIax aiable to comtpens.,ite totr Slow tiitioOsl, II ,lset'isiti\ it\xxth positiotll (lit

ouir IeC\t opert-iltOiols, the apitts\ lhe iirri a oced sO thati ItI rotates about,1

citid im s: the Iimetir vxatjiationinism~n-sitixvitx iIbtit we ht1ive juist postulated xWIllaxeracI-te outt inl the i Cirocr apt a O

Wec made sex era-l attemp-ts`-1 to simiiiil.ite the I -- d sInl ii bhaxor%1 ot litheitppatrint cosnlie-rtx itetisitx7 bx)% thecpi eseilce of- a chamb11er abovx e ad xcixerclose to1 the .ipprarttits. BuIt theC mcii e

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we tried, the more evident it becamethat the slow north-south variation wasan instrumental effect, unrelated to anycavities in the pyramid rock. The fitobtained by using this slow north-southvariation shows no statistically signifi-cant deviations from a solid pyramid.

Conclusions

To be sure that we could have de-tected a chamber of "average size"above the Belzoni Chamber, we pro-grammed the computer to believe thatits simulated pyramid had such a cham-ber filled with material whose densitywas twice that of limestone. The pro-gram then predicted that fewer muonsthan usual would come from the direc-tion of the "chamber," so that thedifference matrix showed positive num-bers, as expected for a hollow chamberin the real pyramid and a pyramid ofuniform density in the simulator. Figure11 shows what we would have seen hadthere been a King's Chamber 40 metersabove the Belzoni Chamber. (The scat-tering of muons in the rock is simu-lated by the computer.) If the King'sChamber were moved farther away,the angular width of the region havingan excess of counts would drop in-versely with distance. We have nodoubt that we could detect a King'sChamber anywhere above the BelzoniChamber within a cone of half-angle35 degrees from the vertical. If the Sec-ond Pyramid architects had placed aGrand Gallery, King's Chamber, andQueen's Chamber in the same locationas they did in Cheops's Pyramid, thesignals from each of these three cavitieswould have been enormous. We there-fore conclude that no chambers of thesize seen in the four large pyramids ofthe Fourth Dynasty are in our "fieldof view" above the Belzoni Chamber.We started by using two methods of

analysis, one photographic and theother analytic. By itself the photo-graphic method was unsatisfactory, be-cause effects due to the apparatus itselfwere so large that they obscured anyeffects from the pyramid. Although theanalytic method could succeed becauseit was able to take these instrumentaleffects into account, it was necessary to"invent" a north-south variation insensitivity to obtain success. By com-bining the two methods of analysis, itis possible to obtain the sensitivity of

the analytic method in a photographicsimulation. The combined method con-sists of plotting the ratio of the ob-served number of events to the pre-dicted number, using bins that areabout 0.15 by 0.15 degrees. Figure 13shows three such scatter plots for thedata in the cone of 35-degree half-angle centered on the vertical. Plot 13bcorrects for instrumental effects butdoes not take into account the fact thatthe instrument is covered by a pyramid.The corners of the pyramid are clearlyindicated in it. The next scatter plot(Fig. 13c) further corrects for the pres-ence of the pyramid with all its surfaceirregularities. Figure 13d shows whatwe would have seen if a "King's Cham-ber" had been in the pyramid, a cham-ber the same in size and location as thatused to obtain Fig. 11. It is evidentthat no effect in the data approachesthe magnitude of the effect producedby a King's Chamber.We have explored 19 percent of the

volume of the Second Pyramid. Wenow hope to rearrange the equipmentso that we can look through the remain-ing 81 percent of the volume of thepyramid. This operation will be greatlysimplified by our new understanding ofthe effects of muon scattering on angu-lar resolution. It is now apparent thatthe iron absorber was not necessary forthe success of the experiment, and wewill omit it in the rebuilt apparatus.Rotation of the detectors about thevertical will thus be facilitated, andthe possibility of "x-raying" some ofthe other large pyramids will be en-hanced.

Summary

Because there are two chambers inthe pyramid of Chephren's father(Cheops) and the same number in thepyramid of his grandfather (Sneferu),the absence of any known chambers inthe stonework of Chephren's SecondPyramid at Giza suggests that unknownchambers might exist in this apparentlysolid structure. Cosmic-ray detectorswith active areas of 4 square metersand high angular resolution have beeninstalled in the Belzoni Chamber of theSecond Pyramid; the chamber is justbelow the base of the pyramid, near itscenter. Cosmic-ray measurements ex-tending over several months of opera-tion clearly show the four diagonal

ridges of the pyramid and also outlinethe shape of the cap of original lime-stone facing blocks, which gives thepyramid its distinctive appearance. Wecan say with confidence that no cham-bers with volumes similar to the fourknown chambers in Cheops's andSneferu's pyramids exist in the mass oflimestone investigated by cosmic-rayabsorption. The volume of the pyramidprobed in this manner is defined by a

vertically oriented cone, of half-angle35 degrees, with its point resting in theBelzoni Chamber. The explored volumeis 19 percent of the pyramid's volume.We hope that with minor modificationsto the apparatus the complete mass oflimestone can be searched for cham-bers.

References and Notes

1. A. Fakhry, The Pyramids (Univ. of ChicagoPress, Chicago, 1961).

2. R. Howard-Vyse and J. S. Perring, OperationsCarried On at the Pyramids of Gizeh (London,1840-42), 3 vols.

3. L. W. Alvarez, Lawrence Radiation LaboratoryPhysics Note 544 (1 March 1965).

4. V. Perez-Mendez and J. M. Pfab, Ntcl. Instr.Methods 33, 141 (1965).

5. E. P. George, Commonw. Eng. (July 1955).6. The Joint U.A.R.-U.S.A. Pyramid Project has

been fortunate in the strong support it hasreceived from many individuals and organiza-tions on two continents. The initial and con-tinuing interest of Dr. Glenn T. Seaborg wasreflected in the financial support of the projectby the U.S. Atomic Energy Commission duringthe period when the detection equipment wasdesigned and built at the University of Cali-fornia's Lawrence Radiation Laboratory. TheU.A.R. Department of Antiquities extendedevery courtesy to members of the project, and,in addition to inviting us to install our equip-ment in the Second Pyramid, they put at ourdisposal an attractive and conveniently locatedbuilding which served as our laboratory andgeneral headquarters. The Smithsonian Insti-tution was generous in its support of theproject, particularly in making available travelfunds that permitted project members fromour two countries to work together both inBerkeley and in Cairo. The Ein Shams Uni-versity and the University of California bothsupported the project in many ways, and wegive special thanks to Vice Rector Salah Kotband Chancellor Roger Heyns. The IBM Cor-poration, the National Geographic Society, theHewlett-Packard Company, and Mr. WilliamT. Golden made important contributions to theproject for which we will always be grateful.The U.A.R. Surveying Department made ac-curate measurements of all external and in-ternal features of the Second Pyramid, withoutwhich we would have been severely handi-capped. The overall guidance of the projectwas vested by our two governments in a"Committee of the Pyramids," under thechairmanship of Dr. Salah Kotb. We are in-debted to the distinguished members of thiscommittee for the warmth and understandingthey displayed in the exercise of their respon-sibilities. All of us take pride in the fact thatthe friendly spirit in which we started theproject survived not only the perils that con-front any interdisciplinary or intergovernmentaleffort but also a break in diplomatic relationsbetween our two countries. In conclusion, weacknowledge important assistance from Ray-mond Edwards, Sharon Buckingham, FredKreiss, William E. Nolan, Kamal Arafa,Sayed Abdel Wahab, Mohamed Tolba, AlyHassan, August Manza, and Vice ChancellorLoy Sammet.

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