Search for Hidden Chambers in the Pyramids

Search for Hidden Chambers
in 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 stand
within a few hundred meters of each
other. 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 Giza
is shown as Fig. 1. Figure 2 shows the
elevation cross sections of the two
pyramids and indicates the contrast in
architectural design. The simplicity of
Chephren's pyramid, compared with
the elaborate structure of his father's
Great Pyramid, is explained by archeologists in terms of a "period of experimentation," ending with the construction of Cheops's pyramid (1). (The
complexity of the internal architecture
of 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 the
sudden 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 interior
of 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 the
United 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 Physical
Society, 30 April 1969.
832
mun in the 9th century A.D., almost
3400 y'ears after its construction. Of
our group only Ahmed Fakhry (author
of The Pyramids, professor emeritus of
archeology, University of Cairo, and
member of the Supreme Council of
Archeology, Cairo) was trained in archeology. As laymen, we thought it not
unlikely that unknown chambers might
still be present in the limestone above
the "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 the
Second Pyramid with cosmic rays (3)
was sent to a representative group of
cosmic-ray physicists and archeologists
with a request for comments concerning its technical feasibility and archeological interest. The principal novelty
of the proposed cosmic-ray detectors
involved their ability to measure the
angles of arrival of penetrating cosmicray muons with great precision, over a
large sensitive area. The properties of
the penetrating cosmic rays have been
sufficiently well known for 30 years to
suggest their use in a pyramid-probing
experiment, but it was not until the
invention 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 measure
of 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 the
United Arab Republic and the United
States 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 the
Second Pyramid at Giza in the spring
of 1967 by physicists from the Ein
Shams University and the University
of California, in cooperation with archeologists from the U.A.R. Department of Antiquities. Initial operation
had been scheduled for the middle of
June 1967, but for reasons beyond our
control the schedule was delayed for
several months. In early 1968 cosmicray data began to be recorded on magnetic tape in our laboratory building,
a few hundred meters from the two
largest pyramids. Since that time we
have accumulated accurate angular
measurements on more than a million
cosmic-ray muons that have penetrated
an average of about 100 meters of
limestone on their way to the detectors
in the Belzoni Chamber.
Proof of the Method
Before any new technique is used
in an exploratory mode, it is essential
that 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 Chamber
of the Great Pyramid, to demonstrate
that the King's Chamber and the Grand
Gallery could be detected. But this
suggestion was abandoned because the
King'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 the
upper chamber would give a large
signal. It was apparent that the only
untested feature of the new technique
involved 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 distant
objects.) 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 of
Mycerinus, 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 not
large features that were nearby but,
instead, small featuLres separated from
the 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 the
detectors than any other points on the
individual faces. (From now on, we
will refer to these ridges as the "corners.")
From the known geometry of the
Second Pyramid, the trajectories of
cosmic-ray muons that pass through a
point on a face 10 meters from a corner
and then down to the detectors can be
shown to traverse 2.3 fewer meters
of limestone than do muLons that strike
the corner. They shoulld therefore arrive with 5 percent greater intensity
than the muons from the corner. SuLch
an increase in intensity, corresponding
to suLch a decrease in path through the
limestone, is abouLt half of what would
be expected to result from the presence
of a chamber of "typical size" (5 meters high) in the pyramid. Since such a
chamber would necessarily be closer to
the detectors, it wotuld for these two
reasons be a muLch "easier object to
see" than the corner.
The detection equipment was therefore installed in the southeast corner
of the Belzoni Chamber, with the expectation that it would first show the
corners in a convincing manner, so that
the 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 of
the pyramiid.
6 FEBRUARY 1970
833
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Distance from the corner (m)
135
180 225 270
360
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 variation
of cosmic-ray intensity with azimuthal
angle (compass direction). The expected
rapid changes in cosmic-ray intensity
in the vicinity of the corners were
clearly shown, and the capability of the
method could no longer be doubted.
An analysis of more data was later
made on the Lawrence Radiation Laboratory's CDC-6600 computer and is
shown in Fig. 4. Here the "second differences" of the counting rate with
distance from each corner are plotted
on planes that are located symmetrically with respect to adjacent faces and
that 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 the
second derivative of counting rate with
respect to distance. The second derivative becomes a second difference curve
when we use bins of a finite size. The
sharpness of the peaks in the second
difference curves shows that the effect
of the scattering of muons in limestone
is somewhat smaller than the conservative estimate made in the original proposal.
We were at first surprised by the
large variations in maximum counting
rate through the four faces of the
pyramid. We knew that the Belzoni
Chamber was not at the exact center of
the base of the pyramid, but we had
not appreciated what large changes in
counting 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 features
of the pyramid.
1) The difference in the maximum
counting rate through the east and west
faces gives the displacement of the
detector toward the east, and similar
measurements in the north-south directions give the displacement to the
north.
2) The azimuthal angles of the dips
corresponding to the corners give a
second, quite independent, and more
sensitive 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 with
a recently surveyed position obtained
by 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. Both
these methods involve the projection
of each recorded muon back along its
trajectory to its intersection with either
a horizontal plane or a sphere that
touches the peak of the pyramid. Figure
5a is a diagram representing the Second Pyramid with the horizontal "film
plane" 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 mapping
of the pyramid structure by this technique is identical to what we would
obtain by x-raying a small model of
the 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 the
spherical shell onto which cosmic rays
were projected for numerical analysis.
Figure 6 is a view of all the equipment, which occupied most of the
southeastern part of the Belzoni Chamber. Figure 7 is a closer view of the
detector. The two spark chambers,
each 6 feet (1.8 meters) square, are
separated vertically by a distance of
1 foot (0.3 meter). Above and below
the spark chambers and just above the
floor level were scintillation counters,
which triggered the spark chambers
when all three counters signaled the
passage 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 of
the 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 are
very clearly indicated. If a Grand Gallery and a King's Chamber were located
in the Second Pyramid as they are in
the Great Pyramid, the Grand Gallery
SCIENCE, VOL. 167
834
d
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 of
an original thickness X, the relative
change in intensity is Al/I = -2AX/X.
four known chambers in the two
The
a
\VU
f
>
large pyramids have an average height
b
Fig. 5. (a) Geometry of the
of about 5 meters. Therefore AX/X
Second Pyramid, showing the
should be -5 percent, and the correprojection technique used to
sponding
value of AI/I should be +10
produLce a simulated x-ray photograph. The plane on the top of the pyramid can be
thought 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 was
sensitive out to approximately +45 degrees from the vertical, our data were
would 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 the
a 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 the
at first hopeful that the north-south shown in Fig. 1 3a.
measured exterior surface of the pyrastreak indicated the presence of a
mid, including the "cap" of original
Grand Gallery above and north of the
limestone 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 that
An 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 came
square 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; the
log books show that whenever the
chambers were flushed with fresh neon
they recovered their substantially uniform sensitivity. By examining the scat-
passed through each of the
five planes containing scintillators or
spark chambers. Unsatisfactory operation of the spark chambers showed up
as small blank areas in the scatter plots
of muons passing through the chambers. Such unsatisfactory operation was
muon as it
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19644372514121300310326518
822 466
,32 246622630201817735014767140401147
14161511
-
6
0
61 27
185 121 85 46 17
438 339 298 215 137
11 99 192 297 413 478 653 820 1017 1230 1423 1418 1586 1666 1673 1757 1672 1607 1445 1427 1230 1012 889 743 613 561 427
15 139 246 356 464 530 709 881 1173 1334 1501 1507 1689 1766 1793 1882 1798 1728 1577 1556 1371 1221 1081 911 750 700 563
25 168 307 439 537 595 761 92771139 1370 1544 1529 1735 1782 1811 1903 1833 1811 1652 1746 1609 1414 1259 1087 887 835 668
38 209 371 527 633 663 815 936 1140 1373 1553 1 534 1729 1763 1641 1933 1804 1819 1796 1965 1831 1633 1438 124 1027 974 772
51 269 638 615 723 760 917 1013 1132 1339 1533 1537 1727 1803 1786 1256 1812 1175 1968 2219 2045 1828 1624 1406 1164 1105 884
66 292 699 600 820 844 1019 1121 1722 1324 0459 1450 1646 1700 1791 1978 1828 2012 2120 2309 2255 2021 1770 1570 1278 1232 993
2227 2595
2470 2199
78 3284171
552 161 882 925 1116 1234 1329 16391494
2
1821 2056
2009 2168
2245 2297
1474 1395
1309 1572 1662 1653 1851
66 f
0
0
9
4141433
243
.1350
1350
S
Fig. 9. An array containing the pr-edicted nuimber of events in each 3- by 3-degree bin
for the best fit to the data.
N
t
-4
-0
0
-1
3.-2 -3.
-3. 0 -3. 0 13
0 -1 0 -1 0
1I.-.
-. 3
0
0
-3.
0
1
1
-1
I
-1-3
-3.
0
2
2
0
0
0
3.
0
0 3 13 1
1 0130
-.1
0 0 2 3.
2 3. 3 1
0 3. -3. -1
I
3.
2
2
0
2
1 -3.
3.
2
0 -3.
0 -3.
0
-3,0 1'
13
0
-3. -2
2 -3
13
0
"
"
2
V
v
I
I
I
-0
A
-1
-3 0 -3. 0 -2 0 3.
0 3. -1 -1 -3. 0 0
0 -3. 0 0 -1 0 0
0
1
0
1 -2 -3.
450
-3.
-3.
0 -1 -2 0 0 -2
3. -3. -3. 3. -20
2 -3. -3. -1 -1 -2
0 -3. -3. 0 0 -2
3.03. 0 -3. -3.
3.2 03 0 2 022
0 0 3. 2 3. 0 0 3. 0
-2 3 3. 2 3. 3. 0 2 -1
3. 0 2 0 3. -2 3. 0 3.
1 0 -3. 0 3 0 2 0 0
2 2 3. 2 -2 -1 0 -3.
I~3 3 -2 -31 -3 -3
3. -3. 2 -1 -2 -2
i
0
3.
1
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
2
-3.
-2
0
-3.
-1I-
0 -2 -3.
0
3.
0
0
-3 -1
3.
0
0
3.
0
2 3.
0 -2
3.2 -3.
03.
0
-3.122
.9L 0
0
0 0
2 02
0 -2 -2 -2
o
900
3
-
-1
2
v
--T-
.3.
3.-1 -3. 3.
-0 0 3. -2
0
-2
0
-1 0 2
0- -3.3 -3.
0
1
0
0 -1
-1 -1
1
1
0
03.3. 2
-3-. -2
-3 -1
-3 -2 01 0
0 0
0 -2
0
0 2
0 -2
0
3.
0 -2
0 0
-2.
-3.
0 -3.
3.
03. 0 0
3 0 0 2
23. -2 0 -3. -1
1 0 3. -3. 3. -3
0 -2 0
0 -3. -3. 0
2 0
2
-3.2
-3.0
-3.
-3.
-.1-1 0 0 -2 -2
Q 0 0-3. 2. 0-3.
0 2 002 3.0
0
3 0 -1 0
3. -3.0
0
2 0'-2 0
.0 0
1 23.1
-3. -3. 0 -3. 0 3. 0
-2 -3.
0 3.
0 3.
3. 0
3. 0
3.
0
0 -0
0 1 1 -1 -1 -1
-3 .-3. -1 -2 -1
S
836
3. -2
2 2
0 2 3
0 -2 -3. 0 2 0 1
3. -3. -3. 0 2
-3.
0 0 0 3.0 -3.
0 -2 0 -3. 0
-3. -3. 0 0 3 0 3.
0 -2 -2 3.3. 2 0
0 -2 3. 3.3. 0 2
,.
-I L-- --,
A
c, 1.
-1 -3. I.-3.1I
0 -.-2 3. -3.
-3. 0 3.3
0 -313
1 3
-3. -1 0 3 1 0 0
1 0 0 -1 3. 0
0 0 0 030
3. 3. -3. -3
0 0 0 3.
3 'I 0 0
-1 A1 0 0
0 3. -2 0
0 -3. 3. 0
0
-2
0
03.
-2 -3.
03.
0 0
-1
0
0
0
0
-3.
-3. -3.
-3.I3
0
0
0
0 -1 -3
0 -2 3
0 0 C
0
-2
0 2 -3. mC
7h%
o
0
0 0 0 C
0
0
3.
3.
3.
3.
E
-1I3
pulw
-T- v-
0O -13. -3
-1
2
2
3.
3.
0
Fig. 10 (bottom left). The differences be-
-32 -1
3. -1
tween the numbers of events measured
3 03.31
0.-3.0 0 3. o -i
-3.
0 2 0 .3
-3. 0 -3.2 3. 0CC
-3. .3. -2
-2
-3. -3. -2 23. -3.
3.
3.
eliminated from the data base about
one-third of the measured muons.
The scatter plo-ts also served as a
check on the resolution and accuracy
of the angle measurements. The edges
of the counters showed up on these
plots as sharp lines at positions that
agreed well with the direct measurements of the counter locations. Neither
the direct measurements of the counter
positions nor the inferred positions of
these counters as obtained from the
data themselves were good enough to
permit 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 was
necessary to make calculations to at
least such an accuracy to make full
use of the data. We first varied the assumed positions of the scintillat-ors by
small amounts in an effort to fit the
expected counts to the measured counts.
This approach was unsatisfactory. Calculations of the desired accuracy were
obtained only after we eliminated the
events that passed near the edge of at
least one of the counters. In effect, each
counter was defined to be slightly smaller than it actually was, and only th-recorded muons that passed through
these 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 of
muons in the iron, and with decreased
sensitivity of the counters near their
edges. About 15 percent of the events
were eliminated in this way. We believe
that the 650,000 muons in the final
selected sample are free of important
biases 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-
0
I
I
-1350
I 35
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 not
used in calculating the XI.)
SCIENCE, VOL. 167
cal parameters of our detection equipm-ient, if we were equally sure of the
cquations describing the cosmic-ray
spectrum, and if we were, in addition,
sure that the pyramid was made of solid
limestone, then we would expect the
x2 of the fit between the actual and the
simulated 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
0
'A
0
1
2
I-
1
u
L
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
1
-1
-1
-1
0
1
-1
1
0 E
1
0
090
0
2313-121011 1 0-3 10 00 0 110 00 0
0
01 10 3 1 0020 -2 -2-1 -1 10 -1 1
1
-10-.i21
stereophotographically determined contours of the pyramid exterior were made
available to us through the courtesy of
the U.A.R. Surveying Department.
Figure 8 is a -matrix showing the
total number of real counts recorded
in each of the 900 3- by 3-degree
bins. Figure 9 is one of the final
simulation runs, and Fig. 10 -is the
difference -between Figs. 8 and 9 expressed as the closest integral number
of standard deviations. [For a bin in
which 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 statistical
in nature, one expects about 87 percent
of the bins to have contents of - 1, 0,
or ± 1, about 12 percent of the bins to
have ±-2, and 1 percent of the bins to
have ±-3. There is one chance in three
of 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 at
least ±+4. Figure 10 contains no bins
-
u
2
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
0 1 1 1 2 0 0 -2 -1 0 2 2 0 0 .2 -1
0 0 0 2 3 1 0 0 -1 2 -1 2 1 -2 0 -1
0 -2 -1 0 2 0 1 1 0 -2 0 1 0 1 -1 1
1-1 -1 0 1 1 -1 -1 2 0 -1 -1 0 0 0 -1
0 0 0 1 0 -1 -1 -1 0 2 1 2 -1 0 0 -1
0-2 0 -1 0 1 1 0 1 2 0 0 1 1 0 -1
-1 -1 0 0 2 0 2 0 -1 1 1 -2 -1. 1 0 -2
0 1- 1-1
0-2 -2 1 0 2 0 -2 -1 1 0 0 1 1 0 0
1 g0
00 1 0-1
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 010266
2-1 -1 1 -1 1 -1 -1-1 -1 0 0 0 2 -1
2 11
3010
1*1A1~.2~
0 0-1 -2 1 1-11-2
-1 0 1-
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
3
0
1
1
-1 -1
1 -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 were
introduced into the simulation, this
drop 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 the
north-south and east-west directions.
In the absence of a cap both on the
real 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 contours
of the pyramid. The generally good
agree-ment of the data points with the
prediction (Fig. 12) shows clearly that
we have detected the presence of the
cap through more than 100 meters of
limestone.
The detection of the cap was much
more difficult than detection of the
corners; together, these two "proofs of
the -method" convinced us that we could
have seen any previously unknown
chamber that might exist in our "field
of view."
showing ±+4.
T
~North
I)etection of the Cap
2
The most distinctive feature of the
Second Pyramid is the cap of original
limestone casing blocks near the top.
All the casing was removed fro>m the
Great Pyramid in the Middle Ages, but
the builders of Cairo, who "quarried"
the pyramids at that time, stopped before completely stripping the Second
0
to South
2 ~t
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 distance
calculated under the assumption that the pyramid has no surface irregularities. The data
tances indicated by the
cosmic rays and are to
.3
'3)
0 0
Chephren's Pyramid
Iof
is observed in this ex-
teds
onsrpeetteds
ponsrersn
Pyramid.
Before the simulation program in the
computer took account of the presence
of 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. When
the cap was properly allowed for in the
Fig. 12. This graph shows
that the cap on the top
i
±
T2
-2
600
900
1200
be compared with the
solid line, which represents the same distance
measured 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
Se:arch for ('avities
pvrI am id's
thc
baIse, the
a)pparenlt chaIIImbe mlapped us1onto
Iil "Is pI 0oc Cerld ddiiiLInc-
A\s theIc
10 LIe
t
di
s2I lx( to1 tbhri 2I11Is
ox
h
pto 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:))l
tlie momenlcltuLli rliii_ce ot eroeic0 (4( to
7t ( 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,'
(Itc
ilaIter- couxIIots )I
st i.ier thec
IcilitsppaIei-l\
abidic
ol i' Ii I'
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
oIItent Iil
ot, thcse
pr esecei
lx tinIerI
missit
iti"
the sonthic1n part ot' the \s \s,ici 0 lacc
ot, the p\vrm iid I-lhe Ici atlI\ C nci C~cas
11pi et
II 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 the
ll(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
aC
d' ",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!lail
ntVC\chad niot
atcipatecd the nieed l'oi sutch aIccur-ate
daIta. I Thec n11t itftcts 55 c obsci x ed tire
fa romi
mecinijone onlyv to sho\s thatIto
seeing, nothing'" thrloughIfont the tinalsIs 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
bfoth the 'ip-
thle 'e,omelllt\
WAhen the sim rLilat(1
ion 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
abhout
nnenIxIocalls tha
tIcl
st
t1
Ic f,I t cIsIIxc
S
a
1istitico x.Bt a[ careu-l look
0I\ it
the 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 Isl
90) 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,
N
a
wA
that the
cosmic.--rtav inltensits
chang1(es in suich ti maniner. but it is,
qulite reasontible to a SII-,LiII thait oLi r'
spark chamber sy sterns had SLuch a
sma ll a~nd sy stema-tic chlange in scnsit ix-
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
dffata
S
In t\\0sctr.t
Samples. one Olca1
sLi edC bxe-ach parof 3- bx 6-too t
1 .8 meter) spark cha-mbi-ers,
WAc knoss tha-lt thc spairk cha-mber-, \%i-c
not un11it orml1v sflsit IxeN oxVer theicIr \% hole
sea dec all diatatirou
arctis. ticl 55 e d1ci
111.9- bx
.i7.
2"'
-
. .$
xx..c xr$$
4
S
't
plo
S..x~
dxsi
ltixx inclie 01luce stajCes in eeiibnda.xxie
d ThanItII erIV.
'iiit ul- ld snix hot
1
ant1d It plot, xx i
LI]smritC
oietd o simdsiieIoH
r
:0H
IIIILIr xx ittiiiat lchmbaII
.ipiao 1 I
Ilxl 'SateC
,Celf.i
12.
Ii
Iax aiable
to
tioOsl,
,lset'isiti\ it\xxth positiotll
II
(lit
sitixvitx iIbtit we ht1ive juist postulated xWIll
cr apt a O
axeracI-te outt inl the i Ciro
d
I IiC dli
ct d rlt.u. Ibt I.t cot rectedi tot- thc ,ceonttic
''p4 ix 1x
IatsI\I,
it
%\e hI,-e ]no technirlueL
comtpens.,ite totr Slow tii
:hinmbcr.s. 13tii
ouir IeC\t opert-iltOiols, the apitts\ l
he iirri a oced sO thati ItI ro tates about,1
citid im s: the Iimetir vx atjiationinism~n-
,.'S
C
xxcr
ross chain ces
runlis inl xxilch thii- ere
itxI omi pioinit to point Ilin th
ill seC,1ivsitv
i
.i Itie cptm
an e
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)% thec
pi 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 became
that 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 that
its simulated pyramid had such a chamber filled with material whose density
was twice that of limestone. The program then predicted that fewer muons
than usual would come from the direction of the "chamber," so that the
difference matrix showed positive numbers, as expected for a hollow chamber
in 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 a
Grand Gallery, King's Chamber, and
Queen's Chamber in the same location
as they did in Cheops's Pyramid, the
signals from each of these three cavities
would have been enormous. We therefore conclude that no chambers of the
size seen in the four large pyramids of
the Fourth Dynasty are in our "field
of view" above the Belzoni Chamber.
We started by using two methods of
analysis, one photographic and the
other 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 the
analytic method could succeed because
it was able to take these instrumental
effects into account, it was necessary to
"invent" a north-south variation in
sensitivity 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 are
about 0.15 by 0.15 degrees. Figure 13
shows three such scatter plots for the
data 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 that
the 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 that
used 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 the
volume 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 that
the iron absorber was not necessary for
the success of the experiment, and we
will omit it in the rebuilt apparatus.
Rotation of the detectors about the
vertical will thus be facilitated, and
the possibility of "x-raying" some of
the 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 in
the 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 meters
and high angular resolution have been
installed in the Belzoni Chamber of the
Second Pyramid; the chamber is just
below the base of the pyramid, near its
center. Cosmic-ray measurements extending over several months of operation clearly show the four diagonal
ridges 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 and
Sneferu's pyramids exist in the mass of
limestone investigated by cosmic-ray
absorption. The volume of the pyramid
probed in this manner is defined by a
vertically 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 of
limestone 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 has
received from many individuals and organizations on two continents. The initial and continuing interest of Dr. Glenn T. Seaborg was
reflected in the financial support of the project
by 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 located
building which served as our laboratory and
general headquarters. The Smithsonian Institution was generous in its support of the
project, particularly in making available travel
funds that permitted project members from
our two countries to work together both in
Berkeley and in Cairo. The Ein Shams University and the University of California both
supported the project in many ways, and we
give special thanks to Vice Rector Salah Kotb
and Chancellor Roger Heyns. The IBM Corporation, the National Geographic Society, the
Hewlett-Packard Company, and Mr. William
T. Golden made important contributions to the
project 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 the
chairmanship of Dr. Salah Kotb. We are indebted to the distinguished members of this
committee for the warmth and understanding
they displayed in the exercise of their responsibilities. All of us take pride in the fact that
the 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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