Search for Hidden Chambersin the Pyramids
The structure of the Second Pyramid of Giza
is 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 situated a few miles southwest of Cairo,
Egypt. The two largest pyramids standwithin a few hundred meters of eachother. They were originally of almost
exactly the same height (145 meters),
but the Great Pyramid of Cheops has
a slightly larger square base (230 meters
on a side) than the Second Pyramid of
Chephren (215.5 meters on a side). A
photograph 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 archeologists in terms of a "period of experimentation," ending with the construction of Cheops's pyramid (1). (Thecomplexity of the internal architectureof the pyramids increased during the
Fourth Dynasty until the time of
Cheops and then gave way to quite
simple designs after his time.)
An alternative explanation for thesudden decrease in internal complexity
from the Great Pyramid to the Second
Pyramid suggested itself to us: perhaps
Chephren's architects had been more
successful in hiding their upper chambers than were Cheops's. The interiorof the Great Pyramid was reached by
the tunneling laborers of Caliph MaThe authors are affiliated with the Joint Pyramid Project of the United Arab Republic and theUnited States of America. They reside either in
Cairo, United Arab Republic, or in Berkeley,
California. The article is adapted from an address presented by Luis W. Alvarez at the
Washington Meeting of the American PhysicalSociety, 30 April 1969.
832

mun in the 9th century A.D., almost
3400 y'ears after its construction. Of
our group only Ahmed Fakhry (authorof The Pyramids, professor emeritus ofarcheology, University of Cairo, andmember of the Supreme Council ofArcheology, Cairo) was trained in archeology. As laymen, we thought it notunlikely that unknown chambers might
still be present in the limestone abovethe "Belzoni Chamber," which is near
the center of the base of Chephren's
Second Pyramid, and that these chambers had survived undetected for 4500
years. [We learned later that such ideas
had occurred to early 19th-century investigators (2), who blasted holes in the
pyramids with gunpowder in attempts
to 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 archeologists
with a request for comments concerning its technical feasibility and archeological interest. The principal noveltyof the proposed cosmic-ray detectors
involved their ability to measure theangles of arrival of penetrating cosmicray muons with great precision, over alarge sensitive area. The properties ofthe penetrating cosmic rays have been
sufficiently well known for 30 years tosuggest their use in a pyramid-probing
experiment, but it was not until theinvention of spark chambers with digital read-out features (4) that such a
use could be considered as a real possibility. [Cosmic-ray detectors with low
angular resolution had been used in
1955 to give an independent measureof the thickness of rock overlying an
underground powerhouse in Australia's
Snowy Mountains Scheme (5)].
The favorable response to the proposal 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 June
1966. Cosmic-ray detectors were installed in the Belzoni Chamber of theSecond Pyramid at Giza in the springof 1967 by physicists from the Ein
Shams University and the Universityof California, in cooperation with archeologists from the U.A.R. Department of Antiquities. Initial operation
had been scheduled for the middle ofJune 1967, but for reasons beyond ourcontrol the schedule was delayed forseveral months. In early 1968 cosmicray data began to be recorded on magnetic tape in our laboratory building,a few hundred meters from the twolargest pyramids. Since that time wehave accumulated accurate angularmeasurements on more than a million
cosmic-ray muons that have penetrated
an average of about 100 meters oflimestone on their way to the detectors
in the Belzoni Chamber.
Proof of the Method
Before any new technique is usedin an exploratory mode, it is essentialthat the capabilities of the technique
be demonstrated on a known system.
We gave serious consideration to a
proposal that the cosmic-ray detectors
be tested first in the Queen's Chamberof the Great Pyramid, to demonstratethat the King's Chamber and the Grand
Gallery could be detected. But thissuggestion was abandoned because theKing's Chamber is so close to the
Queen's Chamber and because it subtends such a large solid angle that earlier (low resolution) cosmic-ray experiments had already shown that theupper chamber would give a large
signal. It was apparent that the only
untested feature of the new techniqueinvolved the magnitude of the scattering of high energy muons in solid matter. (An anomalously large scattering
would nullify the high angular resolution that had been built into the detectors, in the same way that frosted
glass destroys our ability to see distantobjects.) We had no reason to doubt
the calculated scattering, but we were
anxious to be able to demonstrate to
our colleagues in the U.A.R. DepartSCIENCE, VOL. 167

Fig. 1 (top right). The pyramids at Giza.
From left to right, the Third Pyramid ofMycerinus, the Second Pyramid of Chephren, the Great Pyramid of Cheops.
[L National Geographic Society]ment of Antiquities in a convincing
manner that the techniquLe really worked
as we had calculated. For this pturpose
we required as our test objects notlarge features that were nearby but,instead, small featuLres separated fromthe detectors by the greatest possible
thickness of limestone. Fortunately,such features are available in the Second Pyramid; the four diagonal ridges
that mark the intersections of neighboring plane faces were farther from thedetectors than any other points on theindividual faces. (From now on, we
will refer to these ridges as the "corners.")
From the known geometry of theSecond Pyramid, the trajectories of
cosmic-ray muons that pass through a
point 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 arrive with 5 percent greater intensity
than the muons from the corner. SuLchan increase in intensity, corresponding
to suLch a decrease in path through thelimestone, is abouLt half of what would
be expected to result from the presenceof a chamber of "typical size" (5 meters high) in the pyramid. Since such achamber would necessarily be closer tothe detectors, it wotuld for these two
reasons be a muLch "easier object tosee" than the corner.
The detection equipment was therefore installed in the southeast cornerof the Belzoni Chamber, with the expectation that it would first show thecorners in a convincing manner, so thatthe presence or absence of unknown
chambers could later be demonstrated
to the satisfaction of all concerned. In
September 1968 the IBM-1130 compuLter at the Ein Shams University
Computing Center produced the data

(a)
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Fig. 2 (bottom right). Cross sections of (a)the Great Pyramid of Cheops and (b) the
Pyramid of Chephren, showing the known
chambers: (A) Smooth limestone cap. (B)the Belzoni Chamber, (C) Belzoni's entrance, (D) Howard-Vyse's entrance, (E)descending passageway, (F) ascending
passageway, (G) underground chamber,(fl) Grand Gallery, (1) King's Chamber,(J) QuLeen's Chamber, (K) center line ofthe pyramiid.
6 FEBRUARY 1970

833

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Azimuthal angle 4 (deg)Fig. 3 (left). The initial measurement (with zenith angle of counts from 20 to 40 degrees) of the variation of cosmic-ray intensity
Fig. 4 (light).
with azimuthal angle, as observed from the Belzoni Chamber underneath the Second Pyramid of Chephren.
Detection of the northeast and southwest corners of the pyramid obtained by plotting the second differences of the counting
rate on the planes tangent to the corners as a function of distance from the corners.
90

for Fig. 3, which shows the variationof cosmic-ray intensity with azimuthal
angle (compass direction). The expected
rapid changes in cosmic-ray intensity
in 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 Laboratory's CDC-6600 computer and isshown in Fig. 4. Here the "second differences" of the counting rate with
distance from each corner are plottedon planes that are located symmetrically with respect to adjacent faces andthat are tangent to the corner. Mathematically, we would expect to see a
sharp spike at the corner of a sharply
defined pyramid in the plot of thesecond derivative of counting rate withrespect to distance. The second derivative becomes a second difference curvewhen we use bins of a finite size. The
sharpness of the peaks in the second
difference curves shows that the effectof the scattering of muons in limestone
is somewhat smaller than the conservative estimate made in the original proposal.
We were at first surprised by thelarge variations in maximum counting
rate through the four faces of the
pyramid. We knew that the Belzoni
Chamber was not at the exact center ofthe base of the pyramid, but we had
not appreciated what large changes incounting rate would be occasioned by
the actual displacement of the detector
from the center of the base; the equipment is 15.5 meters east and 4 meters
north of the center. There are two independent ways to use cosmic-ray data

to determine the location of the detector with respect to the exterior featuresof the pyramid.
1) The difference in the maximum
counting rate through the east and west
faces gives the displacement of thedetector toward the east, and similar
measurements in the north-south directions give the displacement to thenorth.
2) The azimuthal angles of the dips
corresponding to the corners give asecond, quite independent, and moresensitive measure of the displacements.
We can report that from cosmic-ray
observations alone, "looking through"100 meters of limestone, we can locate
the position of our detectors to within
1 meter. To the best of our knowledge,
no such measurement has ever been
made before. Our cosmic-ray-derived
position agrees to within less than 1
meter in the north-south direction witha recently surveyed position obtainedby the U.A.R. Surveying Department,
but it differs by 2 meters (that is, it
indicates 13.5 rather than 15.6 meters)in the east-west direction.
Simulated X-ray Photographs
We have presented the cosmic-ray
data in two different ways, one photographic and the other numerical. Boththese methods involve the projectionof each recorded muon back along its
trajectory to its intersection with either
a horizontal plane or a sphere thattouches the peak of the pyramid. Figure
5a is a diagram representing the Second Pyramid with the horizontal "filmplane" touching the peak of the pyramid and with a dashed line (representing the path of a cosmic ray) passing
from the detector through a hypothetical chamber to the image of the chamber on the "film plane." (The mappingof the pyramid structure by this technique is identical to what we would
obtain by x-raying a small model ofthe pyramid, with an x-ray source in
the Belzoni Chamber and with an x-ray
film touching the peak of the model
pyramid.) Figure Sb represents thespherical shell onto which cosmic rays
were projected for numerical analysis.
Figure 6 is a view of all the equipment, which occupied most of thesoutheastern part of the Belzoni Chamber. Figure 7 is a closer view of thedetector. The two spark chambers,
each 6 feet (1.8 meters) square, areseparated vertically by a distance of
1 foot (0.3 meter). Above and below
the spark chambers and just above thefloor level were scintillation counters,
which triggered the spark chambers
when all three counters signaled thepassage of a penetrating muon. The
4 feet (1.2 meters) of iron between
the bottom two scintillators was installed to minimize the effects of muonscattering in the limestone.
The simulated x-ray photograph ofthe pyramid shown in Fig. 13a is an
uncorrected (raw data) scatter plot of
700,000 recorded cosmic-ray muons as
they passed through the "film plane."
The four corners of the pyramid arevery clearly indicated. If a Grand Gallery and a King's Chamber were locatedin the Second Pyramid as they are in
the Great Pyramid, the Grand Gallery
SCIENCE, VOL. 167834dtensity in the direction of a new chamber is simply that the integral range
spectrum of the muons is represented
by a power law with an exponent equal
to -2. Therefore, if the rock thickness
is changed by an amount AX, out ofan original thickness X, the relativechange in intensity is Al/I = -2AX/X.
four known chambers in the two
The
a
\VU
f
>
large pyramids have an average heightb
Fig. 5. (a) Geometry of theof about 5 meters. Therefore AX/X
Second Pyramid, showing theshould be -5 percent, and the correprojection technique used tosponding
value of AI/I should be +10
produLce 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 were percent.)
projected for the ntumerical analysis of the data.
Since the counting equipment wassensitive out to approximately +45 degrees from the vertical, our data werewould have shown up clearly but the ways of the pyramid, each square plotted in a matrix with 900 entries,
King's Chamber would probably have chamber comprised two chambers 3 30 X 30 bins, each 3 by 3 degrees.
requLired some computer assistance to by 6 feet (0.9 by 1.8 meters) in area. Figure 5b illustrates this system of
be made visible. There is one unex- Also, each of the large scintillation binning on a sphere that encircles
pected feature in Fig. 13a: on the north counters was divided into sections. The the pyramid. We wrote a computer
face, there appears to be a narrow inactive areas between the two pairs of program to simulate the counting rate
north-south-oriented region that has spark chambers and between the sec- expected in each of these bins. As thea lower cosmic-ray intensity than is tions of the counters led in a predict- simulation program became more sofound in surrounding areas. We were able way to the unexpected signal phisticated with time, it took into account the most detailed features of theat first hopeful that the north-south shown in Fig. 1 3a.
measured exterior surface of the pyrastreak indicated the presence of amid, including the "cap" of original
Grand Gallery above and north of thelimestone casing blocks near the top,
Belzoni Chamber, just as the Grand Numerical Analysis
the surveyed position of the detectors
Gallery is above and north of the
We concluded from our study of the in the Belzoni Chamber, the positions
Queen's Chamber in the Great Pyramid. But we later found a satisfactory simulated x-ray picture that no unex- of the walls and ceiling of the Belzoni
explanation of this feature in the pic- pected features were discernible. But Chamber, and the sizes and positions
tuLre that did not involve any interior since we had been looking for an in- of each of the four spark chambers
structure in the pyramid. The region of crease in intensity of approximately 10 and the fourteen scintillation counters.
lower cosmic-ray intensity resulted percent over a region larger than thatAn important control on the quality
from the construction of the spark to which the eye responds easily, we of the experimental data being comchambers. Since we could not transport then turned to a more detailed numeri- pared with the simulated data camesquare chambers 6 feet (1.8 meters) cal analysis of the data. (The reason for from scatter plots showing the exact
on a side through the small passage- expecting a 10 percent increase in in- x 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

found to be correlated with contaminated neon in the spark chambers; thelog books show that whenever thechambers were flushed with fresh neon
they recovered their substantially uniform sensitivity. By examining the scat-muon as it passed through each of thefive planes containing scintillators or

spark chambers. Unsatisfactory operation of the spark chambers showed up
as small blank areas in the scatter plotsof muons passing through the chambers. Such unsatisfactory operation wasterplots on a day-by-day basis, we

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03. 0 03 0 0 2
23. -2 0 -3. -1
1 0 3. -3. 3. -3

0 2 3
0 -2 -3. 0 2 0 1 1 0 -2 0
0 -3. -3. 0 0 0
3. -3. -3. 0 2-3. -3.2
2 0 0 0
-3.0 2
0 -1 -2 0 0 -2 0 0 0 3.0 -3.
03. 3. 0 -1 -3
0
3. -3. -3. 3. -20 0 -2 0 -3. 0
3.
-2 -3. 3. 0 -2 3
0 -1 1
2 -3. -3. -1 -1 -2 -3. -3. 0 0 3 0
0 -3. -3. 0 0 -2 0 -2 -2 3.3. 2 0 -1 -1 1 0 03. 3.3. 0 0 C
E
0 -1I30 -3. 0 3 13 1 0 3.03. 0 -3. -3. 0 -2 3. 3.3. 0 2 03.3. 2 -10 00
v-1I-1 1 1 01-.130 2 I I IV -0v "A" -1 A,. c,-I1.-1L--3-. -2 0 0 00 -22 -3. mC
7h%
pulw
o
-T-3 -1-3. --,
I.-3.1I-1-3 0 0 2 3. -3 0 -3. 0 -2 0 3. -3. 0 0 -.-2 3. -3. -3 -2 01 0 0 -3. 0 0 0 C
0 0 2 3. 3 1 0 3. -1 -1 -3. 0 0 1 3 3.3 0 -313 0 0 3.
0O -1 -3
-3. 2 0 3. -3. -1 0 -3. 0 0 -1 0 0 -3. -1 0 3 1 0 0 0 -2 0 -2 -3. -3.
2 3. -1
2 0 3. 2 2 0 0 1 0 1 0 0 -1 3. 0 -3.122 0 0 0 0 0 0 -3.I3
2 3. -32 -1
3.2 03 0 2 022 0 0 0 030 0-31 1 -1 -1 -1 -3.
3. 0 3. -1
0.-3. -1 -2 -1 -3. -2.
0 0 3. 2 3. 0 0 3. 0 3. 3. -3. -3 -2 -3.
3 03.31-2 3 3. 2 3. 3. 0 2 -1 0 0 0 3. 0 3. -.1-1 0 0 -2 -2 -3.
0.-3.0 0 3. o -i
3. 0 2 0 3. -2 3. 0 3. 3 'I 0 0 0 3. Q 0 0-3. 2. 0-3. -3.
0 2 0 .3
1 0 -3. 0 3 0 2 0 0 -1 A1 0 0 3. 0 0 2 002 3.0 -3.
3.
-3.2
0CC
0
0
0
-1
3
0
-3.0
2 2 3. 2 -2 -1 0 -3. 0 3. -2 0 3. 0 3.
-3. .3. -2
0 -2
2 0'-2 0
0 -3. 3. 0 .9L 0
I~33. 3 -2 -31 -3 -3-3. -2 23. -3.
-3. 2 -1 -2 -2 -3 -1 3. 0 3. 0 -3.1 23.1 .0 0 -3.
-3. 0 -3. 0 3. 0 3. 0
1 -2 -3. 0 -2 -2 -2 0 0
2
-3.
-2
0
-3.
I

0

0 -3.
0 0 0 -2 0 -3
3. -3. -3. 0 -2 -3.

0 -3. I3 0
3. 3
2 -1 I
13 -3.1I 0 -1 -3.
3. -1 I3.-3. I3 0
3 2 -1 0 0 -2
0
0

3.
0

-1

I

3.

i

450

o

2 02

900

S
836

3

-

-1

2

I

I

-1350

I 35

eliminated from the data base about
one-third of the measured muons.
The scatter plo-ts also served as acheck 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 measurements of the counter locations. Neither
the direct measurements of the counter
positions nor the inferred positions ofthese counters as obtained from thedata themselves were good enough topermit the program to make sufficiently
accurate calculations. In a typical 3by 3-degree bin there are 1600 events.
The statistical uncertainty in this numiber of events is 2.5 percent. It wasnecessary to make calculations to atleast such an accuracy to make fulluse of the data. We first varied the assumed positions of the scintillat-ors bysmall amounts in an effort to fit the
expected counts to the measured counts.
This approach was unsatisfactory. Calculations 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 smaller than it actually was, and only th-recorded muons that passed throughthese defined counter positions were
accepted. This method eli-minated the
problems associated with small displacements of the counters during the experiment, with small-angle scattering ofmuons in the iron, and with decreased
sensitivity of the counters near theiredges. About 15 percent of the eventswere eliminated in this way. We believethat the 650,000 muons in the final
selected sample are free of importantbiases resulting from improper functioning of the equipment.
In the course of the computer analysis, about 40 fits were made to minimize the difference between the matrices of actual and simulated counts.
Although the matrices contain 30 x 30
bins each, some of the bins at the edges
contain so few counts (or none at all)that the effective number of bins is
close to 750. If we knew all the physi-

Fig. 10 (bottom left). The differences be-

tween the numbers of events measured

and predicted expressed in integral numbers of standard deviations for the best
fit to the data for which the XI was 905.
(The bins for which the predicted number of events was less than 30 were notused in calculating the XI.)SCIENCE, VOL. 167

cal parameters of our detection equipm-ient, if we were equally sure of thecquations describing the cosmic-ray
spectrum, and if we were, in addition,
sure that the pyramid was made of solid
limestone, then we would expect thex2 of the fit between the actual and thesimulated data to be about 750. The
carliest fits had X2'S of close to 3000,
but this important parameter dropped
to approximately 1400 by the time the

N

'A

0

2

2

-

u

1

u

L

I-

1

IL

-

1
0-1 0 1 1- -2
2 -3
1 0 1 01 2
1 1-1 2 00 -3
1 0 0 01
1 00 12
2-1 0 0 12 0
11-2 1-1 1 0 2 - -1 2
10-

210
- 0-1
o - 00-1 0
1- -1
1 - 1-1
i2 1

E

0900

2313-121011 1 0-3 10 00 0 110 00 00
01 10 3 1 0020 -2 -2-1 -1 10 -1 1

-10-.i21

stereophotographically determined contours of the pyramid exterior were madeavailable to us through the courtesy of
the 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 final
simulation runs, and Fig. 10 -is thedifference -between Figs. 8 and 9 expressed as the closest integral numberof standard deviations. [For a bin inwhich the number of counts was 2500,
an entry for +2 standard deviations
means that the actual count exceeded
the 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, one
chance in 200 of finding one bin with-+-5, and only one chance in 3 X 104
of finding one bin with ±t6, if the deviations are due only to statistical fluctuations. Thus no single bin has a significant effect unless its contents are atleast ±+4. Figure 10 contains no bins

0

-1 0 1-1 1 -2 2 2 0 -2 1 -1 -1 1 0 2
1 0 -1 1 2 -1 1 0 0 1 -2 0 -2 0 -1 1
1 0 0 0 1 1 1 0 1 -1 -1 0 1 0 0 -1 1
0 1 1 1 2 0 0 -2 -1 0 2 2 0 0 .2 -1 -1
0 0 0 2 3 1 0 0 -1 2 -1 2 1 -2 0 -1 -1
0 -2 -1 0 2 0 1 1 0 -2 0 1 0 1 -1 1 -1
1-1 -1 0 1 1 -1 -1 2 0 -1 -1 0 0 0 -1 0
0 0 0 1 0 -1 -1 -1 0 2 1 2 -1 0 0 -1 1
0-2 0 -1 0 1 1 0 1 2 0 0 1 1 0 -1 -1-1 -1 0 0 2 0 2 0 -1 1 1 -2 -1. 1 0 -2 1
0 1- 1-1
0-2 -2 1 0 2 0 -2 -1 1 0 0 1 1 0 0 0
1 g0
00 1 0-1 1
21 1102 0 112
0-0119~,10
21
0
0 1
0
1
2 -1 -0 -0-2
1
0 -2-1 -0
1 -1
0
1 1 2'
1 10
652 0102662-1 -1 1 -1 1 -1 -1-1 -1 0 0 0 2 -1 0
2 11
3010
1*1A1~.2~
0 0-1 -2 1 1-11-2

0

2
2

0

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

0

2

0

1-1 0
- 3 11 2 1
21 1 0 1 1
13 0 0 2 0 00
1 -1 02 2 203
3-1 1 11 - -21 - -2 - -1 1
12- 2-

1

450

45
0

0
2

0
1

1
1
1

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

-1
0
1

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

0

0
0

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

0

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

0 -2

0

1 1
0 -1

1
0

-1
0
0
1 0
0 0
1 0

0
1
-1

0

-1

0

-1: -1 -1
-1

0

-1

-2

0

0

-1- -1 -2
1 0

1 -1
1 2
2 1

2
1
0

1 1
-1 -1
1 -1

3

0

1

1

1

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

1350

90

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

simulation, the actual counts in this region were no longer systematically lower
than predicted by the computer, and,the value of x2 dropped accordingly.
Although the x2 of the fit between
the actual and simulated data was lowere-d when the features of the cap wereintroduced into the simulation, thisdrop does not constitute the strongest
proof that we were in fact detecting
the cap. Figure 12 compares the measured and cosmic-ray-determined variation in thickness of the limestone cap
in two 24-degree-wide strips that run
over 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 points
to lie along the zero lines of deviation.
The smooth curved lines are obtained
from the simulation program by utilizing the recently determined contoursof the pyramid. The generally good
agree-ment of the data points with theprediction (Fig. 12) shows clearly that
we 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 could
have seen any previously unknown
chamber that might exist in our "fieldof view."

showing ±+4.
T
to South~NorthI)etection of the Cap

2 ~t

2

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, but
the builders of Cairo, who "quarried"
the pyramids at that time, stopped before completely stripping the Second
0

T

o

I

-2

I

I

E

West to East

0

6 FEBRUARY 1970

periment. The quantity
plotted is the difference
between the measured
distance from the detector to the surface of the
pyramid and the distancecalculated under the assumption that the pyramid has no surface irregularities. The datatances indicated by thecosmic rays and are to

.3

'3)

0 0

Chephren's PyramidIof
is observed in this ex-

teds
onsrpeetteds
ponsrersn

Pyramid.

Before the simulation program in thecomputer took account of the presenceof the cap of limestone casing blocks
on. the pyramid, the difference plots(like the plot given in Fig. 11) always
contained a central region with a preponderance of negative entries. Whenthe cap was properly allowed for in theFig. 12. This graph showsthat the cap on the top

i

±

T2

-2

600

900

1200

be compared with thesolid line, which represents the same distancemeasured by the aerial
survey. These distances
have been averaged over

24-degree-wide bands centered on the middle of the pyramid, one running north-south,
the other east-west.
837

(ftthe ceniter of thc pvrI am id's baIse, theSe:arch for ('avitiesa)pparenlt chaIIImbe mlapped us1onto
Iil "Is pI 0oc Cerld ddiiiLInc-

A\s theIc

10 LIe s2Itdilx( to1 tbhri 2I11Isoxhpto led dx ltibhbeil- gceometIciria'1JIta'.
oi-k \x e con~
1It thec coin, e)ot thixIx,
sic crtax intelit Its\ In
Ii meII d tb1itI thei L:))ltlie momenlcltuLli rliii_ce ot eroeic0 (4( to7t ( IC\ 1" siIo ic id has aIn inltexitrd1.-11IoC posse Ix~iwnrld\ ot1 2. .1 r)

ilnrist ot th1I s t ImeIc xx Wxeie e'\cited bx
thei pi e-senlce of' t\\ o iposi tiI\ c rec-io,'(Itcmissit ilaIter- couxIIots )I
oIItent Iil iti"st i.ier thecot, thcse IcilitsppaIei-l\abidicpr esecei ol i' Ii I'
lx tinIerI theC ipx\ ot thl' px riilidtir .iboiit() meiters abox c thc B3elzonii (haiti
betl. BeCanse, rft theC displa"ICCletnet r)t theC
Belzit C iabe to the no01ti~thann cist

the sonthic1n part ot' the \s \s,ici 0 lacc
ot, the p\vrm iid I-lhe Ici atlI\ C nci C~cas
11pi etII LVnoJtjiIne ate 5\ as ab-out'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 habi7Ixxes
SLimCd tha~t theC anomals~tk came1 Ii om1 a(oni"lhe size ot, C~heopsx, k nc's (hani) It
3( meiters-,bei. it hadc to be abouh
ixwxax aind its la poItion turneCd Ont
to he almIos,t Ce\ar 'lx cenItra,l.
L ntoi tona11~tel\V. thIsP In cc LinId pICIsisentsiea.to-cetheir \\ itli at L1i-cci
ac.
Ialler-anIcIilar
SIIL
snL
'Iat
IcnaltI ox Cer
aCd' ",isappea ed
Is x\x Cle 1-inedIImic evict]I,IIl theC diMenions0, ot theC apartisad
olf the pxr amid that '\Cci e impoirtint InI
the s I nIaILt ion p rocr!lailntVC\chad niot
atcipatecd the nieed l'oi sutch aIccur-ate

daIta. I Thec n11t itftcts 55 c obsci x ed tirefa romimecinijone onlyv to sho\s thatIto
seeing, nothing'" thrloughIfont the tinalsIs lpci-tor. xx\e hadtc thiree xcix\ e.\citincs11iunals 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 ats
compleIte andI aPs coilCCi aIS 5\C couldI
mIake- it. thec fit bhtxx ce thec recoi ded
-)

at

01

11)1. -1 he loiml-1

abhoutnnenIxIocalls tha t Ic f,I t cIsIIxc
tIcl

S

t1

s

a

1istitico x.Bt a[ careu-l look
0I\ itthe mati i\ otdiflicnce"s sossed
thaIt
I
L
beinc
loserCl the eNpeCIedI
11.i,case inl
aloeC 0ottabouIt 7 5 )) caLtmec pi- niai lx-1I"

Iim
a-11tl t-itherI Lunit otlminlcrease inl dlit

tIteCe-IC Vx aLuIS root11 s,outh to nor1thl. II
ssIlleCd thtit the cosmic-rtiv m1ienC IS
sitS1 saie
tilcfLs 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 the
N atloe of' 0. 15 (Fig. 101. Suich a \al Lic
01' d1 would corres,pondl to ti smioothi
x rantiton in cosmic-ray inteolsity, f romn
3(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,
thait oLi r'
spark chamber sy sterns had SLuch a
sma ll a~nd sy stema-tic chlange in scnsit ix-

qulite reasontible to a SII-,LiII

N
a

wA

Ouri confidenice inl suich tim explmiii
tion1 " as inlcreased xx heni xx e fotindc th.it
thec reqitit -ed x tiltie ot' the conistant I\5tis dAiftYcent sxhen xwe atdvzedl thec

b

E

S
.i7.

2"'

-

. .$
xx..c xr$$4dffata In t\\0sctr.t Samples. one Olca1
sLi edC bxe-ach parof 3- bx 6-too t
111.9- bx 1 .8 meter) spark cha-mbi-ers,
WAc knoss tha-lt thc spairk cha-mber-, \%i-c
not un11it orml1v sflsit IxeN oxVer theicIr \% holesea dec all diatatirou
arctis. ticl 55 e d1ci
xxcr
ross chain ces
runlis inl xxilch thii- ereitxI omi pioinit to point Ilin th
ill seC,1ivsitv%\e hI,-e ]no technirlueL
Iax aiable to comtpens.,ite totr Slow tii:hinmbcr.s. 13tii
tioOsl,

S

't

,.'S

plo
S..x~

dxsi
ltixx inclie 01luce stajCes in eeiibnda.xxie
d ThanItII erIV.
'iiit ul- ld snix hot
1
ant1d It plot, xx iLI]smritC

I IiC dlian e
ct d rlt.u. Ibt I.t cot rectedi tot- thc ,ceonttic i .i Itie cptm''p4 ix 1x

IatsI\I,itoietd o simdsiieIoH
r:0H
IIIILIr xx ittiiiat lchmbaII.ipiao 1 I
Ilxl 'SateC,Celf.i
12.
Ii,lset'isiti\ it\xxth positiotll(lit

sitixvitx iIbtit we ht1ive juist postulated xWIll
cr apt a O
axeracI-te outt inl the i Ciro

d

C

II

ouir IeC\t opert-iltOiols, the apitts\ lhe iirri a oced sO thati ItI ro tates about,1
citid im s: the Iimetir vx atjiationinism~n-f thle'euel
i.lIaCeptiC.
1

Wec made sex era-l attemp-ts`-1 to simiiii
l.ite the I -- d sInl ii bhaxor%1 ot lithe

itppatrint cosnlie-rtx itetisitx7 bx)% thecpi eseilce of- a chamb11er abovx e ad xcixer
close to1 the .ipprarttits. BuIt theC mcii e
S II

t-1 'xii i

we tried, the more evident it becamethat the slow north-south variation was
an instrumental effect, unrelated to any
cavities in the pyramid rock. The fit
obtained by using this slow north-south
variation shows no statistically significant deviations from a solid pyramid.

Conclusions
To be sure that we could have detected a chamber of "average size"
above the Belzoni Chamber, we programmed the computer to believe thatits simulated pyramid had such a chamber filled with material whose density
was twice that of limestone. The program then predicted that fewer muonsthan usual would come from the direction of the "chamber," so that thedifference matrix showed positive numbers, as expected for a hollow chamberin the real pyramid and a pyramid of
uniform density in the simulator. Figure
11 shows what we would have seen had
there been a King's Chamber 40 meters
above the Belzoni Chamber. (The scattering of muons in the rock is simulated by the computer.) If the King's
Chamber were moved farther away,
the angular width of the region having
an excess of counts would drop inversely with distance. We have no
doubt that we could detect a King's
Chamber anywhere above the Belzoni
Chamber within a cone of half-angle
35 degrees from the vertical. If the Second Pyramid architects had placed aGrand Gallery, King's Chamber, andQueen's Chamber in the same location
as they did in Cheops's Pyramid, thesignals from each of these three cavities
would have been enormous. We therefore 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 ofanalysis, one photographic and theother analytic. By itself the photographic method was unsatisfactory, because effects due to the apparatus itself
were so large that they obscured any
effects from the pyramid. Although theanalytic method could succeed because
it was able to take these instrumental
effects into account, it was necessary to"invent" a north-south variation insensitivity to obtain success. By combining the two methods of analysis, it
is possible to obtain the sensitivity of

6 FEBRUARY 1970

the analytic method in a photographic
simulation. The combined method consists of plotting the ratio of the observed number of events to the predicted number, using bins that areabout 0.15 by 0.15 degrees. Figure 13
shows three such scatter plots for thedata in the cone of 35-degree halfangle centered on the vertical. Plot 13b
corrects for instrumental effects but
does not take into account the fact thatthe instrument is covered by a pyramid.
The corners of the pyramid are clearly
indicated in it. The next scatter plot
(Fig. 13c) further corrects for the presence of the pyramid with all its surface
irregularities. Figure 13d shows what
we would have seen if a "King's Chamber" had been in the pyramid, a chamber the same in size and location as thatused to obtain Fig. 11. It is evident
that no effect in the data approaches
the magnitude of the effect produced
by a King's Chamber.
We have explored 19 percent of thevolume of the Second Pyramid. We
now hope to rearrange the equipment
so that we can look through the remaining 81 percent of the volume of the
pyramid. This operation will be greatly
simplified by our new understanding of
the effects of muon scattering on angular 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 enhanced.

Summary
Because there are two chambers in
the pyramid of Chephren's father(Cheops) and the same number in the
pyramid of his grandfather (Sneferu),
the absence of any known chambers inthe stonework of Chephren's Second
Pyramid at Giza suggests that unknown
chambers might exist in this apparently
solid structure. Cosmic-ray detectors
with active areas of 4 square metersand high angular resolution have been
installed in the Belzoni Chamber of theSecond Pyramid; the chamber is justbelow the base of the pyramid, near its
center. Cosmic-ray measurements extending over several months of operation clearly show the four diagonalridges of the pyramid and also outline
the shape of the cap of original limestone facing blocks, which gives the
pyramid its distinctive appearance. We
can say with confidence that no chambers with volumes similar to the four
known chambers in Cheops's andSneferu's pyramids exist in the mass oflimestone investigated by cosmic-ray
absorption. The volume of the pyramidprobed in this manner is defined by avertically oriented cone, of half-angle
35 degrees, with its point resting in the
Belzoni Chamber. The explored volume
is 19 percent of the pyramid's volume.
We hope that with minor modifications
to the apparatus the complete mass oflimestone can be searched for chambers.

References and Notes
1. A. Fakhry, The Pyramids (Univ. of Chicago

Press, Chicago, 1961).

2. R. Howard-Vyse and J. S. Perring, Operations
Carried On at the Pyramids of Gizeh (London,
1840-42), 3 vols.
3. L. W. Alvarez, Lawrence Radiation Laboratory
Physics 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 organizations on two continents. The initial and continuing interest of Dr. Glenn T. Seaborg wasreflected in the financial support of the projectby the U.S. Atomic Energy Commission during
the period when the detection equipment was
designed and built at the University of California's Lawrence Radiation Laboratory. The
U.A.R. Department of Antiquities extended
every courtesy to members of the project, and,in addition to inviting us to install our equipment in the Second Pyramid, they put at our
disposal an attractive and conveniently locatedbuilding which served as our laboratory andgeneral headquarters. The Smithsonian Institution was generous in its support of the
project, particularly in making available travel
funds that permitted project members fromour two countries to work together both inBerkeley and in Cairo. The Ein Shams University and the University of California bothsupported the project in many ways, and wegive special thanks to Vice Rector Salah Kotb
and Chancellor Roger Heyns. The IBM Corporation, the National Geographic Society, theHewlett-Packard Company, and Mr. William
T. Golden made important contributions to theproject for which we will always be grateful.
The U.A.R. Surveying Department made accurate measurements of all external and internal features of the Second Pyramid, without
which we would have been severely handicapped. The overall guidance of the project
was vested by our two governments in a
"Committee of the Pyramids," under thechairmanship of Dr. Salah Kotb. We are indebted to the distinguished members of thiscommittee for the warmth and understanding
they displayed in the exercise of their responsibilities. All of us take pride in the fact thatthe friendly spirit in which we started the
project survived not only the perils that confront any interdisciplinary or intergovernmental
effort but also a break in diplomatic relations
between our two countries. In conclusion, we
acknowledge important assistance from Raymond Edwards, Sharon Buckingham, Fred
Kreiss, William E. Nolan, Kamal Arafa,
Sayed Abdel Wahab, Mohamed Tolba, Aly
Hassan, August Manza, and Vice Chancellor
Loy Sammet.

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