December 13, 1994

CLEAR EXPLANATION OF THE SCIENTIFIC EVIDENCE

by

Michael A. Stroscio

A man may die, nations may rise and fall, but an idea lives on.

TABLE OF CONTENTS


i. PREFACE

1. SO, WHAT IS THE SCIENTIFIC EVIDENCE?

2. ANALYSIS OF THE ZAPRUDER FILM: HIDDEN SCIENTIFIC EVIDENCE
AND VISUAL CLUES

3. THE SEARCH FOR ACOUSTIC EVIDENCE

4. EPILOGUE

5. SELECTED BIBLIOGRAPHY

6. APPENDICES

APPENDIX A. --- LAWS OF PHYSICS TELL US MUCH ABOUT THE
MOTION OF MR. ZAPRUDER'S CAMERA AND ABOUT THE
RECOIL OF PRESIDENT KENNEDY'S HEAD

APPENDIX B. --- THE SHOCK WAVES CAUSED BY SUPERSONIC BULLETS
FIRED IN DEALEY PLAZA MAY INDEED BE STRONG
ENOUGH TO PRODUCE SIGNIFICANT SUDDEN MOTIONS
OF A HAND-HELD CAMERA OPERATING FROM MR.
ZAPRUDER'S VANTAGE POINT ON NOVEMBER 22, 1963









=
PREFACE


Over the last two decades my work has necessitated frequent
flights into and out of National Airport in Washington, DC. Often
these airline flights are routed over the Potomac River near
Arlington National Cemetery. I confess with some shame that until
recently I did not take advantage of such flights to catch a
glimpse of the eternal flame at the grave site of John Fitzgerald
Kennedy. This has all changed and now I seize these opportunities
to look for the eternal flame at the grave site of this great man.
Why has my appreciation for this man been so heightened, who am I
and why am I writing this monograph?

When President Kennedy was assassinated I was a 14-year-old
high school student in Whiteville, North Carolina. I was too young
to comprehend to full magnitude of this tragic murder and I
certainly did not understand the far-reaching political
implications or the scientific evidence underlying the killing of
this great world leader. Thirty years later and after the now
well-known work District Attorney Jim Garrison, as documented with
some degree of accuracy by movie producer Oliver Stone, I have a
new awareness of the range of possible political implications of
this killing; in this regard, John H. Davis has recently offered
extremely insightful interpretations of many aspects of the murder
of President Kennedy. My understanding of the physical evidence
has been expanded enormously by the photographic interpretations
and evidence put forth by Robert Groden as well as by Dr. Charles
Crenshaw's and David Lifton's exposure of medical records which are
inconsistent with the interpretations of the Warren Commission. It
took me thirty years to understand how the world would be very
different if President Kennedy had lived and it took me thirty
years to realize that the Warren Commission was totally incapable
of grasping the key political and scientific facts underlying this
American tragedy.

Something else has changed. My own career, which began in
1974 when I left Yale University as a new Ph.D. in theoretical
physics, has taken me through many of the sub-fields of physics and
engineering bearing on the recorded scientific evidence in the
assassination. I have made many reliable and trusted acquaintances
with scientists and engineers at all levels throughout government,
industry and academia.

By early 1994, my curiosity concerning the assassination of
President Kennedy had been raised to the point that I found myself
asking if there was any scientific evidence or scientific analysis
that might shed further light on the assassination of JFK. At a
reception in Washington, DC during the spring of 1994, I had the
occasion to ask one of the most respected senior members of
America's science policy circle, Dr. Richard Garwin, if he had
participated in any formal scientific studies relating to the
assassination of President Kennedy. Garwin had indeed contributed
to such inquiries and in just a few minutes he was able to pinpoint
two of the cornerstones of the scientific evidence relating to the
murder of JFK. First, he told me of his contributions to the
National Academy of Sciences study of possible acoustic evidence.
In this case the eminent National Academy of Sciences panel
concluded that there was no known recording of the sounds in Dealey
Plaza, Dallas, Texas during the few seconds when shots were fired
at President Kennedy. This accurate finding should have been
something of an embarrassment to those associated with the U.S.
House of Representatives Committee on Assassinations which put
forth a number of major conclusions in 1979 on the basis of invalid
acoustic evidence. Second, Garwin recalled that the late Physics
Nobel Laureate, Luis Alvarez, had performed an ingenious analysis
of Abraham Zapruder's famous film of the assassination by studying
the jerking motions of the camera and how they are associated with
gunfire near Zapruder's camera. This second observation of Garwin
turned out to be critical. By simply applying the Alvarez analysis
to frames recorded before the first frame consider by the Warren
Commission, frame 171, I found that further scientific analysis
would indeed shed light on the assassination of President Kennedy.
The new scientific insights resulting from this extended analysis
support the now commonly-expressed view that President Kennedy's
murder was the result of a conspiracy and not the work of a lone
gunman.

This monograph focusses on the one aspect of the assassination
of President John F. Kennedy where I have the ability to contribute
to exposing the full truth of the assassination of JFK. By
extending the analysis of Luis Alvarez to frames before frame 171,
new evidence is presented to support the theory that more than one
gunman fired shots at President Kennedy and that some of the shots
were fired from the vicinity of the Grassy Knoll in Dealey Plaza.

In spite of the hundreds of books and numerous official
investigations on the assassination of President John Fitzgerald
Kennedy, there is still a strong division of public opinion on the
causes and motives behind the events that took place in Dealey
Plaza, Dallas, Texas on November 22, 1963. At the heart of the
lingering uncertainties is the question: Did Lee Harvey Oswald act
as a lone assassin or was there a conspiracy involving a group of
people intent on assassinating President Kennedy?

This book probes important scientific information that sheds
light on the assassination of President John F. Kennedy. These
pages contain a straightforward --- but highly revealing ---
analysis of the surviving scientific evidence and clues bearing on
the events occurring during the few seconds when shots rang out in
Dealey Plaza as President Kennedy's limousine made its way down Elm
Street. A particularly compelling conclusion emerges from this
analysis; indeed, by extending the little-known, but extremely
ingenious, examination of the assassination conducted by the late
Nobel Laureate Luis W. Alvarez it is found that new insights
support the theory that there were at least two gunmen firing shots
in Dealey Plaza as the presidential limousine traveled along Elm
Street. By giving simple and direct explanations to illuminate
previous scientific and technical writings, this book gives a clear
account of how the well-known U.S. House of Representatives Select
Committee on Assassinations reached erroneous conclusions in its
1979 report because its conclusions were based on incorrect
scientific data.

The scientific techniques and analyses covered in this book
are explained on terms understandable to a wide group of people not
trained in science. Through elementary treatments of the
scientific concepts underlying the physical laws that govern and
predict the ways that objects move and react to forces as well as
the ways sounds behave when they are produced by the firing of a
gun, this book makes accessible to the general public an analysis
of the key scientific evidence in the assassination of President
John F. Kennedy.

[Figures referenced are available from Dr. Michael A. Stroscio, 206
East Woodridge Drive, Durham, NC 27707.]


CHAPTER 1


SO, WHAT IS THE SCIENTIFIC EVIDENCE?


More than three decades after the tragic assassination of
United States President John Fitzgerald Kennedy hundreds of
millions of people question the official U.S. government
conclusions on the critical issue of whether there was a conspiracy
or the assassination was the work of a single gunman who for
whatever reason operated with amazing efficiency. My own interest
in the assassination of President Kennedy stemmed initially from
the doubts cast on the single-gunman theory of the assassination by
the many available commentaries on the medical and photographic
records as well as the eye-witness accounts relating to the
assassination. These accounts raised serious questions in my own
mind and --- being a physicist --- I became interested in surveying
the scientific evidence that could shed light on the correctness or
incorrectness of the other accounts. Such questions arise from
numerous analyses; indeed, in contradiction to the Warren
Commission findings of 1964, the 1979 U.S. House Report on
Assassinations found probable cause for a conspiracy. These 1979
findings of the U.S. House of Representatives investigation have
been questioned, in part, in the National Academy of Sciences 1982
Report of the Committee on Ballistics Acoustics chaired by
Professor Norman Ramsey, now a Nobel Laureate.

The apparent confusion reflected in official studies of the
assassination of President John F. Kennedy is echoed by the widely
varying public views and perceptions of the events occurring in
Dealey Plaza, Dallas, Texas on November 22, 1963. This confusion
is, in part, fueled by the fact that eye witnesses had different
impressions concerning the number and the directions of the bullets
fired in Dealey on that terrible day in American history. This
problem is compounded as time passes because three decades after
the fact anybody can assert almost anything concerning the
assassination without fear of being proven incorrect.

Fortunately, scientific evidence of any event can be analyzed
by anyone and assuming correct procedures are followed all analysts
will agree on the conclusions. It is, therefore, critical that the
scientific evidence be reviewed in light of other recent probing
analyses of the assassinations. As explained in this book, the
available scientific evidence includes information that can be
gleaned from the famous 8-millimeter movie of the assassination
filmed by Abraham Zapruder. New insights presented in this book
are based on an extension of previous examinations of the motion of
A. Zapruder's camera caused by Mr. Zapruder's reactions to the
sounds of gunshot as well as possibly by the sound and shock waves
associated with passing bullets. Many analysts of the
assassination of President Kennedy have focussed upon the
possibility that recorded acoustic sounds of bullets might be found
among the sounds recorded on November 22, 1963 by the Dallas Police
Department's communications system. The searches for and the
analyses of such acoustic evidence have apparently made a lasting
impression on the general public even though there is good reason
to conclude that there was no recording of any sounds in Dealey
Plaza on November 22, 1963 during the few seconds when gunshots
were being fired!

The scientific evidence is multifaceted but many would agree
that visual recordings of events and acoustic recordings of sounds
in Dealey Plaza on November 22, 1963 have enormous value in
answering the question: Was Lee Harvey Oswald the lone assassin of
President John F. Kennedy or was there a conspiracy involving more
than one gunman? Still other clues are provided by scientific
analyses of the subtle, but potentially revealing, effects of shock
or sound waves associated with bullets passing by hand-held cameras
in use during the time when shots were fired at the presidential
motorcade. Insights into the events occurring in the seconds when
shots rang out in Dealey Plaza are also found by the analysis of
how the operator of a hand-held camera would jerk the camera when
startled by the loud sound of gunfire. In principle, each of these
types of scientific information provides a lasting record that may
be subjected to objective and repeatable analyses of the
assassination of President Kennedy. Emphasized in this account is
the body of recorded scientific evidence concerning actual events
occurring in Dealey Plaza during the few seconds when shots were
fired. Evidence such as that from fingerprints or polygraphs is
not discussed in this book. Numerous forensic scientists are much
more capable of such analyses than I. Acoustical, optical and
electrical "recordings" are analyzed using new techniques which,
for the most part, are very much in the "bag of tricks" of
physicists. In this book each of these categories of information
is considered from a scientific point of view with the purposes of
obtaining new insights into the assassination and of clarifying
numerous misconceptions about what the laws of science tell us of
the events surrounding the assassination.

This book presents a clear explanation of available
scientific information on the assassination of President John F.
Kennedy in terms that make this information understandable to
people who have little or no formal training in science or
mathematics. This book extends Luis W. Alvarez's brilliant
analysis of the Zapruder film and new conclusions are reached
regarding the number and the directions of the bullets fired in
Dealey Plaza at about 12:30 pm on November 22, 1963. In particular
by using Alvarez's techniques to search for motions of Zapruder's
camera caused by bullets, new support is given to the theory that
at least two gunmen fired bullets and that some of the bullets
originated from the direction of the Grassy Knoll in Dealey Plaza.
As illustrated in Figure TEX, one of Alvarez's basic ideas is
simple --- just as the bow shock, also known as the sonic boom, of
a supersonic jet can cause the windows in a house to shake or even
break, it is theoretically possible for the bow shock or blast wave
of a supersonic bullet to cause a hand-held camera to jiggle about
a preferred pointing direction. As argued in Appendix B, such
jiggling may indeed be caused by a supersonic bullet but due to the
usually weak strength of the bow shock and due to a number of
uncertain events --- such as whether the camera merely rotated in
place or was moved (translated) in its entirety --- it is, in
general, difficult to know on a case-by-case basis if a particular
bow shock will move the camera in a way to cause significant
streaking of the film. Using Alvarez's techniques to determine the
directions and magnitudes of the camera's jiggling motions, new
insights concerning the number of bullets emerge immediately upon
a simple analysis of the motion of A. Zapruder's camera before
frame 171 of the Zapruder film which was the first frame considered
in the Warren Commission Report. As discussed in Appendix B, his
new evidence does not prove that a gunman fired from the Grassy
Knoll but it is consistent with such an interpretation since the
motion of A. Zapruder's camera between frames 152 and 170 is
entirely consistent with that expected for a camera "pushed" by the
"pressure wave" of a supersonic bullet fired at close range from
Zapruder's right-hand side where the Grassy Knoll was located.

There is clear scientific evidence that none of the known
acoustic records of the sounds in Dealey Plaza on November 22, 1963
was made during the critical seconds when shots were fired. This
matter has been the subject of great controversy and it played a
major role in the deliberations and findings of the U.S. House of
Representatives Select Committee on Assassinations which published
its report in 1979. The impression made on the public by the House
Select Committee Report appears to be hard to correct even though
clear scientific evidence refuting the Report has been cited
frequently and recently, as by Dr. Richard Garwin in a Letter to
the Editor of the March 28, 1992 New York Times, that the so-called
recorded sounds of gunshots were taped about one minute after the
assassination of President Kennedy.

The visual evidence in the assassination of President John F.
Kennedy is extensive and probing inquiries based on the recorded
visual evidence have been reported widely. A notable recent
publication on the available visual evidence is The Killing of a
President by Robert J. Groden. Moving picture records of the
assassination were made by Marie Muchmore, Orville Nix and Abraham
Zapruder. By far the most studied of these films is the Zapruder
film which provides a continuous record of the motion of President
Kennedy's limousine during most of the time that it was on Elm
Street. This is a critical period of time since researchers are in
general agreement that available evidence leads to the conclusion
that all the shots were fired when the President's limousine was on
Elm Street. By chance, Abraham Zapruder had an excellent vantage
point to make a clear moving picture record of the tragic events in
Dealey Plaza on November 22, 1963. The numerous still pictures of
scenes in Dealey Plaza before, during and after the assassination
also provide invaluable records; they provide exact information on
the relative positions of President Kennedy and Governor Connally
at critical moments and they give graphic evidence of strange
occurrences such as a man holding and moving an umbrella on a
clear, cool day as he stood near the edge of Elm Street within feet
President Kennedy as shots rang out in Dealey Plaza. As shall be
demonstrated in this book, such graphic information provides
extremely convincing evidence when interpreted in conjunction with
other lasting clues gathered on November 22, 1963.

Indeed, there is some evidence that shock waves or sound waves
associated with bullets as well as human reactions to the sounds of
gunfire can be discerned through analysis of the Zapruder film.
These scientific phenomena are exploited fully in the analyses of
this book. The findings from these suggestive analyses take on
added significance when we consider them in conjunction with
available visual evidence. Based on these analyses it is not
possible to provide a credible scenario that naturally supports the
findings of the Warren Commission.


Dealey Plaza


To understand the visual evidence it is essential to have a
clear picture of the layout of Dealey Plaza as well as an accurate
description of the route taken by the presidential motorcade.

Just as announced in The Dallas Morning News three days
before the assassination, the presidential motorcade proceeded from
.. "Love Field to Mockingbird Lane, alone Mockingbird Lane to
Lemmon, then Lemmon to Turtle Creek, Turtle Creek to Cedar Springs,
Cedar Springs to Harwood, Harwood to Main, Main to Houston, Houston
to Elm" [and was then to continue on] "Elm under the Triple
Underpass to Stemmons Expressway and on to the Trade Mart" ... [for
a] ... "nonpartisan luncheon". The intersections of Main and
Houston and of Houston and Elm are shown in this overhead view
(Figure AAA) of Dealey Plaza, Dallas, Texas as illustrated in the
1979 Report of the Select Committee on Assassinations, U.S. House
of Representatives, Investigation of the Assassination of President
John F. Kennedy, Ninety-Fifth Congress. In this overhead view of
Dealey Plaza the picket fence on the Grassy Knoll is shown on the
north side of Elm Street just to the north of the trees lining Elm
along the approach to the Triple Underpass. The Texas Schoolbook
Depository (TSBD) is shown on the northwest corner of Elm and
Houston. The Dal-Tex Building (D-TB) is shown on the northeast
corner of Elm and Houston. To the south of the D-TB are the Dallas
County Records Building (DCRB), the "new" Dallas County Criminal
Courts Building (DCCCB), and the "old" DCCCB; the so-called new
DCCCB was a part of the Dealey Plaza landscape in 1963 so it was
considered to be "new" in 1963. A three dimensional perspective of
Dealey Plaza, Dallas, Texas (Figure BBB) illustrates the path of
President Kennedy's automobile along Houston, onto Elm past the
Texas Schoolbook Depository, the much-discussed Texas live oak, and
to the position just in front of Abraham Zapruder where the
President was struck in the head by a bullet as recorded on frame
313 of the now-famous 8 millimeter motion picture film made by
Dallas businessman Abraham Zapruder. President Kennedy's location
on Elm Street is marked in this overhead (Figure CCC) at selected
positions corresponding to specific frames of the Zapruder film.
The locations of Abraham Zapruder, Phil Willis and Mary Moorman are
marked with the letters "Z", "W" and "M". It is widely accepted
that most, if not all, of the shots that rang out in Dealey Plaza
on November 22, 1963 were fired during the time interval
corresponding to approximately frames 150 and 335 of the Zapruder
film. At about frame 150 President Kennedy comes into view of an
observer looking straight along the top edge of the picket fence on
the Grassy Knoll. Between frames 198 and 224 President Kennedy is
located between the left and right extremes of the projection of a
road sign but the President is not hidden from Zapruder's view
during this entire period; the President appears to be just above
the sign until frame 207 when he disappears from view until frame
225 when his head, neck and hands are again visible just to the
right of the edge of the road sign as viewed by Mr. Zapruder. And
at frame 297 President Kennedy is on the imaginary line joining
Abraham Zapruder and Mary Moorman.

CHAPTER 2
ANALYSIS OF THE ZAPRUDER FILM:
HIDDEN SCIENTIFIC EVIDENCE AND VISUAL CLUES

The most interesting body of available scientific evidence on
the assassination of President John F. Kennedy was uncovered by the
amazingly insightful physicist, Luis W. Alvarez.* In his

---

*Several of the scientists highlighted in this account of the
available scientific information on the assassination of President
John F. Kennedy are among the most noted of the century. Dr. Luis
W. Alvarez is a case in point. Not only did Alvarez explain how
the jiggles of Abraham Zapruder's camera could be associated with
the bullets fired in Dealey Plaza, he amazed and delighted the
scientific community by giving a very credible explanation that a
meteorite caused the extinction of dinosaurs on Earth. As detailed
in Adventures in Experimental Physics Alvarez also spearheaded a
fascinating search for hidden chambers of the Egyptian pyramids
using cosmic rays! In Alvarez's own words, "I first saw the
pyramids in 1962 ... on the way to Geneva ... [and] it seemed far
more likely to me that Chephren's architect would put four chambers
in his pyramid, rather than no chambers [as architects had
assumed], as our best information now indicates." The information
Alvarez was referring to was acquired through his brilliant ideas
on the use of cosmic rays to "see" into the pyramids!
characteristic brilliance, Alvarez guessed that the streaks in some
frames of A. Zapruder's movie were a result of the fast shaking
motion of Zapruder's camera caused by two effects: on the one hand,
Alvarez realized that the shock wave or sound wave associated with
a bullet fired while A. Zapruder recorded his famous film could be
strong enough to cause detectable motions of the hand-held 8-
millimeter camera; on the other hand, Alvarez's experience in
analyzing laboratory photographs and his hobby of photography gave
him the insight to know that Abraham Zapruder's neuromuscular
reactions to stimuli such as the crack of a bullet or the sight of
President Kennedy reacting to bullet wounds could also cause the
camera to undergo a fast shaking motion. Even Alvarez did not come
to these realizations immediately. Indeed, in his 1976 article, A
Physicist Examines the Kennedy Assassination Film, Alvarez
describes his thoughts over the Thanksgiving weekend of 1966 as he
examined frames of the Zapruder film just published in the November
25, 1966 edition of Life magazine:
"My attention was drawn to the way the flag, at the left front
fender of the President's car, changed its shape from frame to
frame in the Life photographs. I remembered that [in 1945] at
Almagordo, [New Mexico], Enrico Fermi had almost instantly
measured the explosive yield of the first atomic bomb by
observing how far small pieces of paper which he 'dribbled'
from his hand, were suddenly moved away from 'ground zero' by
the shock wave. (He had a precomputed table of numbers in his
pocket, so he knew the explosive energy of the bomb long
before any of the official measurements had been analyzed.)
I thought I had detected the deformation of the Presidential
flag under the influence of the shock wave generated by a
nearby bullet. From an elementary calculation involving the
known properties of shock waves from bullets, and an
assumption as to the surface density of the flag, it seemed to
me reasonable to believe that the motions I detected were
indeed due to the action of shockwaves. If such a conclusion
could be confirmed, the vexing questions concerning the timing
of the shots might be solved. (My knowledge of the strength
of shock waves from bullets came from an experience I had in
World War II, with W. K. H. Panofsky, who had built and was
testing a "firing error indicator." This device was towed
behind a plane, in a "sleeve," at which gunners fired for
practice. It contained two microphones that recorded the
shock waves from passing bullets.)'
'The frames reproduced in Life showed a total of only 1.3 sec
of the critical moments in Dallas, so I had to wait until the
following Monday to examine the sequence of 160 frames in the
Law School Library's copy of the Warren Commission 'exhibits.'
When I saw the full set of frames* it was clear to me that

---

*Here Alvarez is referring to the "full set of frames" that
appeared in the Warren Commission Report. As described in detail
in this book, the Warren Commission did not publish any number of
extremely enlightening frames before frame 171.

---

flag was simply flapping in the breeze. But the thought that
effects of the individual bullets might show in the film was
still very much in my mind. As I scanned the selected color
photographs in Life and the full set of black and white copies
in the exhibits, I noticed a striking phenomenon in frame 227
... [of the Zapruder film]. All of the innumerable point-like
highlights on the irregular shiny surface of the automobile
were stretched out into parallel line segments, along the 8
o'clock-2 o'clock direction. In the plane of the automobile,
the parallel streaks appeared to be 10 in. long."

The shock and blast waves referred to by Fermi and Alvarez
have very different origins --- Fermi's is a hemispherical blast
wave that emanates from "ground zero" of an atomic bomb and
Alvarez's is a conical shock wave that is formed near a supersonic
bullet and trails the bullet in an ever-expanding conical shape ---
but they share the common feature that there is a sudden change in
atmospheric pressure when the shock front, i.e. shock wave, passes
by an object or a person. Perhaps, the most familiar evidence of
a shock front is the sonic boom that trails a jet in supersonic
flight. As for the case of a bullet traveling faster than the
speed of sound, the supersonic jet produces a shock front because
the sound waves emanating from the jet cannot disperse fast enough
to prevent a localized "piling up" of the sound waves. Indeed,
since the sound waves cannot travel faster than the speed of sound,
which is about 1,100 feet per second in air at room temperature,
they cannot "keep pace" with an object moving at supersonic speeds
such as a bullet moving at, say, 2000 feet per second. In such a
case the spherical wavefronts of the sound waves formed at each
point along the trajectory of the bullet have an envelope which is
shaped like a cone as shown in Figure GGG'. This conical envelope
forms the shock front sometimes referred to as the bow shock. This
bow shock is somewhat like the V-shaped bow wave that is formed
behind a boat moving faster than the speed of the water waves
emanating from the bow of the boat and trailing behind the boat as
it moves forward. In the case of a gun firing a bullet traveling
faster than the speed of sound there are at least two distinct
sound "disturbances" or pressure pulses: the supersonic bow shock
is accompanied by a so-called muzzle blast which is a spherically-
expanding sound wave that emanates from the tip of the gun barrel.

The 1979 Report of the Select Committee on Assassinations,
U.S. House of Representatives, Investigation of the Assassination
of President John F. Kennedy, heard testimony from a number of
expert witnesses who analyzed the effects that would be caused by
bow shocks and muzzle blasts emanating form various locations in
Dealey Plaza. Two of the illustrations presented by these
witnesses are useful in understanding how bow shocks and muzzle
blasts passing by Abraham Zapruder would cause his hand-held 8-
millimeter camera to "shake". In particular, Figure GGG shows the
bow shock and the muzzle blast patterns produced by a bullet at two
different positions along its trajectory. The cone-shaped bow
shock moves forward at the speed of the bullet which is roughly
twice the speed of sound. The muzzle blast expands in a spherical
pattern at the speed of sound. In addition, Figure HHH shows how
the pressures evolve with time for a bow shock wave and a muzzle
blast at distances of 10 feet from the path of the bullet and 30
feet from the tip of the rifle, respectively. These pressure
profiles are given for two different rifles: the Mannlicher-Carcano
rifle which was found on the sixth floor of the Texas Schoolbook
Depository Building on November 22, 1963 and the M-1 rifle. The
pressure pulses, i.e. pressure fluctuations, shown in Figure HHH
last a few milliseconds ("a few thousandths of a second", which we
abbreviate as "a few ms") and they are manifested by fluctuations
in the atmospheric pressure that last the same amount of time.

Based on Figure HHH from the 1979 Report of the Select
Committee on Assassinations, U.S. House of Representatives,
Investigation of the Assassination of President John F. Kennedy
as well as on the known geometrical scaling factors for the
strengths of the bow shock and the muzzle blast, it is possible to
construct Figure III which provides a convenient graphical
representation of the pressure of the bow shock wave and the muzzle
blast for a Mannlicher-Carcano rifle. (The magnitudes of the
pressures given in Figure HHH, and used to construct Figure III,
are relative to 20 millionths (20/1,000,000 --- that is, twenty
parts in a million) of a Newton per square meter; one atmosphere of
pressure is equal to about one-hundred thousand (100,000) Newtons
per square meter.) Appendix A explains the physical units used in
our discussions of pressure. Appendix B provides additional
information underlying the analysis leading to Figure III. In this
Chapter we will just take on faith that the information in Figure
HHH is accurate; this information is justified and explained in
detail in Appendix B. The distance in feet has two meanings: for
the bow shock wave this distance is the distance from the path of
the bullet and for the muzzle blast this distance is the distance
from the tip of the rifle. A typical value for the pressure in
Figure III is about one-half of a milli-atmosphere, that is, one-
half of a thousandth of an atmosphere. To appreciate the
significance of such a pressure level it is necessary to consider
that a camera with cross-sectional dimension of 4 inches by 8
inches alone its side experiences a pressure of about 500 pounds;
that is, 4 inches multiplied by 8 inches multiplied by 15 pounds
per square inch. One one-thousandth of this 500 pounds is one-half
pound so a shock having a pressure jump of one-half of a milli-
atmosphere produced a force of about one quarter pound on the side
of the camera. Thus, during the few milliseconds of interaction
between the camera and a shock, the camera is subjected to a
impulsive force of about one-quarter of a pound.

Suppose a bullet is fired such that the pressure front
associated with the bullet's bow shock is incident on the left-hand
side of a hand-held camera as shown in Figure JJJ. In this case,
if the shock is strong enough the increased pressure at the shock
front will initially push the camera to the right. To make our
observations more relevant to understanding the events occurring in
Dealey Plaza on November 22, 1963 consider the different effects of
bullets fired from Abraham Zapruder's left-hand and right-hand
sides: from Figure KKK it is clear that Abraham Zapruder's camera
would be pushed to the right by bullets emanating from the general
vicinity of the Texas Schoolbook Depository Building or the Dal-Tex
Building; Figure LLL makes it clear that the effect of bullets
fired from the Grassy Knoll is to push the camera to the left.

In Appendix B it is demonstrated that pressure increases of
about a milli-atmosphere could reasonable cause one end of the
camera to move to with a velocity of roughly a millimeter per
second, abbreviated as a mm/sec. A millimeter is about the
thickness of a dime so such a velocity may not, at first thought,
seem significant until one considers the effect of such a velocity
on the scene being recorded at a relatively large distance from the
camera. For example, if one end of a 20-centimeter-long camera is
suddenly (meaning in a few milliseconds) set into motion at a
velocity of 5 mm/sec, a scene 20 meters from the camera will appear
to move 500 mm/sec (0.5 meter per second)! This is indeed a
dramatic addition to the camera's normal panning motion when one
considers that the apparent change in speed of 0.5 meter per second
occurs in a few milliseconds! Since the exposure time for each
frame of the Zapruder movie was about one-thirtieth of a second,
all of the change normally occurs during one frame of the Zapruder
film!

The significance of the streaking of frame 227 and of many
other frames of the Zapruder film is now easy to appreciate since
it is clear that the scene recorded on each frame of the moving
picture is not an instantaneous snapshot, but rather a time
exposure that lasts for about one-thirtieth of a second. The one-
thirtieth-of-a-second exposure time comes about as follows: it is
now generally accepted that the Zapruder camera was operating at a
speed of 18.3 frames per second which would permit a maximum
exposure time of (1/18.3 second) = 0.055 second for each frame;
however, the actual exposure time is only a fraction of this 0.055-
second time interval and is, in fact, only one-thirtieth of a
second which is about 0.033 of a second. For a particular frame to
be completely clear with no streaks, it is necessary that the
camera's axis move so that the camera points to the same place on
the automobile during the one-thirtieth of a second while the scene
is being recorded on the frame. On the other hand, if streaks are
present, the camera's axis must point to different places on the
automobile during the exposure time that lasted about one-
thirtieth of a second for Mr. Zapruder's camera. As Luis Alvarez
states in his 1976 article, A Physicist Examines the Kennedy
Assassination Film, "If most of the frames [of the Zapruder film]
had shown streaking, one would simply have concluded that Mr.
Zapruder was a 'sloppy tracker' who couldn't follow the motion of
the President's car as it moved past him, as he 'panned' his camera
to keep the President in his field of view." Alvarez further
concludes that Zapruder was a good tracker since ..."the highlights
[on President Kennedy's automobile] showed as sharp points of light
in most of the frames."

A detailed prescription of the procedure used by Dr. Alvarez
to analyze the motion of the camera axis relative to President
Kennedy's position is contained in his letter of July 27, 1967 to
Mr. Raymond J. Marcus of 97 Beaumont Street, Newtonville,
Massachusetts. Alvarez explains that the magnitude of a streak
length for a specific frame is not important but that it is
necessary to ... "attribute importance to the algebraic difference
in the length of streaks from one picture to the next. Let me
explain this in a little more detail; I assigned a length to each
streak, and an algebraic sign --- I would call the length of a
certain streak +3 units or -1 unit, etc. depending upon which way
the camera was being displaced relative to the automobile, looking
down on the camera from above. (To find the sign, one has to look
at the frames on either side - to see the sign of the
displacement.) I called clockwise displacements, (looking down on
the camera) positive and counterclockwise displacements negative.
Such displacements are proportional to what we in physics would
call the angular velocity of the camera axis relative to the moving
car, and by themselves they say nothing about the shots. By
subtracting the length of the streaks, algebraically, including the
sign, one finds the angular accelerations of the camera line of
sight. The angular accelerations, are proportional to the torques
exerted by the cameraman's muscles on the camera, and these have
some significance, in relation to the firing of shots. On all of
my graphs, I plotted the difference in the streak lengths on two
successive pictures, and plotted it at the midpoint; for example,
if the streak length was +3 units on frame 10 and -1 unit on frame
11, I would plot a streak difference of +4 units (+3-(-1)=+4) at
the position 10 1/2. I did all of my analysis from such angular
acceleration curves, which I believe are the only ones of
significance." One of the larger streak lengths visible on frames
150 to 334 is that of frame 318 which is taken to have a magnitude
of 4 units.

A simple example of the procedure used by Alvarez is
represented by the scenario shown in Figure TCF where an automobile
is shown in three successive frames for a movie film. The first
frame contains the image of an automobile with clear features.
(The two square objects on the left side of the frame are sprocket
holes used to advance the film; these sprocket holes resemble those
in the full-sized frames of the Zapruder film.) The second frame
reveals that the direction of the camera axis has moved toward the
rear of the automobile. This situation is illustrated in Figure
PAM where the direction of the camera axis has moved from a point
on the front door of the automobile to a point on the back door.
Thus, the pointing angle of the camera axis sweeps through a range
of angles during the one-thirtieth of a second exposure time; in
the vernacular of the physicist, one would say: "The optical axis
of the camera has an angular velocity relative to the axis of the
original pointing position. The presence of doubled features, or
streaking, in the second frame indicates that the optical axis of
the camera has moved and that the camera is not tracking the motion
of the automobile nearly as well as during the first frame which is
relatively clear. In the third frame of Figure TCF, the automobile
has continued to move to the right in the frame of the camera; that
is, the axis of the camera is pointing farther to the rear of the
automobile. Following Alvarez's prescription, the streak lengths
for the first and third frames are zero since the images are clear.
Taking the magnitude of the streaking in the second frame to be two
units of length and noting that the axis of the camera is moving
counterclockwise relative to an axis that points to the same
location on the automobile, the streak length for the second frame
is -2. (For purposes of comparison the streak length of frame 318
is -4 units; frame 318 provides a convenient standard of reference
for streak lengths since it has the largest streak length among
those considered by Luis Alvarez.) The values for these streak
lengths are summarized in Table LLL along with the change in streak
length which is determined by subtracting streak lengths for
adjacent frames.




TABLE LLL
Frame Comments Streak Length Change in Length

First Frame Relatively clear 0 0
Second Frame Less space in front -2.0 (-2.0) - (0) = -2
of the automobile
Third Frame Relatively clear and 0 (0) - (-2.0) = +2
less space in front
of the automobile

The streak length for each frame provides a record of the angular
motion of the pointing direction of the camera axis during the
exposure time of the frame which lasts about one-thirtieth of a
second; in other words the streak length provides information about
the angular velocity of the camera axis relative to the pointing
direction the camera axis would have had if Zapruder had been
panning his camera precisely at the same point on the automobile
during the entire exposure time of the frame. The difference
between the angular velocities between two adjacent frames
represents the angular acceleration during the roughly one-
eighteenth-second time interval between the first frame and the
second frame. The concept of acceleration in this case is similar
to the acceleration of a automobile from one velocity to another in
a fixed time interval; the greater the change in automobile's
velocity during the fixed time interval, the greater the
acceleration of the automobile. (In the case of an automobile's
acceleration the change in the automobile's forward velocity during
the fixed time interval is referred to as the linear acceleration;
in our case, the quantities of interest are the analogous angular
velocities and angular accelerations.) Thus, the changes in the
lengths of the streaks between the adjacent frames of Mr.
Zapruder's film correspond to the angular accelerations of the
camera axis during that time interval. As Luis Alvarez explained
so clearly these angular accelerations are the quantities of
significance. This is so because the motion of the camera is
caused by forces such as those produced by a shock pushing or
pulling the camera and those exerted by Mr. Zapruder during his
muscular reactions to the sound of a bullet being fired. In either
case it is known from the laws of physics that any force on an
object is related directly to the acceleration of the object; this
is a statement of Newton's Second Law of Motion, published in the
year 1687, which requires any force, F, to be related to the
object's mass, m, and the object's acceleration, a, through the
famous equation F = ma. Thus, the angular acceleration is the
physically meaningful quantity needed to estimate the force on Mr.
Zapruder's camera. Newton's Laws of Motion are explained in detail
in Appendix A since they are central to understanding the motions
of A. Zapruder's camera.






Table of Streak Lengths


Frame Comments Streak Length Change in Length

152 Relatively clear 0 0
153 Less space in front -1 (-1) - (0) = -1
154 Less space -5 (-5) - (-1) = -4

155 to 156 Frames missing

157 Less space -5
158 More space +2.5 (+2.5) - (-5) = 7.5
159 More space +3.5 (+3.5) - (+2.5) = 1
160 Less space -2.5 (-2.5) - (+3.5) = -6
161 Less space -2.0 (-2.0) - (-2.5) = .5
162 Less space -3.0 (-3.0) - (-2.0) = -1
163 More space +2.5 (+2.5) - (-3.0) = 5.5
164 More space +2.5 (+2.5) - (+2.5) = 0
165 More space +3.5 (+3.5) - (+2.5) = 1
166 Less space -3.0 (-3.0) - (+3.5) = -6.5
167 Less space -0.5 (-0.5) - (-3.0) = +2.5
168 Less space -0.5 (-0.5) - (-0.5) = 0
169 Relatively clear 0 0

170 to 179 Relatively clear 0 0

180 Relatively clear 0 0
181 Relatively clear 0 0
182 Less space -2.0 (-2.0) - (0) = -2
183 Less space 0 (0) - (-2.0) = 2
184 Less space -1.0 (-1.0) - (0) = -1
185 Relatively clear 0 (0) - (-1.0) = +1

186 to 188 Relatively clear 0 0

189 Relatively clear 0 0
190 More space +2.0 (+2.0) - 0 = 2
191 More space +2.0 (+2.0) - (+2.0) = 0
192 More space +1.0 (+1.0) - (+2.0) = -1
193 More space 0 (0) - (+1.0) = -1
194 Less space -2.0 (-2.0) - (0) = -2
195 More space +3.0 (+3.0) - (-2.0) = +5
196 More space +1.0 (+1.0) - (+3.0) = -2
197 Less space -3.0 (-3.0) - (+1.0) = -4
198 More space 0 (0) - (-3.0) = +3
199 Less space -1.0 (-1.0) - (0) = -1.0
200 Less space 0 (0) - (-1.0) = +1
201 Less space -2.0 (-2.0) - (0) = -2
202 Less space 0 (0) - (-2.0) = +2
203 Less space 0 0
204 Less space 0 0
Table of Streak Lengths (Continued)

Frame Comments Streak Length Change in Length

205 to 219 Relatively clear; 0 0
some frames missing

220 Relatively clear 0 0
221 Less space -2.0 (-2.0) - (0) = -2
222 Less space 0 (0) - (-2.0) = +2
223 Relatively clear 0 0

224 Relatively clear 0 0
225 Relatively clear 0 0

226 Relatively clear 0 0
227 Less space -2.0 (-2.0) - (0) = -2
228 Less space 0 (0) - (-2.0) = +2
229 Relatively clear 0 0

230 to 239 Relatively clear 0 0

240 Relatively clear 0 0
241 Less space -2.0 (-2.0) - (0) = -2
242 Relatively clear 0 0 - (-2.0) = +2
243 Relatively clear 0 0

244 to 288 Relatively clear 0 0

289 Relatively clear 0 0
290 More space +2.0 (+2.0) - (0) = +2
291 Less space -0.5 (-0.5) - (+2.0) = -2.5
292 Less space 0 (0) - (-0.5) = +0.5

293 Relatively clear 0 0
294 Relatively clear 0 0
295 Less space -0.5 (-0.5) - (0) = -0.5
296 More space +1.5 (+1.5) - (-0.5) = +2
297 Relatively clear 0 (0) - (+1.5) = -1.5
298 Less space -2.0 (-2.0) - (0) = -2
299 Less space -1.0 (-1.0) - (-2.0) = +1
300 Relatively clear 0 (0) - (-1.0) = +1

301 to 311 Relatively clear 0 0

312 Relatively clear 0 0
313 More space +2.0 (+2.0) - (0) = +2.0
314 More space +0.5 (+0.5) - (+2.0) = -1.5
315 Less space 0 (0) - (+0.5) = -0.5
316 Less space 0 0
317 Less space 0 0
318 Less space -4.0 (-4.0) - (0) = -4
Table of Streak Lengths (Continued)


Frame Comments Streak Length Change in Length

319 Less space -1.0 (-1.0) - (-4.0) = +3
320 Less space -1.0 (-1.0) - (-1.0) = 0
321 More space +0.5 (+0.5) - (-1.0) = +1.5
322 Less space -0.5 (-0.5) - (+0.5) = -1.0
323 More space 0 (0) - (-0.5) = +0.5
324 About the same 0 0
325 More space +0.5 (+0.5) - (0) = +0.5
326 More space +0.5 (+0.5) - (+0.5) = 0
327 Less space 0 (0) - (+0.5) = -0.5
328 About the same 0 0
329 Less space -0.5 (-0.5) - (0) = -0.5
330 Less space -1.0 (-1.0) - (-0.5) -0.5
331 Less space -3.0 (-3.0) - (-0.5) = -2.5
332 Less space -0.5 (-0.5) - (-3.0) = +2.5
333 Less space 0 (0) - (-0.5) = +0.5
334 More space 0 0



Figure NNN shows the time series for the angular
accelerations based on the numbers in this table. The six vertical
lines in this figure are labelled by the frame numbers from 150 to
335 and the angular accelerations are plotted in arbitrary units
with positive acceleration values shown to the left of the vertical
line and negative values to the right. We shall return to this
figure and offer a detailed analysis of its meaning.

Volumes II and VI of the 1979 Report of the Select Committee
on Assassinations, U.S. House of Representatives, Investigation of
the Assassination of President John F. Kennedy, present alternative
analyses of the streaking and departure from perfect panning of the
Zapruder film; in particular, the analyses of W. K. Hartmann and F.
Scott. The nature of these alternative methods is described in
Volume II of the Hearings when the examiner, Mr. Cornwell questions
Dr. Hartmann:

Mr. Cornwell: Did the procedures which were selected, were
they followed both by you and Mr. Scott, the same procedure?

Dr. Hartmann: No. We used separate procedures. We both made
a series of measurements on the film., but each decided for himself
what system might be best to record in a quantitative way these
blurs or juggles.

Mr. Cornwell: Just very briefly, would you tell us what the
differences were between the two approaches that you took?

Dr. Hartmann: Briefly, I measured the amount of blur or
smearing of the image in each frame of the film, one frame at a
time, and what Mr. Scott did was to follow from one frame to the
next the position of the camera, where it was pointed in the
landscape, and to see how smooth that tracking was between one
frame and the next frame.

Mr. Cornwell: So then would it be accurate to state that you
measured the blur internally within the frame and Mr. Scott
measured the blur which occurred between two frames?

Dr. Hartmann: Yes, in a real sense mine is a measure of the
blur that occurred from the middle of the time the shutter was open
on one frame to the time it was open on the next frame?

Dr. Hartmann was also asked questions concerning the Alvarez
analysis:

Mr. Cornwell: Now, in addition to the two approaches you have
described, are you aware of any other way in which jiggle might be
measured?

Dr. Hartmann: Yes. The physicist, Luis Alvarez, has in 1976
published in the American Journal of Physics an analysis of the
same film using a third method, and that method was basically to
take the set of blurs similar to what I described first, what I was
quoting in my method, and his reasoning is as follows: That if the
blur, if the amount of blur stays the same from one frame to the
next to the next, then essentially nothing is happening. But if
there is a sudden change in the amount of blur, then that is a
sensitive measurement of a disturbance. And so what he plotted was
the difference in blur from one frame to the next. So that is a
third set of measurements.

Mr. Cornwell: When did you first become aware of Dr. Alvarez
---.

Dr. Hartmann: That paper was circulated to us on the photo
panel some months ago, but I purposely did not study his results
until I finished mine and Scott's.

At this point in the testimony, Dr. Hartmann presented a
graphical summary of the three different analyses; the same
information is presented in a more convenient form in the Appendix
to Hearings before the Select Committee on Assassinations of the
U.S. House of Representatives, Ninety-Fifth Congress, Second
Session, Volume VI: Photographic Evidence, March 1979, where Figure
II-1 on page 20 and Figure II-5 on page 26 provide graphical
summaries of the analyses of W. K. Hartmann, Frank Scott and L.
Alvarez. These figures are reproduced here as Figures HSA1 and
HSA2. Referring to JFK Exhibit F-177, page 14 of Volume II, ibid.,
which contains the results of Figure HSA2, Mr. Cornwell continued
to question Dr. Hartmann as follows:

Mr. Cornwell: I would like at this time to show you exhibit
177 and ask you if you can identify it.

Dr. Hartmann: Yes, sir. This is an analysis or a plot
showing all three sets of information on the same time scale now.
So, for the first time we have a chance to really compare what the
three independent and different types of measurements show, the
same boxes here with the same set of frame numbers and the same
timings, and, incidentally, I have noted some events as they happen
along the sequence in the film, just to give you a reference to
what is happening in the motorcade. Now above the little line are
the peaks, the greatest blurs that were measured by my technique,
this is taken directly off that earlier graph. Below the line is
just a flipped over image of the blurs or jiggles measured by Mr.
Scott's technique, and I think you find some pretty good agreement
there. And down at the bottom in red has been added directly,
hand-copied from Alvarez's graph published in his paper, the set of
measurements that he made, and, incidentally, they jiggle in both
directions because he kept track of either what he called a
positive blur in one direction or a negative in the other
direction, so his are a kind of a squiggle, and ours are just
motions up or down.
After JFK Exhibit F-177 is entered into evidence the dialogue
between Cornwell and Hartmann continues:

Mr. Cornwell: Dr. Hartmann, can you tell us, from the
analysis that you have just described, precisely when the shots
were fired?

Dr. Hartmann: Well, in my opinion, if you look only at this
record of blur, in spite of the fact that there is pretty good
agreement, it would be very difficult to say that a particular
episode of jiggling here, a particular set of blurs, is the
response to a gunshot.
The question is, we believe, that if there could have been
other kinds of reactions that would cause jiggles, just false
alarms. And so on the basis of looking just at the blur, I would
say no.
However, if we then look at the photo visual evidence of what
is happening in the parade, I think we can begin to identify some
of these as gunshots.

Mr. Cornwell: Would you explain if you could the relationship
to frame 313 --

Dr. Hartmann: Yes.

Mr. Cornwell [continuing]: Where the gunshots occurred?
Dr. Hartmann: That, in particular, is the most significant
one, where we know that there has been a gunshot. And we see that
there is a very strong episode of this jiggling initiated at that
time. The lapse time the jiggles begin -- of course one has to
define how do you detect when the jiggle really begins?
And perhaps the best way is to go, is to look at the frame
group from when the jiggle initiates to when it reaches a maximum.
In this case that is about 313 to 319. The shot was probably fired
at 310, as I mentioned before, and that number of frames is
consistent with the measures of startle reaction time that were
reported in the book that I mentioned. So I think that is a good
confirmation that we are really seeing here the reaction to both
the sound of the gunshot and probably the visual sight of what
happened on the shot.

Mr. Cornwell: And would it be accurate to state that the
second largest area of blur or jiggle, apart from the one which
occurred shortly after the head shot, would be in the earlier
portion of the film?

Dr. Hartmann: That is correct.

Mr. Cornwell: What frame is that associated with?

Dr. Hartmann: About frames 190 to 200 there is a strong blur
reaction initiated. So having concluded that this is in fact, that
the blur sequence around 313 to 319 is in fact a response to the
gunshots, I would think that the logical inference would be that
the blur sequence, the blur episode, running typically from 190 to
200 is also a response to a possible gunshot. And we know that the
President emerged from behind the sign somewhat later, some frames
later, showing in fact a reaction to such a wound. So this could
very well be the blur or startle reaction to the gunshot that
caused the back wound to the President.

Mr. Cornwell: And, what, if any, corroboration is provided by
this analysis to the Warren Commission's conclusion that the
President and the Governor may have been shot in the vicinity of
frame 210?

Dr. Hartmann: Yes, they picked 210. I would say that to pick
210 in the face of this current evidence, to pick 210 as the time
for that first shot, which is the Warren Commission's conclusion,
would not be warranted from the evidence, because the blur before
frame 210, from 190 to 200, is clearly much larger than any blur
after frame 210. In fact, there is really very little evidence for
a blur in the appropriate amount of time after frame 210.
Furthermore, there is some photo evidence that tends to
support the thought of a shot in the time frame shortly before 190.
For example, there is the Phillip Willis photograph which shows Mr.
Zapruder in the background and the motorcade passing in between.
Because the motorcade is in between, it is quite possible, quite
easy, to determine exactly which Zapruder frame that corresponds
to, because you can tell which part of the motorcade is passing
between Zapruder and Willis. And Willis said that he took that
photograph as a reaction. He pressed the shutter as a reaction to
what he perceived as the first shot, at least a shot.
Well, it turns out that frame is 202. So that means that Mr.
Willis is telling us that he pressed the shutter as part of his
reaction to a shot, and he was reacting at frame 202, while here we
see that Mr. Zapruder is in the middle of his reaction at frame
202. So that is very nice consistent evidence that something
happened, say, at 190 or shortly before 190.


A related analysis of the photographic evidence is given in
Volume VI of the 1979 Appendix to Hearings before the Select
Committee on Assassinations, U.S. House of Representatives, where
"blur episodes" were classified into six separate groups. These
six groups were identified from the onsets of the blurs of
Hartmann, the tracking errors of Scott, and the angular
accelerations of Alvarez. The signals of largest magnitude were
designated by two subgroups A1 beginning at frames 312 or 313 and
A2 which began at frames 330 or 331; the variation in the time of
onset is due to the fact that each of the three methods is
sensitive to a different type of signal. The signal of second
largest magnitude was designated as Group B with a time of onset of
189 to 193. The third most intense group, Group C, had an onset at
about frames 220 to 226. The fourth most intense group, Group D,
had an onset at frame 158 and the group with the fifth most intense
magnitude, Group E, began at frame 290 or 291.

Groups A1 and B are the groups considered previously in the
exchange between Dr. Hartmann and Mr. Cornwell. Regarding Groups
C, D, and E, the Appendix to the Hearings, Volume VI, page 29,
summarizes key observations.

"The third, fourth, and fifth largest blur episodes, which are
similar to one another in magnitude, are listed respectively as C,
D, and E.'
'It is difficult to determine with certainty whether any of
these represents an additional shot or shots. Blur episode C,
detected by all three analysts, occurs at frames 220-228, just
before movements of Governor Connally in which his cheeks suddenly
puff out and his face contorts in a grimace, followed by two
apparent outcries in which his mouth opens wide in what appears to
be a shout of pain.'
'Another shot could have caused blur episode D at frames 158-
160. It occurs much earlier in the motorcade than had been
considered possible for a shot by either the Warren Commission or
most Warren Commission critics. Nonetheless, this brief blur was
detected by both Hartmann and Scott; Alvarez published no data for
such an early part of the motorcade because he used the Warren
Commission volumes which do not even reproduce Zapruder frames
earlier than the mid-170's. The most interesting thing about this
hypothetical shot is that Mrs. Kennedy and Governor Connally
testified before the Warren Commission and Governor Connally
testified before the select committee that they turned to their
right when they heard the first shot, and both are seen in the film
beginning a turn to the right immediately after this hypothetical
shot. This appears particularly striking in the case of Governor
Connally, whose head turns from mid-left to far right in less than
half a second, beginning at frame 162.'
'A fifth episode (E) possibly associated with a shot occurs at
frames 290-293. Although it contains a very small blur detected by
both Hartmann and Scott, as well as a more substantial blur in
Alvarez's data, the Panel found no visual indications of reaction
to a shot by the limousine's occupants coinciding with this segment
of the blur in the film."

Prior to learning of the work of W. K. Hartmann and F. Scott,
I had known of the Alvarez analysis of the Zapruder film and
extended the Alvarez analysis to frames earlier in time than those
considered previously; my analysis of these earlier frames and a
plot of the corresponding angular accelerations between frames 152
and 170 may be found in Bulletin of the American Physical Society,
November 1994. (In fact, I first learned of the Alvarez analysis
many years ago during the period from 1975 to 1978; during this
period Dr. Alvarez presented his analysis in a seminar at the Los
Alamos Scientific Laboratory, now the Los Alamos National
Laboratory, where I was a research scientist exploring laser-
produced shocks, relativistic effects on laser-produced plasmas and
laser fusion.) Although Luis Alvarez did not publish an analysis
of frames before frame 171, the physical insight gained from
reading his paper in the 1976 American Journal of Physics makes two
key points very clear: first, the physically meaningful quantity is
the angular acceleration of Mr. Zapruder's camera about the nominal
pointing direction for perfect panning and, second, the expected
jerking motion could reasonably cause blurring that is very
localized in time as well as an associated oscillatory motion of
the camera's pointing direction. The many available public
versions of the Zapruder film serve as ready sources for anyone who
is interested in examining Zapruder frames before those published
in the Warren Report. Of particular interest is the very visible
blurring and the pronounced oscillations between frames 152 and
167. In fact, the striking nature of these effects is surprising
given the fact that they correspond to Group D which had only the
fourth largest magnitude in the analyses of Hartmann and Scott.
This apparent dilemma is explained, in part, by the following
observations. First, the Alvarez analysis is sensitive to both
blurring, as in the case of Hartmann's analysis, as well as changes
in the direction and rate of panning, as in Scott's analysis; in a
approximate sense, the physically-based angular acceleration used
by Alvarez includes both blurring and panning effects. Second, by
Newton's Second Law of Motion it is known that any angular forces
on the camera are related directly to the angular accelerations
used by Alvarez; the angular acceleration is the physically-
meaningful quantity. Third, since the typical duration of a shock
front of several milliseconds is less than the thirty millisecond
(about one-thirtieth of a second) exposure time of each frame in
the Zapruder movie, it is possible that considerable blurring, or
streaking, may be localized to one frame with the adjacent frames
being relatively clear and unblurred; hence, the change in the
streak length between adjacent frames is a sensitive indicator of
a sudden, brief disturbance acting on the camera. Frames 220 to
223 as well as frames 312 to 316 provide clear examples of such a
phenomenon. The angular acceleration used as the basis of the
Alvarez analysis is calculated by subtracting the algebraic values
of the streak lengths between adjacent frames and it is therefore
extremely sensitive to rapid changes in motion between adjacent
frames. To appreciate this effect it is instructive to consider
frames 157 to 160 and frames 190 to 192 of Figure HSA1. Hartmann's
blur length is about 2.5 % of the field-of-view of the frame for
each of these blur episodes. However, the change in the blur
length from frame 191 to frame 192 is less than that from frame 159
to frame 160. Thus, the angular acceleration should reflect a
larger effect and, indeed, it does as shown on Figure NNN.

The angular accelerations of Mr. Zapruder's camera for frames
150 to 334 are plotted frame by frame in Figure NNN. The frame
numbers run vertically from frame 150 to frame 334 along the six
vertical lines. The angular accelerations are plotted to the right
and left of the vertical lines in arbitrary units; accelerations
plotted to the right are counterclockwise as view from above the
camera and those plotted to the left are clockwise as viewed from
above. In his original analysis, Dr. Alvarez considered only the
angular accelerations plotted along the second through sixth of the
vertical lines. He simply did not consider the angular
accelerations plotted on the first of the six vertical lines
because the Warren Commission did not include frames before 171 in
its report; that is, he did not consider the angular accelerations
plotted on the first vertical line of Figure NNN. In view of the
considerable angular accelerations evident in frames 152 to 168 it
might have been prudent for the Warren Commission to have paid more
attention to events before frame 171 of the Zapruder film. Alvarez
associated the time series along the sixth vertical line with the
direct interaction of the shock wave with Mr. Zapruder's camera as
well as with the subsequent reaction of Mr. Zapruder to the crack
of the bullet and the sight of seeing President Kennedy wounded.
Indeed, in his American Journal of Physics article Alvarez states,

"Angular accelerations plotted to the left correspond to
motions of the camera axis that are 'clockwise looking down.'
(The motion of the car and of bullets from the Book Depository
are also clockwise looking down, as seen by Mr. Zapruder.)
Thus the torque acting on the camera between frames 312 and
313 was 'negative,' meaning that it could have been caused by
a direct interaction of the shock wave from the bullet that
hit the President in frame 313, with the left hand side of Mr.
Zapruder's camera. (This is important because the impact of
the bullet can be seen in frame 313, and there isn't enough
time available for the relatively sluggish neuromuscular
system to have produced the observed torque on the camera
axis.)

Concerning the neuromuscular reaction time, Alvarez states,

"...we see that the obvious shot in frame 313 is accompanied
immediately by an angular acceleration of the camera, in the
proper sense of rotation to have been caused directly by the
shock-wave pressure on the camera body. The human nervous
system cannot transmit signals fast enough for the angular
acceleration between frame 312 and 313 to have been caused by
Mr. Zapruder's muscles reacting to impulses from a brain that
had been startled by the shot that killed the President. The
expected neuromuscular reaction occurs about one-quarter to
one-third of a second later, as shown by the large
accelerations near 318."

Based on this delay of five frames, Alvarez took five frames as A.
Zapruder's reaction time. A five-frame delay is about one-third of
a second. In summary, in the sixth vertical line of the angular-
acceleration time series there is the initial shock-driven
acceleration followed by a sequence of accelerations spaced about
one-third of a second apart which resembles the motions expected
from neuromuscular responses.

In interpreting the angular-acceleration time series of the
second and third vertical segments of Figure NNN, Alvarez assumes
that these time series are due solely to neuromuscular responses.
Indeed, he comments specifically on the third sequence:

"We further note that the initial pulse of the series at 221.5
is not in the proper direction to have been caused by a direct
interaction of the shock wave with the camera; the camera
turns toward, rather than away from the shock wave. The shock
wave from a bullet fired from the Book Depository toward the
car in its position at the time of frame 221 would have been
considerably weaker at Mr. Zapruder's station than the shock
wave in frame 313, so the lack of a direct physical
interaction at the time of this earlier shot is not
surprising. I therefore conclude that the accelerations at
220.5 and 221.5 were caused by Mr. Zapruder's neuromuscular
response to an earlier stimulation. If we use Mr. Zapruder's
thereby observed oscillation period of about five frames
(which is close to the expected value), we place the shot ...
at about 215.5."

From Figure CCC it is apparent that a bullet coming from the TSBD
and striking its target at frame 221 would indeed produce weaker
shock waves at Mr. Zapruder's position than a bullet traveling from
the TSBD to the position of President Kennedy at frame 313.
Indeed, from Figure III the pressure of the shock would have been
several times weaker for the bow shock assuming the bow shock
continued to propagated so that it interacted with A. Zapruder's
camera. However, a bullet fired from the Grassy Knoll would have
produced a substantial shock pressure at Zapruder's location and it
would have caused the angular acceleration pattern with the initial
direction as in 221.5. Dr. Alvarez, however, does not consider the
possibility directly. Instead, he notes that such a pattern could
not be produced by the direct interaction with the shock of a
bullet emanating from the direction of the TSBD and, therefore,
concludes that the oscillations must be caused by the neuromuscular
reactions evident five frames after the crack of the bullet was
heard by A. Zapruder. However, the bullet causing the acceleration
pattern beginning at 221.5 could have come from either the general
direction of the TSBD or the Grassy Knoll.

Having associated the angular acceleration of the second,
third and sixth vertical lines with the three bullets acknowledged
by the Warren Commission, Alvarez then explains the angular-
acceleration time series of the fifth vertical time series as being
due to A. Zapruder's neuromuscular reaction to the sound of a siren
blast that occurred within seconds of the time of frame 313 of the
Zapruder film. As evidence to support the notion that a siren
blast did in fact occur at about frame 285, Alvarez noted that the
speed of President Kennedy's limousine was reduced abruptly during
the approximate time interval between frames 290 and 310. Figure
ZOA illustrates the result of Alvarez's determination of the speed
of President Kennedy's limousine between frames 220 and 320.
(Alvarez used a rock in the background grass of the center of
Dealey Plaza as a reference marker for determining the limousine's
speed.)

Indeed, a consistent explanation results if it is assumed
that the driver of President Kennedy's limousine momentarily took
his foot off the accelerator at the same time that A. Zapruder
heard the siren. That is, the slowing of the limousine and the
motion of A. Zapruder's camera at about the time between frames 290
and 300 could have both been explained as reactions to a siren
blast at about frame 285. The only problem with this explanation
is that witnesses claimed that the siren blast occurred many frames
after 313. Alvarez was aware of this discrepancy and he cited
credible results which call into question the precision of eye-
witness accounts to crime but he does acknowledge that "...I can't
prove that this is the way it happened."

Through his brilliant insights as a physicist Luis Alvarez
was able to use the sudden motions of A. Zapruder's camera to
obtain an interpretation consistent with but not proving the
findings of the Warren Commission if it is assumed that:

- any initial shock-driven acceleration patterns consistent
with a shot fired from the Grassy Knoll were actually only
neuromuscular reactions to the crack of gunfire, and,

- the angular accelerations occurring between frames 290 and
300 were stimulated by the sound of a siren that occurred
after frame 313 according to eye witnesses.

Thus, consistency could be obtained with two reasonable --- but
certainly questionable --- assumptions.

If Alvarez had analyzed frames before 171 he would have had
still another observation to explain --- the two angular-
acceleration time-series beginning at about frames 151 and 181 are
separated in time by only 1.6 seconds. This 1.6-second time
interval is too short to have resulted from the firing of a single
Mannlicher-Carcano which requires 2 seconds to cock and fire!
Furthermore, the initial angular acceleration between frames 151
and 154 is in the proper direction to have been caused by a bullet
fired from the general direction of the Grassy Knoll. A shot fired
from the corner of the picket fence or directly down the picket
fence from any position along the picket fence would have been
expected to push his hand-held camera to the left. The angular-
acceleration time series between frames 151 and 154 is consistent
with A. Zapruder's camera being pushed to the left. It is possible
that there was no direct interaction with a shock wave and the
motion of the camera was caused by a stimulation of A. Zapruder's
neuromuscular system; this stimulation could have resulted from his
reaction to the crack of a bullet or some other disturbance.
However, since the time between frames 151 and 180 is less than the
time needed to fire a Mannlicher-Carcano it does not seem
reasonable to insist that all bullets came from Lee Harvey Oswald's
post in the TSBD --- the same rifle just could not have been
responsible for the two closely spaced, but distinct, angular-
acceleration time-series commencing at frames 151 and 180! If
these were both caused by the direct interaction with a shock-wave
produced by a bullet or by the neuromuscular stimulation caused by
a bullet, they could not have been caused by bullets fired from
the same gun! Furthermore, the motions of A. Zapruder's camera are
just as intense during the time interval from frames 151 to 168 as
they are between frames 180 and 202; if the latter of these was
caused by a bullet, it is entirely reasonable to conclude that the
former was likely caused by a bullet. Indeed, the time-series of
angular accelerations between frames 151 and 154 is consistent with
a bullet fired from the Grassy Knoll.

Figure OOO contains an estimate of the "area" or "strength"
associated with each time sequence. The cross-hatched regions for
the six vertically-plotted angular-acceleration time-series in
Figure OOO are given by 16, 15, 6, 0, 6 and 11, respectively, where
the units are based on the arbitrary units used for angular
acceleration as well as on time units where the time between frames
is one unit of time. The total area of each segment of the time-
series gives an indication of the intensity of each of the episodes
of jerky (high frequency) motion of A. Zapruder's camera. The
areas for each of the five sequences of jerky motion provide only
a crude means of comparing the intensities of these episodes.
Indeed, the apparent streak lengths of the President's limousine
must be adjusted for the fact that at frames 150 and 180 the
limousine was roughly twice as far from A. Zapruder's camera as at
frame 313; at frame 220 the limousine was roughly 1.5 times farther
from A. Zapruder's camera than at frame 313. To make an
approximate adjustment for this effect the areas for the sequences
beginning at 152 and 180 may be divided by 2 and that beginning at
220 may be divided by 1.5. The six adjusted areas are then 16/2 =
8, 15/2 = 7.5, 6/1.5 = 4, 6 and 11. That is, the approximate
relative intensities of the episodes discussed by Alvarez are as
follows: intensity of the episode associated with the "first shot"
is 7.5; intensity of the burst associated with the "wounding shot"
(magic bullet shot) is 4; intensity of the jerking episode
associated with what was hypothesized as a "siren" (seconds before
some eye witnesses claimed to be the actual time of the siren) is
approximately 6; the intensity of the pattern of accelerations
associated with the wounding of President Kennedy in the head is
11. The episode beginning at frame 152 has a relative intensity of
8 even without the "areas" of the 2 missing frames included; this
sequence was not considered by L. Alvarez because it occurred
before frame 171. These adjusted relative areas provide only very
crude indications of the jerking episodes; however, it is
noteworthy that the intensity of the episode associated with the
magic bullet shot is about half that of that of those beginning at
frames 152, 180 and 313. This raises the possibility that each of
these sequences could possibly be associated with more than one
bullet. An alternative explanation for a greater intensity level
for the episode beginning at about frame 152 is that a gun fired
from the Grassy Knoll would have passed within only roughly 20 feet
of A. Zapruder; this close distance of approach would naturally
result in one of the strongest bow shocks and, depending on the
location of the gun along the picket fence, possibly one of the
strongest blast waves at Zapruder's location. It is also possible
that his neuromuscular reaction would have been greater for a shot
fired at closer range. It is, however, also possible that his
neuromuscular reaction would have varied from shot to shot even for
shots fired from the same location under identical conditions. It
appears to be impossible to prove or disprove on the basis of these
relative intensities whether more than one bullet is associated
with a given jerking episode.

Some light is shed on the question of the cause of each
particular sequence of angular accelerations by examining the human
reactions and events recorded visually in the Zapruder film. These
recorded visual clues are described in Table III along with the
times of the jerking episodes. The times given are the times a
stop watch would have given at the first frame in each sequence if
the stop watch started at frame 151.

The first jerking episode occurs between frames 151 to 168
and is labeled by "1." in Table III as well as by an arrow in
Figure NNN. This episode is coincident with the quick movement of
President Kennedy's head from left to right; in the early portion
of this sequence President Kennedy is looking to his left but he
then quickly turns his head to the right, he stops waving, and he
looks in the direction of the Grassy Knoll. The quick turning
motion of President Kennedy's head is also coincident with frames
155 and 156 which are missing from the Zapruder film! The film was
spliced to connect frames 154 to 157. The splice is visible as a
horizontal line running across the spliced frames and is easy to
identify on the many readily available home videos containing the
Zapruder film. With a little patience and trial-and-error in
pausing a home video this splice as well as the streaking due to
the jerking of Zapruder's camera are readily observable by any home
video viewer. Frame 154 occurs very close to the time when the
right front wheel of President Kennedy's limousine is passing a man
with a black hat who is standing on the side of Elm Street. These
visual clues are consistent with President Kennedy's hearing
gunfire on the Grassy Knoll before frame 155; the time-series of
angular accelerations is also consistent with this interpretation.
Thus, there is reasonable evidence of a shot fired considerably
less than 2 seconds before the first jerking episode identified by
L. Alvarez; this second episode is the first occurring after frame
171, the first frame in the Warren Commission's report. This
second episode is labeled "2." in Table III as well as by an arrow
in Figure NNN. In other words, if both of these jerking episodes
were caused by bullets, they could not have been fired by the same
gun.

Between frames 188 and 202 President Kennedy's right hand
moves at a slower rate and is about a foot in front of his chin
when he disappears behind the edge of the sign on Elm Street; when
he emerges from behind the sign at frame 225 both of his hands are
on his throat but Governor Connally is still showing no signs of
distress. In other words, the correlation of the time of the
jerking motion and the occurrence of visual clues supports the
notion that President Kennedy may have been struck by a bullet at
roughly frame 190, or slightly earlier, and Governor Connally was
not struck before frame 224; this is not consistent with the magic
bullet theory of the Warren Commission. The second, third and
fourth jerking episodes, labeled by "2.", "3." and "4." in Table
III, commence during the time interval between frames 180 and 224.
As emphasized by Alvarez,two closely-spaced episodes such as "2."
and "3." may have been caused by a single bullet which resulted in
an extended neuromuscular reaction. On the other hand, the third
episode is characterized by a distinct angular acceleration pattern
and it is entirely possible that it was caused by a separate bullet
--- the third bullet fired in Dealey Plaza on November 23, 1963

At frame 225, the right hand side of Governor Connally's
jacket is pushed up. If this sudden, brief flapping of Governor
Connally's lapel was due to a bullet, it must be concluded that he
was struck after President Kennedy had be hit at least once. The
telling visual clue associated with the sudden flapping of
Connally's lapel occurs at the time of the fifth jerking episode,
"5.", as labeled in Table III; these events are highlighted by an
arrow in Figure NNN. Alvarez's analysis treated the three jerking
motions beginning at frames 220, 225 and 240 as being associated
with one bullet --- the "magic bullet" of the Warren Commission.
If all three of these bursts were caused by one bullet it is
extremely difficult to understand why Governor Connally's lapel is
pushed up violently at the time of only the second of these bursts
--- the burst occurring at frame 225. It appears likely that there
were at least two bullets in the interval in question: one at frame
220 and one at frame 225.

L. Alvarez speculated that the jerking episode occurring
between frames 290 and 300 was associated with a siren that
startled A. Zapruder. This is not consistent with eyewitness
accounts which placed the time of the siren many frames after frame
313; however, as pointed out by Alvarez, eyewitness accounts are
frequently erroneous. Since the angular acceleration pattern
beginning at frame 290 is consistent with that expected from a shot
from the general direction of the Texas Schoolbook Depository
(TSBD) it may be that the jerking episode starting at frame 290 is
associated with the bullet which caused the fragment that struck
James Tague in the cheek. In fact, since James Tague was standing
near the triple underpass on the west side of Dealey Plaza, it is
certain that he was struck by an object travelling west on Elm
Street. Furthermore, a projectile moving to the west at the time
of frame 290 would have likely caused a direct shock-wave
interaction with A. Zapruder's camera; this is entirely consistent
with the angular acceleration pattern commencing at frame 290.

As discussed at length by L. Alvarez as well as in Appendix
A, the jerking episode commencing at frame 312 is consistent with
a bullet fired from the general direction of the TSBD. The bullet
associated with this jerking episode is tragically the bullet which
struck President Kennedy in the head. Alvarez's analysis of this
seventh episode is compelling and is completely consistent with the
behavior expected from a bullet fired from the general vicinity of
the TSBD or the Dal-Tex Building; indeed, just as expected, the bow
shock pushes the camera to the right at the same instant that the
visual evidence of the head shot is manifest. As explained so
clearly by Alvarez in his article "A Physicist Examines the Kennedy
Assassination Film," the recoil of President Kennedy's head
immediately after frame 313 is fully consistent with the laws of
physics and does not necessitate the conclusion that the bullet
striking President Kennedy at frame 313 was fired from his front.
This seventh jerking episode is labeled by "7." in Table III and is
highlighted by an arrow in Figure NNN.
Since Governor Connally was holding his hat well after he was
wounded, many analysts of the assassination conclude that he was
struck in the wrist some time after a bullet shattered his rib. In
particular, in the movie JFK, Oliver Stone speculates that the
bullet which wounded Governor Connally's wrist was fired after
President Kennedy was struck in the head. Stone's reasonable
interpretation cannot be verified or refuted from the angular
acceleration patterns of Figure NNN; however, if correct, it may
require yet another bullet.

When viewed together with the visual clues in the Zapruder
film, the sequence of jerking motions described in Table III
supports the conclusion that more than three bullets --- perhaps
many more --- were fired at President Kennedy's limousine as it
travelled down Elm Street on November 23, 1963. Since eyewitnesses
claimed to have heard from two to six shots, the question arises as
to the maximum number of shots one could reasonably believe was
actually fired. Estimating such a number is made difficult for two
reasons: some of the candidate shots, such as at frames 220 and
frames 225, occur so close in time that the second sound would be
hard to distinguish from an echo if it were noticed at all; it is
impossible to rule out the use by one or more gunmen of a silencer
which would greatly reduce the sound of the muzzle blast but would
not eliminate the bow shock and its effect on the jerking of A.
Zapruder's camera.


Table III. Correlations between Frame Numbers where Angular
Accelerations Occur and Other Significant Events

Frame Numbers when Significant Events
Angular Accelerations Occur
(Jerking Episodes)

1. 0 seconds (at 151)
151 to 170 President Kennedy Stops Waving and Turns His Head Abruptly from Left to Right to Look at the Grassy Knoll

2. 1.58 seconds (at 180)
180 to 185 President Kennedy Has Started to
=
Wave Once More

3. 2.02 seconds (at 188)
188 to 202 President Kennedy's Hand Slows
=
in the Middle of the Last Wave
=
of His Hand; His Right Hand is
=
about a Foot in Front of His
=
Chin

4. 3.72 seconds (at 219)
219 to 222 President Kennedy and Governor
=
Connally are behind the Road
=
Sign as Viewed through Mr.
=
Zapruder's Camera

5. 4.04 seconds (at 225)
225 to 228 At Frame 225 President Kennedy
=
Emerges from behind the Sign and
=
both of His Hands are on His
=
Throat. At Frame 224 Governor
=
Connally is in Full View and is
=
Sitting Erect with no Sign of
=
Distress; At Frame 225 the Right
=
Side of Governor Connally's
=
Jacket is Pushed Up.

6. 7.60 seconds (at 290)
290 to 300 Possibly the Time when James
=
Tague was Struck in the Cheek.

7. 8.80 seconds (at 312)
312 to 333 President Kennedy is Struck in
=
the Head at Frame 313.




CHAP=
TER 3
THE SEARCH FOR ACOUSTIC EVIDENCE
The 1979 Report of the Select Committee on Assassinations,
U.S. House of Representatives, Investigation of the Assassination
of President John F. Kennedy concludes that "scientific acoustical
evidence establishes a high probability that two gunmen fired at
President John F. Kennedy." This finding appears to have been
widely published, as for example in the final credits of the well-
known movie JFK; however, less well-known is the fact that a very
prestigious Committee on Ballistic Acoustics established by the
National Research Council* demonstrated quite convincingly that the

---

*The National Research Council's Committee on Ballistic Acoustics
was chaired by Norman F. Ramsey, Harvard University, who is now a
Nobel Laureate in Physics. Members of the Ramsey Committee
included: Luis W. Alvarez, Lawrence Berkeley Laboratory, University
of California; Herman Chernoff, Massachusetts Institute of
Technology; Robert H. Dicke, Princeton University; Jerome I.
Elkind, Xerox Palo Alto Research Center; John C. Feggeler, Bell
Laboratories (Holmdel); Richard L. Garwin, IBM Thomas J. Watson
Research Center and Adjunct Professor at Columbia University; Paul
Horowitz, Harvard University; Alfred Johnson, Bureau of Alcohol,
Tobacco and Firearms, National Laboratory Center, Department of
Treasury; Robert A. Pinney, Princeton University; Charles Rader,
Lincoln Laboratory, Massachusetts Institute of Technology; and
William F. Sarles, Trisolar Corporation, Bedford, Massachusetts.
acoustic evidence considered by the Select Committee on
Assassinations was recorded about one minute after the
assassination.

The acoustic evidence analyzed for both the U.S. House
Committee and the National Research Council* consisted of sounds
recorded by the Dallas Police Department on one of its Dictaphone
belt recorders located at the Dallas Police Department
Headquarters; these sounds were recorded on Channel I of the Dallas
Police Department communications system which was used largely for
communications not related to the presidential visit, and not on
Channel II which was devoted to the presidential motorcade on
November 22, 1963. Channel II was inactive at the time gunshots
were fired and the sounds suspected as being caused by gunshots
were recorded on Channel I at about 12:30 pm; it was assumed that
these sounds recorded on Channel I were transmitted to the recorder
by way of a microphone that had been stuck open or left open
unintentionally on a Dallas Police Department motorcycle. Since
communications on Channel I were unrelated to the presidential
motorcade it was initially taken for granted that it would not be
possible to pinpoint the precise times of the suspected gunshots

---

* The National Research Council is the operating arm of the
National Academy of Sciences which was established by President
Abraham Lincoln for the purpose of giving unbiased, independent
advice to the U.S. Government.
relative to the times of motorcade voice transmissions just before
or after the seconds when shots rang out in Dealey Plaza on
November 22, 1963. Indeed, the times at which the separate
recordings on either Channels I and II were made were not gotten
from the same clock and so a recording on Channel I that was
labelled as being recorded at, say, 12:31:05 pm (31 minutes and 5
seconds after noon) on November 22, 1963 could have been recorded
at, as examples, 12:29:18 pm or 12:31:02 pm or perhaps even
12:32:09 pm; likewise, because a different clock was used to label
the times on Channel II, there was a similar but unrelated
uncertainty in the actual time of a recording on Channel II.

Throughout the deliberations and studies conducted for the
U.S. House Committee on Assassinations the precise times of the
suspected shots were not determined relative to the times of events
occurring just before or after the period of time during which the
sounds suspected of gunshots were recorded. In contrast, the
National Research Council's Committee on Ballistic Acoustics, which
had been directed by the Department of Justice to examine the
"acoustic evidence" in the assassination, demonstrated convincingly
that the noise-like sounds suspected of being gunshots were
recorded about one minute after President Kennedy had been wounded
fatally. This finding takes on special meaning when it is
recognized that of all the known recordings made on November 22,
1963 this segment of the Channel I recording was singled out as the
only one containing sounds that could possibly be attributed to
gunfire. In other words, there is no known recording of the sounds
in Dealey Plaza during the few seconds when gunshots were fired at
the presidential motorcade!

Nevertheless, the finding of the U.S. House Committee on
Assassinations that "scientific acoustic evidence established a
high probability that two gunmen fired at President John F.
Kennedy" appears to have made a deep impression on those with an
intense interest in the assassination as well as on large segments
of the general public. For this reason it is important to review
the acoustical evidence that appears to have been used incorrectly
to conclude that two gunmen fired at President Kennedy.

James E. Barger, Scott P. Robinson, Edward C. Schmidt and
Jared J. Wolf of Bolt, Beranek and Newman, Inc. (BBN) and later M.
Weiss and E. Aschkenasy of Queens College (QC) of New York were
commissioned by the U.S. House Committee on Assassinations to
perform a scientific analysis of the Dictaphone belt recording of
Channel I believed to have been recorded at about the time of the
assassination of President John F. Kennedy.

After listening to recordings of Dallas Police Department
Channels I and II including the five-and-one-half minute recording
made on Channel I when a police motorcycle transmitter was stuck
open, the BBN team found that noise on the recordings made it
difficult to determine conclusively that the noise-like sounds
recorded on November 22, 1963 were, in fact, the sounds of
gunshots. Indeed, the QC team later noted in their report to the
Select Committee on Assassinations that "... these sounds resembled
static much more than they did a gunshot ... [;however, the Dallas
Police Department] ... radio dispatching system was not designed to
handle sounds as intense as a gunshot ... [so] ... these static-
like sounds could be distorted gunshot sounds ... [or they] ...
could have been generated by a number of other sources, some
acoustic, some related to electrical or mechanical disturbances
..." Confronted with the noisy recordings, the BBN team concluded
that experiments to record the sounds associated with bullets fired
in Dealey Plaza might be usefully compared with the sounds recorded
on the noisy tapes which presumably contained acoustic evidence of
potential relevance in determining the number of gunshots fired in
Dealey Plaza as well as from which direction the shots were fired.

The BBN team conducted a series of over 400 test shots fired
in Dealey Plaza from both the Texas Schoolbook Depository and the
Grassy Knoll, with a variety of guns and bullets. (As shown, in
part, in Figure ZZZ which depicts the locations of three sets of
twelve microphones which were placed at various locations on
Houston and Elm Streets.) During these tests in August 1978 the
BBN team recorded the sounds of direct gunfire and the sounds of
echoes at a large number of locations on Houston and Elm Streets
along the route the presidential motorcade had taken in November
1963. The recorded sounds from these test shots were assumed to
closely reproduce the sound patterns that occurred under similar
conditions fifteen years earlier. Each of the over 400 test shots
examined by the BBN team produced a specific pattern of sounds at
each of the many microphone locations; each specific pattern of
sounds consisted of a time sequence of pulses of sounds determined
by the primary sound waves from each gunshot as well as by the
sequence of echoes following each primary sound. Thus, there is a
specific time sequence of sound pulses at each microphone which may
be thought of as a "fingerprint" for a gunshot fired at a given
location. By comparing all of the fingerprints collected from the
BBN test shots with the patterns of sounds on the relevant Channel
I and Channel II recordings made on November 22, 1963, the BBN team
carried out a search for evidence of gunshots. Their technique for
searching for assassination shots was to look for matches between
patterns of sound on Channels I and II that had pulse-like sound
peaks similar to those of the over 400 test shots.

In simplified terms, the BBN team defined a mathematical
prescription of determining how well the sounds of a given test
shot matched a given pattern of sound on the Channel I recording.
This mathematical prescription was used to determine a number,
known as a correlation coefficient, which was defined so that a
relatively good match resulted in a number close to one and a
relatively poor match produced a number close to zero; the
correlation coefficient was defined so that it was equal to one for
a perfect match and zero of a complete mismatch. Specifically, the
BBN team computed this correlation coefficient by counting the
number of large peaks that were within six one-thousandths of a
second (6/1,000 of a second) of each other and then by dividing by
the square root of the product given by the number of candidate
peaks in the fingerprint multiplied by the number of candidate
peaks in the sound patterns being examined. (The square root of a
number is another number such that this other number multiplied by
itself is just the original number; for example, the square root of
25 is 5 since 5x5 ("5 times 5") is equal to 25.) In each case, the
fingerprint was aligned manually relative to the pattern of sound
being analyzed. As an example, if the fingerprint and a similar
pattern of sound from Channel I or II each contained 4 large peaks
of which 3 peaks could be aligned simultaneously in matching pairs
(within 6/1,000 of a second), then the correlation coefficient, C,
was computed to be,

C = {3}/{Square Root of (4x4)} = 3/4 = 0.75.

Similarly, if the fingerprint contained 5 candidate peaks, a sound
pattern from a suspected assassination shot contained 4 candidate
peaks, and 3 of these peaks could be aligned simultaneously to
within 6/1,000 of a second, then the correlation coefficient, C,
was given by,

C = {3}/{Square Root of (5x4)} = 3/4.47 = 0.67.

Based on their full and detailed analysis the BBN team stated
in their report to the Select Committee that several "... echo
patterns from the acoustical reconstruction matched sufficiently
well with ... four impulse patterns that we were able to place the
motorcycle behind the Presidential limousine, at distances varying
from 120 ft to 160 ft ... [and] ... that four shots may have been
fired, as follows:

1. time 0.0 sec - one shot from the Texas School Book
Depository (TSBD) aimed between the limousine posi-
tions seen in frames 160 and 313 of the Zapruder
film

2. time 1.6 sec - one shot from the TSBD aimed near the
limousine position seen in frame 313

3. time 7.8 sec - one shot from behind the fence on the
knoll aimed near the limousine position seen in
frame 313

4. time 8.3 sec - one shot from the TSBD aimed between
the limousine position seen in frame 313 and the
triple underpass."

In a subsequent analysis the QC team provided a supplementary
analysis of a shot suspected of coming from the Grassy Knoll and
concluded that the results of their analysis supported "... the
following findings:

1. The recording very probably contains the sound of a
gunshot that was fired from the grassy knoll. The
probability of this event is computed to be at least
95 percent.

2. The microphone that picked up the sounds of the
probable gunshot was on Elm Street and was moving at
a speed of about 11 miles per hour in the same
direction as the motorcade. At the time the
probable gunshot was fired, the microphone was at a
point about 97 feet south of the TSBD and about 27
feet east of the southwest corner of the building.
(For both distances, the uncertainty is ñ 1 foot.)

3. The probable gunshot was fired a point along the east-
west line of the wooden stockade fence on the grassy
knoll, about 8 feet ñ 5 feet west of the corner of
the fence."

On the face of it, the separate findings of the BBN team and
the QC team seem to reinforce each other. However, on page 10 of
the BBN report to the Select Committee, BBN Report No. 3947
(reprinted beginning on page 33 of the Appendix to the Hearings
before the Select Committee on Assassinations of the U.S. House of
Representatives, Ninety-Fifth Congress, Volume VIII, Acoustics,
Polygraph, Handwriting, and Fingerprint Reports, U.S. Government
Printing Office, March 1979), a footnote concerning the time of the
shot identified by the BBN team as a probable grassy knoll shot
states, "The time was obtained from the independent study of Weiss
and Aschkenasy, and it differs by about 0.2 sec from the time
obtained by our correlation detector." This discrepancy was, of
course, obvious immediately to the Ramsey Committee as highlighted
by Dr. Richard L. Garwin, member of the Ramsey Committee and IBM
Fellow, in his contribution to the book Discovering Alvarez; Garwin
wrote ---

"The Ramsey Committee had met with the previous investigators
and had done enough analysis to question seriously the
identification of signals on Channel I as the imprints of
'shots' and to demonstrate that the stretch of noiselike
recording identified by the BBN workers as containing the
'shot from the grassy knoll' was displaced more than 200
milliseconds [more than 0.2 second] from that identified by
the Queen's College workers. Both sets of workers could not
be correct."

The National Research Council's Committee on Ballistic
Acoustics illustrated this difference graphically in Figure 2 of
its final report which is reproduced here as Figure WWW.
One of the principal lines of thought of the Ramsey Committee
was described by Richard Garwin in Discovering Alvarez where he
recalls, "It had occurred to some that evidence might
serendipitously be found on one of the two channels being recorded,
because a microphone on one of the mobile radios was stuck in the
'on' position for many minutes at about the time of the
assassination. If the vehicle with the mobile radio had been in
Dealey Plaza at the time of the assassination, it could well have
recorded important evidence for constructing or refuting a
hypothesis of the assassination." This line of inquiry did indeed
have a major influence on the outcome of the Ramsey Committee's
work as explained in the Report of the Committee on Ballistic
Acoustics:
"A private citizen, Steve Barber of Mansfield, Ohio,
voluntarily wrote to the Committee that he was convinced from
his own listening that there are clear instances in which
phrases recorded on Channel II tape were distinctly audible on
the Channel I tape as well. This is quite naturally explained
by assuming that the motorcycle with the open microphone
(Channel I) was near another police radio receiving a
transmission from Channel II, so that transmissions over
Channel II would issue from its loud speaker and be picked up
by the open microphone and rebroadcast on Channel I. In
addition there are simultaneous broadcasts by the dispatcher
onto Channels I and II. Both kinds of cross talk are
perfectly clear in many cases. The existence of such
identical portions of speech on both channels would allow one
to establish precise time synchronizations between specific
portions of the two recordings. The specific time
synchronizations would not apply to the recording in their
entirety, because Channel I ran continuously during the period
of interest while Channel II was sound activated and operated
intermittently. However, such matching features would enable
one to determine the relative timing between many events on
Channel I and other events on Channel II.'

















'Barber identified several such matching sections on the two
tapes. Four of them are quite clear, but they occur several
minutes after the assassination and involve various police
communications connected with the follow-up to the shooting;
however, they demonstrate clearly that there was cross talk
from Channel II to Channel I. As will be seen, they also
provide a clear demonstration of Channel I heterodynes*

---

* These so-called heterodynes are tones with a narrow range of
sound frequencies. The narrow tones were generated (when Channel
II radio transmissions were received on Channel I) by the
difference between the carrier frequencies for Channels I and II.
The Dallas Police Department (DPD) radios contained automatic gain
control circuits that automatically suppressed radio signals that
increased suddenly. For great importance is the fact that the
Ramsey Committee verified that this automatic suppression (of
recording onto Channel I of the cross talk originating from Channel
II) was triggered by the heterodynes of Channels I and II. By
noting that this automatic suppression occurred rapidly (in a few
hundredths of a second as expected for the DPD automatic gain
control circuits), the Ramsey Committee demonstrated that the cross
talk was indeed received through the DPD radio system rather than
recorded, intentionally or unintentionally, on the original tape at
a later time. In the case of a simple over-recording the sound
level would not be suppressed; it would simply be recorded "on top
of" whatever sounds were already on the tape.
suppressing the recording onto Channel I of cross talk from
Channel II, which suppression we later also show exists in the
interval containing the impulses and shows that the cross talk
was recorded through a radio receiver. Two events are
especially important for fixing the time of the section of
tape analyzed by BRSW [James Barger, Scott Robinson, Edward
Schmidt and Jared Wolf] and WA [Mark Weiss and Ernest
Aschkenasy] relative to the assassination. The first is a 4-
second fragment of speech that overlaps the conjectured 3rd
and 4th BRSW shots on Channel I. Barber there identifies a
phrase, which he says begins with the words 'hold everything
...' as identical to the phrase '... hold everything secure
until the homicide and other investigators can get there...,'
clearly recorded on Channel II. The significance of this
proposed match is that the section on Channel I is concurrent
with the last two of the conjectured BRSW shots, whereas on
Channel II that communication is part of a clear sequence of
emergency communications that followed the shooting and
occurred approximately one minute after the assassination. It
is, in fact, part of Sheriff Decker's instructions to his men
in response to the assassination. This time synchronization,
if correct, would prove that the BRSW/WA conjectured shots
were unrelated to the sounds of the assassination gunshots.
The section of Channel I recording with the BRSW/WA
conjectured shots would then correspond to a period of time
well after the assassination.'
'The second crucial event is the transmission 'You want me ...
Stemmons', which occurs several minutes after the
assassination and is clearly intelligible on both channels.
It provides a common reference point for timing events on the
two channels. We used it to determine whether the section of
the recording containing the conjectured shots occurred before
or after Chief Curry instructed the motorcade to 'Go to the
hospital.'"

Since many members of the Ramsey Committee were not convinced
that they could hear the "hold everything" phrase identified by
Barber, the Committee felt that it was essential to obtain access
to sophisticated equipment that could aid in the demonstration that
Steve Barber had indeed identified phrases proving that there was
cross talk between Channels I and II. Specifically, and without a
doubt to the dissatisfaction of those who question the Executive
Branch's unbiased role in the matter of the assassination of
President Kennedy, the Committee used such equipment at the Federal
Bureau of Investigation (FBI) --- but steps were taken to ensure
that Committee members supervised the use of the FBI equipment. In
addition, and of great importance to many observers, the Ramsey
Committee also digitized and analyzed the Channel I and Channel II
recordings in separate studies that did not involve the use of the
FBI equipment. As explained in the National Research Council's
Report on the Committee of Ballistic Acoustics:

"Initially, the poor quality of the 'hold everything...'
portion of the recording made it appear unlikely that a convincing interpretation of the badly garbled speech on Channel I coul=
d be made and the Committee was aware of the power of suggestion, or cueing effect, in which a listener to
a garbled message will often be convinced he has heard what he
has been coached to hear.'

'For these reasons, arrangements were made through Bruce
Koenig and others of the FBI Technical Services Division for
members of the Committee to utilize the Division's excellent
sound analysis equipment to obtain sound spectrograms
("voiceprints") of the relevant communications on Channels I
and II. The spectrograms were prepared under the supervision
of the Committee members."

The sound spectrograms prepared under the supervision of the
Ramsey Committee members were in the form of charts containing
plots of the sound frequency along the vertical axis and the times
at which the sounds were recorded along the horizontal axis; the
intensity (or magnitude) of the sound at a given frequency is
indicated on the spectrogram by the darkness of the plot at that
frequency. The sound spectrograms of the all-important "... hold
everything ..." phrase are reproduced from Figure 4 of the Ramsey
Report as Figure WSWS; in these spectrograms the black dots denote
27 separate features that are found to be in common in both
spectrograms. Since the recorders for Channels I and II were
operating at slightly different speeds --- times appear to be 6.7%
longer on Channel I than on Channel II --- a 6.7% "scaling" or
"shrinking" of Channel I had to be performed (by speeding up
Channel I) relative to Channel II to obtain the charts of Figure
WSWS. To examine the possibility that Channel I contained the
cross talk from Channel II, the Ramsey Committee constructed a plot
of the times of the 27 separate features; in their plot, which is
shown as Figure QYQ, the vertical axis is labelled by the times,
T', at which the 27 features occur on Channel I and the horizontal
axis is labelled by the times, T", at which the 27 features occur.
The 27 special features are indeed present on both recordings at
the same adjusted times --- that is, they fall on a straight line
in Figure QYQ --- and Steve Barber's claim of being able to hear
"... hold everything ..." as cross talk was thus given extremely
great credibility by the analysis of the Ramsey Committee. (The
one point in Figure QYQ, at T" = 1.195 seconds, that does not
appear to be a perfect match is for the incorrectly identified
characteristic "I" as discussed in the Committee's final report.)
The Ramsey Committee performed a statistical analysis to calculate
the probability "...of obtaining such close agreement by random
occurrence of the features at their observed average spacing..."
would be about 2 in ten trillion (2 in 10,000,000,000,000). In
other words, for all practical purposes the 27 features would not
be so precisely correlated in time as a result of chance. The only
explanation that makes sense is that the sound features had a
common origin and were recorded as cross talk between the two
channels. (Since suppression due to heterodyning is evident in the
recordings, there is no possibility that the cross talk was simply
due to the intentional or unintentional recording of Channel II
onto Channel I at some time after Channel I had been initially
recorded.)

As an independent verification of these results, the Ramsey
Committee performed two additional analyses of the Channel I and
Channel II recordings during the time interval containing the
"...hold everything..." phrase: first, they determined the
frequency ratios for a number of the distinct features in the
spectrograms of Channels I and II; and, second, as described in
"Signal Processing Analysis of the Kennedy Assassination Tapes," by
R. C. Agarwal, R. L. Garwin and B. L. Lewis, one of the Committee
members, Dr. Richard L. Garwin and two of his colleagues, performed
a digital analysis of the data that permitted sound spectra to be
constructed without using the FBI equipment needed to produce the
spectrograms. The results of the first study revealed that the
frequency ratio was consistent with a 6.7% difference in the speeds
of the recorders. The second study the digitized data were used to
calculate correlations between the spectra of Channels I and II;
these results confirmed the conclusion that there was cross talk at
the time of the "...hold everything..." phrase.

The National Research Council's Committee on Ballistic
Acoustics concluded its study with unanimous agreement that:

"The acoustic analyses do not demonstrate that there was
a grassy knoll shot, and in particular there is no
acoustic basis for the claim of 95% probability of such
a shot.'

'The acoustic impulses attributed to gunshots were
recorded about one minute after the President had been
shot and the motorcade had been instructed to go to the
hospital.'

'Therefore, reliable acoustic data do not support a
conclusion that there was a second gunman."

These conclusions are clear and, in my view, they are not
open to serious doubt; however, these conclusion are supported
further by comparing the times of possible bullet sounds as given
by the Alvarez analysis with those of the BBN analysis. According
to the Alvarez analysis, there must be an angular acceleration of
the Zapruder camera's optical axis about its nominal pointing
direction for one of the following times:

- when the bow shock or muzzle blast interacts directly with
the camera;

or,

- about one-third second (the time expected for a
neuromuscular response to the sound of a bullet)
after the sound of a bullet reached A. Zapruder's ears.

Since the frame rate of A. Zapruder's camera was 18.3 frames per
second, these times for expected angular accelerations should be
within about six frames of each other. Figure PPP shows when the
bullets would have been fired according to the Bolt, Beranek and
Newman, Inc. analysis of the Dallas Police Department radio
recording which was shown by the National Academy of Sciences to
have been recorded about one minute after the assassination of
President Kennedy. The comparison is made for two separate cases:
the last BBN shot is assumed to be at frame 313 and; the next to
the last BBN shot is assumed to be at frame 313. In either case
there is not a consistent match even if one assumes that a silencer
was used on some of the guns firing shots.

Stated another way, the analyses presented in this Chapter
lead to the conclusion that there is no known recording of the
sounds in Dealey Plaza, Dallas, Texas during the few seconds of
time when shots were being fired. The findings of the Ramsey
Committee do not support or refute the single-gunman theory; they
simply underscore the absence of any known recording of the sounds
in Dealey Plaza when shots were being fired at the presidential
motorcade. Indeed, the Ramsey Committee concluded that the time
interval when the Channel I microphone was stuck open occurred
after the President had been struck by bullets. Channel II which
had been reserved for communications of the presidential motorcade
was inactive during the period when shots were fired in Dealey
Plaza. The hand-held movie recorders used by Zapruder, Nix and
Muchmore did not record sounds; they recorded silent frames
consistent with the norm in 1963. In short, there is no known
acoustic evidence bearing on the assassination of President John F.
Kennedy.
















EPILOGUE

The scientific evidence embodied in the jerking episodes of
A. Zapruder's camera and the supporting visual clues in the
Zapruder film cannot be explained credibly by the three-bullet,
single-gunman theory of the Warren Commission. Indeed, the
combined evidence of the jerking episodes and visual clues lends
support to the conspiracy theory where there were two or more
gunmen with at least one gunman firing bullets from the general
direction of the Grassy Knoll. Similar conclusions are reached
through the independent analyses of the photographic evidence by
Robert Groden as presented in the Killing of a President and the
medical evidence by Charles Crenshaw as presented in JFK:
Conspiracy of Silence. These recent works are, of course,
supplemented by the numerous findings of the pioneer in the
investigation --- Harold Weisberg; Weisberg's recent book Case
Open, provides an extremely enlightening and insightful discussion.

I believe it is important to expose to the American public
the insights gained by applying the Alvarez analysis to the frames
of the Zapruder film which were ignored by the Warren Commission.
In my view, these new findings make it impossible to accept the
single-gunmam, three-bullet theory of the Warren Commission. As an
established physicist with a substantial record in research,
government service and teaching at the university level, I have
been reluctant to publish these new insights because they are not
as reliable as those gained in the normal research environment
where experiments can usually be repeated to verify and test the
theory describing the phenomena in question. I have also been
reluctant because of bizarre events surrounding the assassination
of President Kennedy such as the large number deaths among those
who could potentially have been witnesses in the case. My fear in
this regard has been overcome by my sense of responsibility as well
as by the example set by the life of President John Fitzgerald
Kennedy and his words in Profiles in Courage:


"In whatever arena of life one may meet the challenge of
courage, whatever may be the sacrifices he faces if he follows
his conscience - the loss of his friends, his fortune, his
contentment, even the esteem of his fellow men - each man must
decide for himself the course to follow. The stories of past
courage can define that ingredient - they can teach, they can
offer hope, they can provide inspiration. But they cannot
supply courage itself. For this each man must look into his
own soul."
















For all those whose cares have been our concern,

the work goes on, the cause endures, the hope still lives,

and the dream shall never die.


=
Edward Moore Kennedy


























SELECTED BIBLIOGRAPHY

Alvarez, Luis W., "Search for Hidden Chambers in the Pyramids using
Cosmic Rays," in Adventures in Experimental Physics, edited by
Bogdan Maglich, 1st issue, pages 157 to 186, publ. by World
Scientific Communications, Princeton, New Jersey, 1972.

Alvarez, Luis W., "A Physicist Examines the Kennedy Assassination
Film," American Journal of Physics, Vol. 44, page 813, 1976.

Agarwal, R. C., Garwin, R. L., and Lewis, B. L., "Signal Processing
Analysis of the Kennedy Assassination Tapes," IBM Research Report
RC 9771, IBM T. J. Watson Research Center, Yorktown Heights, NY,
December 27, 1982.

Davis, John H., "The Kennedy Contract," New York, Harper
Paperbacks, Harper Collins Publishers, 1993.

Crenshaw, Charles A. (with Jens Hansen and J. Gary Shaw), "JFK:
Conspiracy of Silence," New York, Signet, Penguin Books, 1992.

Edgerton, Harold E., Electronic Flash, Strobe, Massachusetts
Institute of Technology Press, Cambridge, 1992.

Edgerton, Harold E., and Killian, James R., Jr., Moments of Vision:
The Stroboscopic Revolution in Photography, Massachusetts Institute
of Technology Press, Cambridge, 1979.

Garrison, Jim, On the Trail of the Assassins, New York, Warner
Books, Inc., 1991.

Garwin, Richard L., Examining the Kennedy Assassination Evidence,
pages 203 to 209 in Chapter 18 of Discovering Alvarez: Selected
Works of Luis W. Alvarez with Commentary by His Students and
Colleagues, edited by W. Peter Trower, 1987?

Garwin, Richard L., "Acoustic Evidence in the Kennedy Shooting
Fails," Letter to the Editor, New York Times, March 28, 1992.

Glass, I. I., Shock Waves & Man, Toronto, University of Toronto
Press, 1974.

Groden, Robert J., The Killing of a President, Viking Studio Books,
published by the Penguin Group, Penguin Books USA, New York, 1993.

Harlow, Francis H.,and Amsden, Anthony A., Fluid Dynamics, Los
Alamos Scientific Laboratory Report LA-4700, UC-34, June 1971.

JFK Assassination: Trial Exhibits, film prepared by Spectus
Technologies, Visual Engineering Services, 149 Commonwealth Drive,
Menlo Park, CA 94025, December 1992; this 30-minute film contains
segments of the Zapruder film as well as visual exhibits and
analyses of Spectus Technologies used in the American Bar
Association's 1992 Mock Trial of Lee Harvey Oswald.

Kennedy, John F., Profiles in Courage, Harper and Brothers, New
York, 1956.

Life, "A Matter of Reasonable Doubt," Vol. 61, No. 22, pages 39-53,
November 25, 1966.

Lifton, David S., Best Evidence: Disguise and Deception in the
Assassination of John F. Kennedy, Carroll & Graf Publishers, 1988.

Marrs, Jim, Crossfire: The Plot that Killed Kennedy, New York,
Carroll & Graf Publishers, Inc., 1989.

Olson, Harry F., Music, Physics and Engineering, Dover
Publications, Inc., New York, 1967.

Ramsey, N. F., Alvarez, L. W., Chernoff, H., Dicke, R. H., Elkind,
J. I., Feggeler, J. C., Garwin, R. L., Horowitz, Johnson, A.,
Phinney, R. A., Rader, C., and Sarles, F. W., Report on the
Committee on Ballistic Acoustics, National Academy Press,
Washington, DC, 1982; also summarized in Science, Volume 218, page
127, 1982.

Report of the President's Commission on the Assassination of
President John F. Kennedy, Investigation of the Assassination of
President John F. Kennedy, with twenty-six volumes on Hearing and
Exhibits, U.S. Government Printing Office, 1964; of special
interest is Volume XVIII, Exhibits 885 to 1053, which contains
photographic reproductions of frames 171 to 334 of the Zapruder
film as well as selected photographic reproductions of selected
frames of the Nix and Muchmore films along with photographs of the
Commission's re-enactment; also published by Associated Press,
Bantam, Doubleday, McGraw-Hill, and Popular Library, 1964.

Report of the Select Committee on Assassinations, U.S. House of
Representatives, Investigation of the Assassination of President
John F. Kennedy, with supporting appendices and volumes on
Hearings, U.S. Government Printing Office, 1979; of special
interest is the Appendix to the Hearings before the Select
Committee on Assassinations of the U.S. House of Representatives,
Ninety-Fifth Congress, Volume VIII, Acoustics, Polygraph,
Handwriting, and Fingerprint Reports, U.S. Government Printing
Office, March 1979; the Report was also published by Bantum, New
York, as The Final Assassination Report, 1979.

Report of the U.S. Secret Service on the Assassination of President
Kennedy, U.S. Treasury Department, Washington, DC, 1964; on file at
the National Archives, Washington, DC and available to the public
since declassification in 1965.

Stiefel, Lugwig, editor, Gun Propulsion Technology, Vol. 109 of
Progress in Astronautics and Aeronautics, published by the American
Institute of Aeronautics and Astronautics, Inc., Wash., DC, 1988.

Stroscio, Michael A., "Extended Time-Series Analysis of Angular
Accelerations of a Levitated Object due to the Interaction with a
Shock Front," Bulletin of the American Physical Society, Vol. 39,
No. 8, 1808, 1994; this brief abstract contains a graph depicting
the angular acceleration of Mr. Zapruder's camera between frames
150 and 170; see also, Stroscio, Michael A., "Analysis of the Time-
Series of Angular Accelerations of A Levitated Object Interacting
with a Conical Shock Wave," Bulletin of the American Physical
Society, Vol. 39, No. 9, 1864, 1994.

Weisberg, Harold, Case Open, Carroll & Graf, Inc., New York, 1994;
see also the numerous other books by Harold Weisberg as referenced
in Case Open; Weisberg is in fact given credit by L. Alvarez in his
1976 American Journal of Physics article as being the first person
to attribute significance to the streaking of the Zapruder film.

Whitham, G. B., "The Behavior of Supersonic Flow Past a Body of
Revolution, Far from the Axis," Proceedings of the Royal Society,
Series A, Volume 201, pages 89-109, 1950.

Whitham, G. B., "The Flow Pattern of a Supersonic Projectile,"
Communications of Pure and Appl. Math., Vol. 5, pp. 301-348, 1952.
Appendix A
THE LAWS OF PHYSICS TELL US MUCH ABOUT THE MOTION
OF MR. ZAPRUDER'S CAMERA
AND
ABOUT THE RECOIL OF PRESIDENT KENNEDY'S HEAD

The changes in the lengths of the streaks between the
adjacent frames of Mr. Zapruder's film correspond to the angular
accelerations of the camera axis during the interval of time
passing between frames. The brilliant analysis of Luis Alvarez
relates these angular accelerations to the forces on Mr. Zapruder's
camera. One type of force, albeit weak, (cf. Appendix B) exerted
on Mr. Zapruder's camera was that due to the pressure of the shock
waves of the bullets fired in Dealey Plaza as he filmed the
President's motorcade. Still another type of force was that due to
muzzle blast waves emanating from the barrel blast waves that
travel away from the weapon's muzzle at the speed of sound. As
discussed previously, both the bow shock and a muzzle blast are
normally expected to be present when a supersonic bullet is fired.
These waves exert a brief, direct pulse of pressure on any object
in the direct line of sound of the weapon --- such objects may be
a hand-held camera like Mr. Zapruder's or the eardrums of people
listening to gunfire. Still other rapid motions --- probably most
of the "rapid motions" --- of Mr. Zapruder's camera were caused by
forces such as those exerted by Mr. Zapruder during his muscular
reactions to the sound of a bullet being fired. To understand the
details of how Mr. Zapruder's camera moved in response to each of
these forces, it is necessary to apply the laws of physics
governing the motion of bodies.

Before the time of Sir Issac Newton, the motions of bodies
such as the planets, comets and the pendulum of a clock were not
understood in detail and important quantities describing these
objects --- like position, velocity and acceleration --- could not
be predicted mathematically. But with the enormous awakening
brought about by the discovery of Newton's laws all of these
quantities could be calculated and, even more important in many
practical situations, they could be related to each other and the
forces causing the motion. These laws tell us how the forces
exerted on a body are related to the acceleration of the body as
well as its velocity and the changes in its position. The ability
to relate these quantities has had an enormous impact on modern
society in uncountable endeavors such as civil engineering,
mechanical engineering, and space flight. Newton's laws allow us
to analyze the motion of an object and to verify that its apparent
motion is consistent with the laws of nature. Of special
significance to us, these laws permit us to study the motion's of
Mr. Zapruder's camera and to determine if the camera's
acceleration, velocity and position at a specific instance in time
are consistent with each other and if they have the values expected
for an object subjected to a force of a certain magnitude.

Armed with the laws of motion we can verify that the
acceleration of Mr. Zapruder's camera is consistent with the force
associated with the shock front of a passing bullet or that the
changes in the position of the camera as time passes are consistent
with the velocity of the camera. Relating the position to the
velocity may not seem important and, in fact, it can usually be
assumed since the velocity is defined as the time rate of change of
the position! Consider, however, the possibility that someone
altered the presentation of the Zapruder film by --- say, for
example --- publishing the still pictures of each frame with some
frames interchanged from their proper time sequences as was done in
the Warren Commission Report with frames 314 and 315 of the
Zapruder film; the laws of motion permit us to check instantly for
such inconsistencies. They also allow us to check that individual
frames have not been moved to the left or to the right to create
and illusion.

As an example if uncovering such inconsistencies, Luis
Alvarez in his American Journal of Physics article states that by
applying the laws of motion he could relate the pointing direction
of Mr. Zapruder's camera to the direction of the velocity of the
camera about its axis except in for one pair of frames --- frames
314 and 315. Alvarez states, "A closer examination showed that the
numbering of these frames had simply been interchanged in the
'exhibits' ...." Dr. Alvarez had thus used the laws of motion to
demonstrate almost trivially that the motions apparent in these
frames were not consistent with the laws of nature! It is now well
known that the Federal Bureau of Investigation (FBI) did in fact
interchange frames 314 and 315 of the Zapruder film in the
"exhibits" of the Warren Commission Report. The published and
widely-distributed Warren Commission Report is a living testament
to the error made by the FBI. Incidentally, interchanging frames
314 and 315 makes it appear that President Kennedy's head moves
forward instead of backward after being struck by a bullet.

In this Appendix, we will consider the possibility that
frames of the recorded have been altered -- by artifically moving
them to the right or left --by examining the pointing directions
and the velocities of Mr. Zapruder's camera as revealed by frames
151 to 168 of various copies of the Zapruder film. By
demonstrating that these quantities are consistent we can at the
very least increase our confidence that the film has not been
altered in ways that produce deceptive information concerning the
motion of Mr. Zapruder's camera. As we will argue, Mr. Zapruder's
camera executes motion during frames 151 to 168 that are consistent
with the interaction of a shock wave from a bullet emanating from
the right side of Mr. Zapruder's camera --- that is, from the
direction of the Grassy Knoll in Dealey Plaza.

For all forces, including those exerted on Mr. Zapruder's
camera, it is known from the laws of physics that any force on an
object is related directly to the acceleration of the object. This
is a statement of Newton's Second Law of Motion, published in the
year 1687. To supplement this law we need a law of motion dealing
with situations where there are no forces; this supplementary law
is known as Newton's First Law and is a restatement of Galileo's
Principal of Inertia: if an object is not disturbed by the presence
of forces it will continue to move with a constant velocity in a
straight line if it was moving originally; if it was not moving in
the first place it will continue to remain at rest as long as no
forces act on the object. A familiar example of Newton's First Law
is a hockey puck moving across a sheet of ice with no apparent
change in velocity.

The great majority of our analyses of the motions of Mr.
Zapruder's camera are based on Newton's Second Law which may be
reformulated as a statement that the motion of an object is changed
by forces as follows: the time-rate-of-change of a quantity called
momentum is proportional to the force. Momentum is defined as the
product of an object's mass, m, times its velocity, v. For a fixed
velocity, less massive objects have smaller values of momentum and
more massive objects have larger values of momentum. The mass of
an object is a basic measure of its inertia. The mass of an object
represents a basic property of the object as distinct from its
weight; indeed, the weight of an object is identical to the
gravitational force acting on the object. Thus, an object of a
given mass will weigh more on the earth than it does on the moon
where the gravitational attraction is smaller than on the earth;
however, the mass does not change. In exactly the same manner a
person in a supersonic fighter jet can weigh several times his or
her weight on earth in situations where the jet is "pulling several
Gs" as a result of rapid accelerations of the jet; the person's
mass does not change, but the person's weight changes in accord
with Newton's Second Law.

In the metric system of units, the distance, d, is measured
in units of the meter, abbreviated as m, and mass is measured in
units of the kilogram which we abbreviate as kg. Velocity, v, is
measured in meters per second, abbreviated as m/sec; the
acceleration, a, which is the time-rate-of-change of the velocity
is measured in meters per second per second, abbreviated as m/sec2.
In the metric system, force, F, is measured in units of the Newton,
abbreviated as N. The metric system of units is sometimes called
the mks system based on the use of the meter-kilogram-second
quantities. Comparisons with the perhaps more familiar system of
units based on the foot-pound-second, or fps, system may be useful.
For purposes of comparison, the meter is a little over 3 and 1/4
feet in length and a mass of one kilogram accelerated at one G
produces a force, or equivalently a weight, of about 2.2 pounds.

In our analysis of the Zapruder film it will be convenient to
calculate velocities and accelerations using approximate formulas
giving rough estimates that scientists frequently refer to as "back
of the envelope" results. As shown in Figure PAM', small
deflection of a hand-held camera in the amount, d', at the front
edge of the camera produces an apparent motion, d, in a scene when
the scene is a distance, l, from the camera. Suppose the apparent
motion during the exposure time of frame i is from an initial
position d(1,i) to final position d(2,i); the average velocity,
v(i), of the apparent motion for frame i is then,

v(i) = {d(2,i) - d(1,i)}/{1/30 second).

In words our simple equation states that the approximate apparent
velocity associated with frame i is the time-rate-of-change of the
displacement during the exposure time of 1/30, one-thirtieth, of a
second. Here we adopt Luis Alvarez's convention that clockwise
displacements as seen from looking down on the camera are positive;
counterclockwise displacements are taken as negative. Thus, the
average velocity of the apparent motion is positive if the camera's
optical axis experiences a net motion to Mr. Zapruder's right;
likewise, velocities are negative if the net motion of the camera's
optical axis is to the left. Keeping track of these positive and
negative signs is an essential part of the proper application of
the laws of motion. Without these signs, the correct relationships
between displacement, velocity and acceleration cannot be
maintained from frame to frame. Put more directly, it is
impossible to satisfy the laws of nature if these signs are
ignored. The Alvarez analysis includes these signs and as stated
previously an inconsistence in the sign of the left-right motion of
the camera's optical axis allowed Luis Alvarez to conclude that
frames 314 and 315 had been reversed in the Warren Report. The
techniques used by W. K. Hartmann and F. Scott to analyze the
motions of Mr. Zapruder's camera included magnitudes of streak
lengths and changes in pointing directions but they did not include
such positive and negative signs; accordingly, their techniques
must be viewed as signal detection methods and not as
representations of the physical processes governing the camera's
motion. In particular, the absence of the directional information
associated with signs makes it impossible to use the Hartmann or
Scott techniques to determine the directions of the forces causing
the motions of Mr. Zapruder's camera. This is not, in principle,
the case with Luis Alvarez's physically based analysis.

Adopting our "back of the envelope" treatment for the case of
acceleration, it follows by analogy that the apparent acceleration,
a(i + 1/2), between frames i + 1 and i is,

a(i + 1/2) = {v(i + 1) - v(i)}/{1/18.3 second};

in words this equation states that the apparent acceleration in a
scene at distance, l, from the camera during the time interval
between frames i + 1 and i is the time-rate-of-change of the
velocity between frames i + 1 and i. In this equation the index i
+ 1/2 is used to indicate that the approximate acceleration is
being calculated at the instant in time midway between the two
frames denoted by i + 1 and i. Now for a constant mass, m, the
time-rate-of-change of the momentum is just the product of the mass
and the time-rate-of-change of the velocity; thus, Newton's Second
Law of Motion may be stated as follows:

F(i + 1/2) = m * a(i + 1/2),

since the mass times the acceleration is identical to the time-
rate-of-change of the momentum for the case of a constant mass. In
our case the mass is indeed constant since Mr. Zapruder's camera
did not change its mass during his filming at Dealey Plaza. (In
some cases such as during the launch of a rocket the mass of the
rocket does change so the proper application of Newton's Second Law
requires that the mass not be treated as a constant; however, we
have no such concern in our analysis of the Zapruder film.)

In our calculations of v(i) and a(i + 1/2) the apparent
values of these quantities have been obtained for a scene a
distance l from the camera. That is, the calculations were based
on the apparent displacements d(2,i) and d(1,i) rather than the
actual displacements d(2,i)' and d(1,i)' at the front edge of the
camera. Since the angular displacement of the camera's optical is
the same irrespective of the distance from the camera, it
inconvenient to consider such angular displacements. The angle
between the axes pointing to the positions d(2,i) and d(1,i) is
given by {d(2,i) - d(1,i)}/l; when d(2,i) - d(1,i) is equal to l
the angle has a value of one radian or, equivalently, about 57
degrees. In exactly the same manner the angular velocity is
defined by v(i)/l and the related angular acceleration is defined
by a(i +1/2)/l. Thus, to convert apparent displacements,
velocities and accelerations to angular displacements, velocities
and accelerations, it is necessary only to divide by the by
"apparent" values by the distance l. It is these angular
velocities and accelerations that Luis Alvarez used in his original
analysis.

Figure NNN and the Table of Streak Lengths both show that
there was a significant angular acceleration of Mr. Zapruder's
camera between frames 151 and 168. Now that we are armed with an
understanding of the laws of motion, it is possible to check that
the apparent displacements and apparent velocities are consistent
with each other. If, as examples, some of the frames had been
interchanged or displaced to the right or the left relative to
other frames, the time-rate-of-change of the displacement would
not, in general, equal the appropriate velocity. The measured
streak lengths and the associated positive and negative signs
provide estimates of the average apparent velocities for each
frame. In addition, the time-rate-of-change of the measured
apparent displacements provide an independent estimate of the
average apparent velocities. By comparing the apparent velocities
determined from these two sets of independent measurements it is
possible to check that the angular displacements and velocities are
consistent with each other.

During the time interval from frame 151 to 168 of the
Zapruder film the President's automobile was about 150 feet from
Mr. Zapruder and was moving down Elm Street from his left to right.
On the edge of Elm Street with his back to Abraham Zapruder's
camera was a man wearing a black hat. As frames 151 to 168 were
recorded, the President's automobile moved past this man in such a
way that at the time frame 157 the front wheel of the automobile
passed the imaginary line drawn between Abraham Zapruder and the
man with the black hat. Prior to frame 157 the wheel is to the
left of the man's black hat as viewed by A. Zapruder and after
frame 157 the wheel is to the right of the man's hat. Now, if A.
Zapruder had panned his camera with perfect precision the man with
the black hat would have moved from the right side of the film to
the left side with roughly a constant speed; that is, he would move
to the left about an equal amount every 1/18.3 of a second --- the
time corresponding to the interval between frames. On the other
hand, any angular acceleration on the camera would be reflected in
deviations about this hypothetical constant speed. In Figure QQQ
the positions of the man's hat are plotted for frames 151 to 168.
The apparent motion of 5 feet or, equivalently, about 1.5 meters
between frame 151 and 168 is expected based on the automobiles
approximate speed and its oblique direction of travel relative to
A. Zapruder's line of sight. (Based simply on speed, the distance
traveled between frames 151 and 168 was about 14 feet but the
apparent distance was only 5 feet since the automobile was moving
at an oblique angle to Mr. Zapruder's line of sight.) In Figure
QQQ a straight line has been drawn between the positions at frames
151 and 168. Since the initial frame, frame 151, and the final
frame, frame 168, do not contain pronounced streaks it is assumed
that the tracking during the exposure time of each of these frames
was highly accurate. Accordingly, at any frame between frames 151
and 168, man's black hat should always fall on the line connecting
these points. However, from Figure QQQ it is clear that for many
of the frames in question the man's hat appear to the right of the
expected position for perfect panning. In other words, the optical
axis of the camera is pointing to the left of the direction
expected for perfect panning. Furthermore, during the roughly one-
tenth of a second between frames 152 and 154 the apparent
displacement of the scene at the automobile is about one foot.
This could occur in at least two ways: the camera was pushed to the
left and the automobile thus appeared to move to the right or,
alternatively, these frames were artificially moved to the right
with the consequent illusion that the automobile moved to the
right. There is a significant difference between these two cases:
if the camera was pushed to the left, the images in these frames
should, in general, contain streaks since the camera's optical axis
could not have been panned properly during the exposure time of
each frame; however, if the frames for the actual film were moved
physically to the right through advertent or inadvertent tampering
with the film, streaks would not necessarily be present. To check
that the average velocities calculated from the observed
displacements are consistent with the observed streak lengths a
Table of these quantities is constructed. Since the displacements
of the camera appear to be to the left the displacements are taken
as negative and the apparent displacement in frame 160 is taken to
have a magnitude of about one unit. This arbitrary choice of the
magnitude is convenient since it is about one-eighth of the
magnitude of the displacement of frame 157 which exhibits the
maximum magnitude of any frame in the interval being considered.
Assigning displacement magnitudes accordingly, calculating the
corresponding average velocities from our "back of the envelope"
approximation" and referring to Table of Streak Lengths our new
Table is constructed. By comparing the calculated velocities (*)
with the measured "streak-length" velocities it is clear that there
is good tracking between the two sets of numbers and the signs
agree in all cases. The fact that the signs agree is convincing
evidence that the actual time-rate-of-change of the displacement is
consistent with the measured velocity for any particular frame.
The absolute magnitudes of the two velocities should, in fact, be
different since our assignment of one unit of displacement to frame
160 is arbitrary and has no specific relationship to the arbitrary
set of streak lengths selected when the separate Table of Streak
Lengths was constructed. We have merely picked arbitrary units in
the two cases.




Frame Displacement Velocity (*) Streak Length (+)

152- 2
153- 2 (-2) - (-2) = 0 -0.5
154- 6 (-6) - (-2) = -4- 3.5
155 ? (Missing Frame)
156 ? (Missing Frame)
157- 8
158- 6 (-6) - (-8) = +2 +2.5
159 0 ( 0) - (-6) = +6 +3.5
160- 1 (-1) - ( 0) = -1- 2.5
161- 2 (-2) - (-1) = -1- 2.0
162- 4 (-4) - (-2) = -2- 3.0
163- 3 (-3) - (-4) = +1 +2.5
164- 2 (-2) - (-3) = +1 +2.5
165 0 ( 0) - (-2) = +2 +3.5



The rough agreement between the two independently determined
velocities for each of these frames provides good evidence that the
apparent motions of the Zapruder camera actually represent the
motions of his camera when he was filming frames 152 to 165 on
November 22, 1963. In other words, the laws of motion have
provided a way for us to check that selected frames of the film
were not advertently or inadvertently shifted to the right or the
left of the original positions they occupied immediately after A.
Zapruder recorded the movement of President Kennedy's limousine on
November 22, 1963. The same laws of motion allowed L. Alvarez to
relate the streaking in A. Zapruder's film to forces on his hand-
held camera! The beauty of the laws of motion is that they provide
consistent relationships between displacements, velocities and
accelerations which allow us to determine that apparent motions of
A. Zapruder's camera are those required by the physical laws of the
universe.

To conclude this Appendix the last of Newton's Laws, Newton's
Third Law, is explained briefly and applied to explain the fact
that President Kennedy's head moved violently toward the rear of
the presidential limousine starting at frame 314 of the Zapruder
film. Newton's Third Law states that for every driving force there
is an opposite reactive balancing force. Stated differently, if
all active and reactive forces are taken into account the sum of
all the forces is zero. Since Newton's Second Law relates force to
the time-rate-of-change of momentum, it follows that the total
momentum must be constant (since the total force is zero and the
time-rate-of-change of a constant is zero) or, mathematically,

Sum of all "sources" of momentum = A Constant.

This mathematical statement is frequently referred to as the law of
conservation of momentum and it has been applied and verified
widely in many branches of physics; it is one of the cornerstones
of modern physics. Following the approach taken by Alvarez in his
American Journal of Physics article, consider the "system"
consisting of a moving bullet and a stationary mellon. Before the
impact of the bullet, the total momentum is given by the momentum
of the bullet alone (since the mellon's momentum is zero as a
consequence of the fact that the mellon's velocity is initially
zero); that is,

Total Momentum = Initial Momentum of Bullet = A Constant.

When the bullet strikes the mellon, a large fraction of the
bullet's energy is used in setting the mellon into motion as well
as in producing a jet of material composed of the mellon's interior
that is ejected in the same direction as that of the bullet; hence,
after the collision there are three contributions to the total
momentum:

Total Momentum = Final Momentum of Bullet

+ Momentum of the Jet

+ Momentum of the Rest of Mellon

= A Constant.

But the law of conservation of momentum requires that the total
momentum have the same value before and after any collision such as
that of the bullet and the mellon. Thus,

Initial Momentum of Bullet = Final Momentum of Bullet

+ Momentum of the Jet

+ Momentum of the Rest of M=
ellon.


For the simple (and unrealistic) case where the bullet stops
in the interior of the mellon and the bullet does not produce a jet
of material, the law conservation of momentum requires that,

Initial Momentum of Bullet = Momentum of the Mellon.

As discussed previously, momentum is defined as the product of an
object's mass, m, times its velocity, v; hence, our last equation
may be rewritten as,

mb x vb = Mm x vm,

where mb, Mm, vb, and vm denote the mass of the bullet, the mass of
the mellon, the velocity of the bullet, and the velocity of the
mellon, respectively. Upon dividing both sides of this equation by
Mm, the velocity of the mellon after the collision is,


vm = (mb x vb)/Mm.


In this illustration it will be assumed that the mass of the bullet
is about 10 grams. Taking the mass of the mellon to be 10
kilograms (10,000 grams) and assuming the bullet is traveling at
about 2000 feet per second, it follows from our last equation that
the mellon moves in the direction of the bullet's initial path with
a speed,


vm = (10 grams x 2000 feet/second)/(10,000 grams)

= 2 feet per second;

thus, the mellon moves in the same direction as the bullet. That
is, the mellon moves away from the rifle and not closer to the
rifle. Many people have argued that this is exactly what should
happen and that President Kennedy's head must have been struck from
the front since his head appeared to have been thrust back in frame
314 of the Zapruder film. As pointed out by Alvarez, this line of
reasoning is flawed critically since it omits a very important
consideration: in frame 314 of the Zapruder film it is apparent
that a jet of material is escaping predominantly from the front of
President Kennedy's head. By Newton's Third Law, which was
published in the year 1687, there is an opposite reactive balancing
force for every driving force. In our illustration with the
mellon, this means that in the realistic situation where a jet is
projected forward the mellon will be thrust backward (by the
opposite reactive force); this is an excellent example of the
application of Newton's Third Law and this is exactly what occurs
in the familiar scenario of a rocket being propelled in the
direction opposite to the direction of the escaping gases.

To calculate the recoil velocity of the mellon due to the
reaction to the jet of escaping material it is necessary to
consider a quantity known as the kinetic energy. The kinetic
energy, KEi, of a mass, mi, moving with a velocity, vi, is given by,

KEi = (1/2) x mi x vi x vi.

If we follow Alvarez and assume that only 10% of the kinetic energy
of the bullet is used to propel 10% of the mass of the mellon in an
escaping jet, it is clear that,

KEj = 0.1 x KEb,

mj = 0.1 x Mm = 100 x mb.

Thus the momentum of the jet times itself may be written as,

(mj x vj) x (mj x vj) = 2 x mj x KEj

= 2 x (100 x mb) x (0.1 x KEb)

= 10 x (2 x mb x KEb)

= 10 x (mb x vb) x (mb x vb).

Thus, the momentum of the jet times itself is 10 times larger than
the momentum of the bullet times itself. This last equation may be
rewritten in an approximate form as,

(mj x vj) = 3.16 x (mb x vb).

(To verify that this new result is true, it is only necessary to
multiply the right-hand side of the last equation by itself and
then multiply the left-hand side of the last equation by itself.)
Since, the momentum of the jet, (mj x vj), is directed oppositely
from the momentum imparted to the mellon by the jet, (Mm x vm'), it
follows that,

(Mm x vm') = - (mj x vj) = - 3.16 x (mb x vb),
or upon dividing both sides of the last equation by Mm,

vm' = - 3.16 x (mb x vb) / Mm,

where vm' is used to denote the recoil velocity acquired by the
mellon in reaction to the escaping jet. Upon taking the mass of
the bullet to be 10 grams, the velocity of the bullet to be 2000
feet per second, and the mass of the mellon to be 9,000 grams (90%
of the original mass of the mellon) we find,

vm' = - 3.16 x (10 grams x 2000 feet/second)/(9000 grams)

= - 7.02 feet per second.

Thus, the recoil velocity of the mellon due to the reaction to the
jet is three-and-a-half times larger (- 7.02 feet per second
instead of 2 feet per second) and in the opposite direction of the
velocity the mellon would have had if the bullet had simply stopped
in the mellon. Therefore, the net motion of the mellon in our
simple example is in the direction from which the bullet was fired!

In any actual case the magnitude of the recoil velocity will
depend on many factors such as the fraction of the bullet's kinetic
energy which is used to propel the jet of material, the mass of
material in the jet, and the geometrical details determining the
precise angle at which the jet exits. All of these factors will
change the recoil velocity but they cannot change the fact that the
reaction to an escaping gas under a wide variety of physically
realistic cases can be expected to cause the mellon to be thrust in
the direction from which the bullet came. As Luis Alvarez said so
well in his American Journal of Physics article, "... we must
remember that the important question at issue here is not the
magnitude of the velocity, but its direction!" In summary,
Newton's Laws of Motion demonstrate that the backward motion of
President Kennedy's head would have been entirely possible in the
case that a bullet struck the back of his head; in particular, it
is not necessary to assume that a bullet was fired from a frontal
or side position such as the Grassy Knoll.














=
Appendix B
THE SHOCK WAVES CAUSED BY SUPERSONIC BULLETS FIRED IN DEALEY
PLAZA MAY INDEED BE STRONG ENOUGH TO PRODUCE SIGNIFICANT
SUDDEN MOTIONS OF A HAND-HELD CAMERA OPERATING FROM MR.
ZAPRUDER'S VANTAGE POINT ON NOVEMBER 22, 1963

In his 1976 American Journal of Physics article, Luis Alvarez
attributes the jerking episodes of A. Zapruder's camera to two
distinct phenomena: jerking due to the direct interaction of a
supersonic bow shock with the camera and jerking caused by
neuromuscular reactions to the sounds of bullets and other stimuli
such as emotion provoking sights. The effects associated with
neuromuscular reactions are hard to doubt but it is not intuitively
clear that the shock wave of a supersonic bullet is strong enough
to cause the observed jerking motions such as those at frames 313
and 314 of the Zapruder film. In this regard, Alvarez --- who
considered himself to be an expert on such phenomena --- stated
that he believed it was possible that the shocks were strong enough
to produce the observed jerking motions in some frames but he did
not provide any mathematical analysis to support his belief. In
this appendix it is argued that the shock waves may indeed be
strong enough to cause substantial streaking in some frames of the
Zapruder film.

The 1979 Report of the Select Committee on Assassinations,
U.S. House of Representatives, Investigation of the Assassination
of President John F. Kennedy contains testimony from the BBN and QC
teams describing the characteristics of the bow shock waves of
supersonic bullets and the muzzle blast wave produced when high
power rifles are fired. In this Appendix the basic properties of
these shock waves will be presented from an intuitive point of view
and some of the key physical characteristics of these disturbances
will be explained.

The bow shock waves are similar to those produced by a
supersonic jet; in both cases the motion is considered to be
supersonic if the object is moving at a speed greater than the
speed of sound. In the cases of both the supersonic jet and the
supersonic bullet, the air is disturbed by the oncoming supersonic
"object" and initially the pressure changes just in front of the
object. These localized changes in pressure are unstable and the
air molecules move in a attempt make the pressure uniform once
more. (This phenomenon is familiar from opening a container that
has an excess or deficit of gas inside; the gas will rush in the
appropriate direction to equalize the pressure. In the classroom
this might be described by saying that nature abhors a vacuum.)

However, the speed at which pressure disturbances (or
pressure waves) move in air is the speed of sound. As long as the
object is moving at speeds less than the speed of sound, the
pressure disturbances can efficiently move away from the object; on
the other hand, at supersonic speeds the object is moving faster
than the speed of sound and the pressure disturbances cannot move
away from the supersonic object fast enough to prevent the
formation of a region near the object where there is an abrupt
change in the pressure of the air. This abrupt change in pressure
is a dominate feature of a shock wave. In other words, the
pressure disturbances produced by a supersonic object form a shock
wave because the pressure disturbances "pile up" just in front of
the object. To the right front and the left front of the object
there is also a shock wave as shown in the high speed photographs
of Figures GHK and GHL. In these figures the bow shocks are
visible as shock fronts which are roughly conical in shape. In
Figures GHK and GJL a complex pattern of shock fronts is seen for
each supersonic projectile. These shock fronts mark the loci of
points where the pressure changes abruptly. It is know
experimentally that these shock fronts can extend hundreds of
meters from the location of the bullet. These pressure changes as
experienced by a person who is near a passing supersonic bullet are
as follows: before the shock front arrives at the person there is
no "sound" to provide a clue that the supersonic bullet is coming;
when the front edge of the shock front arrives at the persons ear
there is a sound --- similar to but in general weaker than the
sonic boom of a jet --- produced by the sudden increase in
pressure; the pressure then decreases and becomes slightly less
than the normal atmospheric pressure until the rear shock front
(see Figures GHK and GHL) arrives at the person about five
thousandths of a second (0.005 second or 5 milliseconds) after the
front shock has passed the observer; after the rear shock passes
the pressure is restored to the normal atmospheric pressure within
a few milliseconds. The net effect of these pressure changes on an
object such as a piece of paper or a hand-held camera is to push
the object away from the direction of travel of the shock front.*
The muzzle blast produced by a the firing of a high power
rifle also produces a pressure disturbance. The muzzle blast is
the sound wave produced by the gases escaping from the gun barrel.
This sound wave travels away from the end of the gun in a spherical
pattern at the speed of sound. Since the speed of sound is about
1000 feet per second, the muzzle blast just one millisecond (1/1000
second) after the gun is fired forms a spherical wave with a radius
of 1 foot (that is, {1000 feet per second} x {1/1000 second}); this
wave is propagating in all directions away from the end of the gun.

---

*Indeed, this is exactly the phenomenon used by Nobel Laureate
Enrico Fermi to measure the strength of the first atomic bomb ---
he sprinkled pieces of paper in the air at the time the shock wave
from the bomb was passing by and he watched the pieces of paper
being pushed away from the bomb. By knowing the expected size of
the pressure change for each possible strength of the atomic bomb,
Fermi was able to calculate how far the pieces of paper would move
for every possible strength of the atomic bomb. Thus, by looking
at the actual motion of the pieces of paper Fermi could estimate
the strength of the first atomic bomb.

After one hundredth of a second, the radius of this spherically
diverging sound wave is 10 feet (that is, {1000 feet per second} x
{1/100 second}). After one tenth of a second the muzzle blast is
s spherical sound wave with a radius of 100 feet. The strength of
the shock per unit area decreases as the area spherical shock front
expands. Since the surface area of a sphere of radius, r, is 4 x
ã x r2, where ã is just a number equal to about 3.14, it follows
that the strength of the shock front falls off in proportion to
{1/area}, or equivalently, {1/{4 x ã x r2}; that is, it is
frequently said that "the strength of the shock front falls off as
1/r2." For example, the strength of the shock front one second
after the blast is one-hundredth of that at one-tenth of a second
after the blast. This type of scaling is known as "inverse square
law scaling" and it occurs in many fields of science. Indeed, the
law of gravitation which describes how a spherical planet attracts
an much smaller object is frequently referred to as the inverse
square law; in this case the 1/r2 factor comes in because the area
of the area of the surface of the gravitational field increases as
4 x ã x r2.
The "fall-off" rate of the bow shock strength is not as rapid
as the 1/r2 rate of the spherical muzzle blast. In fact,
measurements of the fall-off rate for the strength of the conical
bow shock show that the scaling is close to 1/r; accordingly, the
rate of decrease with distance is slower than for the spherical
muzzle blast.
The magnitudes of the pressures for bow shocks and the muzzle
blasts were given in the 1979 Report of the Select Committee on
Assassinations, U.S. House of Representatives, Investigation of the
Assassination of President John F. Kennedy as testimony from the
BBN and QC teams. Figure SSS depicts the pressure variations for
the bow shock, labelled "Shock Wave" in the figure, and the muzzle
blast, labelled "Muzzle Blast" in the figure. The pressure rise
associated with the bow shock of a Mannlicher-Carcano with Western
ammunition at a distance ten feet from the line of the bullets path
is given as 130 dB; dB is an abbreviation for the decibel. The
value of 130 dB is relative to a pressure of 2/100,000 Newton per
meter squared. The Newton is a unit used to designate the
magnitude of a force and its size is such that one atmosphere of
pressure corresponds roughly to 100,000 Newtons per meter squared.
(Recall that pressure is usually expressed in units of force per
unit area --- indeed, a common way to write one atmosphere is
about 15 pounds per square inch.) If we convert the relative
pressure denoted by 130 dB into Newtons per meter squared, the
number we get is about 64 Newtons per meter squared. Likewise, the
muzzle blast of a Mannlicher-Carcano with Western ammunition at a
radius of 30 feet has a pressure of 137 dB relative to a pressure
of 2/100,000 Newton per square meter; if we convert this relative
pressure we get the value 142 Newtons per square meter for the
muzzle blast at 30 feet from the end of the barrel of the gun. The
bow shot for the M-1 has a relative pressure of 140 dB which
converts to a pressure of about 200 Newtons per meter squared at a
distance of feet; the M-1 muzzle blast pressure at 30 feet is about
twice this large. From these values of pressure and the 1/r2 and
1/r scaling rules we find,

Bow Shock Pressure = (65 N/m2)/(r/10 ft) ,

(where the factor (r/10 ft) means the radius in feet is divided by
10 feet and the square root of this ratio is calculated) and,

Muzzle Blast Pressure = (142 N/m2)/(r/30 ft).

These equations are plotted on Figure III of Chapter 2. A typical
value of the pressure is roughly one-half milli-atmosphere or less.

A pressure of one-half milli-atmosphere (0.5/1000 of an
atmosphere) may, on first consideration, seem insignificant.
However, the real significance of such a pressure is grasped when
it is realized that the atmospheric pressure on the side of a hand-
held camera with a height of about 4 inches and a length of about
8 inches is:

Pressure = 4" x 8" x 15 pounds per square inch = 480 pounds.


A force of 480 pounds is certainly not insignificant! The reason
we are unaware of such a force is that there is a opposite
balancing force on the other side of the camera. The total side-
to-side force due to the atmospheric pressure is zero and the
person holding the camera is unaware that the atmosphere is
exerting a 480-pound force on each side of the camera. Now we can
appreciate that the one-half milli-atmosphere of pressure due to
the shock wave of a bullet is sufficient to exert a force of about
one-quarter pound on each side of the camera. That is,

Force = 480 pounds x (0.5/1000) = 0.24 pound.

What is more, this quarter-pound force is exerted in less than one-
hundredth of a second! This is a most unusual force. It is almost
as if a fish had tugged quickly on a piece of fishing line attached
to one side of A. Zapruder's camera! A shock wave coming from his
right would seem like a fish tugging from the left --- a shock wave
coming from his left would "feel" like a fish "pulled" from his
right.

A simple application of Newton's Second Law tells us very
crudely how much the camera moves in response to such a tug. Since
one atmosphere of pressure is 100,000 Newtons per square meter
(same as 15 pounds per square inch), it follows that the pressure
of one-half milli-atmosphere is about the same as a pressure of 50
Newtons per meter squared; that is, 100,000 N/m2 x (0.5/1000) = 50
N/m2. The 4"-by-8" area is roughly equivalent to a 0.1-meter-by-
0.2-meter area. Let us assume that the mass of the camera is about
one kilogram. (A one-kilogram mass weighs about 2.2 pounds.) Let
us also make the realistic assumption that the shock wave has a
length (in time) of about 5 milliseconds (5/1000 of a second). The
force, F, is just the pressure times the area (F = pressure x area)
and we know from Newton's Second Law (cf. Appendix A) that this
force must equal the time-rate-of-change of the momentum. Since
the time-rate-of-change of momentum is the mass, m, (m = 1 kg in
our case) times the change in velocity, v', divided by the length
of time (5/1000 of a second) it takes for the velocity to change,
Newton's Second Law requires that,

F = pressure x area =
(m x change in vel.)/(time of change in vel.),

or for the present case,

50 N/m2 x 0.1 m x 0.2 m = (1 kg x v')/(5/1000 second).

For the right- and left-hand sides of this equation to be equal, v'
must equal 0.005 meter per second. Thus, after shock wave pushes
the camera for 5/1000 of a second, the change in velocity is about
0.005 meter per second which is the same as 5 millimeters per
second. (The thickness of a dime is one millimeter.) Going
through the same calculation for a shock wave with the shorter time
duration of 1 millisecond, which it could be realistically, we find
that v' is only 1 millimeter per second. Similarly, if the
pressure is assumed to be only one-tenth of a milli-atmosphere and
the duration of the shock is assumed to be 5/1000 of a second, we
find that v' is only 1 millimeter per second. As illustrated in
Figure PAM' of Chapter 2, a 5 millimeters per second velocity at
one end of the camera can cause the appearance of a 500 millimeters
per second velocity of an object located a distance of 20 meters
(same as about 66 feet) from the camera. (In this "back-of-the-
envelope" calculation two compensating effects have been neglected;
first, the camera is twisting instead of moving uniformly; second,
the shock wave pressure is not maintained at its maximum value
during the time the shock is exerting a pressure on the camera ---
instead the pressure varies over a range of values less than the
maximum pressure. The shock's effectiveness is thus reduced;
however, the same level of "effectiveness" is not needed since the
twisting motion can be accomplished with as little as about ten
times less force.) During the 1/18.3 of a second between frames an
object 20 meters from the camera would appear to move about 27
millimeters; that is, 500 millimeters per second times 1/18.3 of a
second equals 27.3 millimeters. One inch is equal to 25.4
millimeters so a shock with a one-half milli-atmosphere pressure
lasting about 5 milliseconds causes an apparent motion of very
roughly an inch per frame for an object located about 20 meters
from the camera. This apparent motion of an inch per frame is "in
the ball park" of the sorts of motion found by Alvarez in his
analysis of the Zapruder film. Such "ball park" estimates are
referred to frequently as "order-of-magnitude estimates" to make it
clear that the estimates are indeed only rough approximations to
the actual values.
A second "back of the envelope" approach to estimating the
force exerted on a hand-held camera by a muzzle blast is based on
assuming that the energy in the muzzle blast is contained in a
uniform expanding spherical shell which is centered roughly at the
end of the gun. The assumption that the spherical wave
representing the muzzle blast is uniform is equivalent to requiring
that the energy per unit area of the muzzle blast is constant.
This assumption is generally reasonably accurate but there are some
exceptions, notably just in front of the rifle at close range where
the strength of the muzzle blast will exceed the value predicted by
assuming the muzzle blast is represented as a uniform spherical
shell. The surface area of such a sphere of radius, r, is 4 x ã x
r2, where ã is just a number equal to about 3.14. In addition, the
thickness of the spherical shell is the same as the thickness, T,
of the muzzle blast which is given by the speed of the muzzle
blast, c, times the length of time, dt, that it takes for the
muzzle blast to pass an observer located a distance, r, from the
end of the gun. The speed of the muzzle blast is the speed of
sound, c, which is taken as 300 meters per second. It then follows
that the energy per unit volume in the muzzle blast disturbance is
given by,

Energy per volume = E/[{4 x ã x r2}*c*dt],

where E is the total energy in the muzzle blast. A. Zapruder was
standing about 10 meters from the corner of the picket fence
closest to the Texas Schoolbook Depository. For the case of a shot
fired from the corner of the picket fence, it is possible to use
this equation to estimate the energy per unit volume in the muzzle
blast as it passed Zapruder's camera. But to make this estimate it
is necessary to know the energy in the muzzle blast, E, and the
time, dt, that it takes for the muzzle blast to pass Zapruder's
camera. A crude estimate of the energy in the muzzle blast, E, is
about 1000 Joules which is very roughly about a third of the total
energy liberated when the in the bullet's charge is fired; see Gun
Propulsion Technology for supporting details. This estimate of
1000 joules in the muzzle blast is a reasonable value for a high-
power rifle but, of course, we do not know with certainty what
weapons may have been fired at President Kennedy. From Figure SSS
it is clear that it takes about 5 milliseconds for the muzzle blast
to pass an observer located 30 feet, or roughly 10 meters, from the
end of the gun. Thus, dt is roughly equal to 5 milliseconds for a
muzzle blast that has travelled about 10 meters. Again, the speed
of the muzzle blast is the speed of sound, c, which is equal to
about 300 meters per second. With these values of E, r, c, and dt,
it follows that,

Energy per volume = 0.5 Joule per cubic meter.

From the laws governing the compression of gases it is known that
the energy "stored" in a gas is equal to the pressure time the
volume; thus, the pressure is given approximately by the energy per
unit volume and it follows that the pressure is about 0.5 Joule per
cubic meter. Since one Joule is equal to one Newton times one
meter, this pressure is equivalent to 0.5 Newton per square meter.
Newton's Second Law requires that this pressure acting on a mass,
m, cause a change in velocity given by the relationship,
F = pressure x area =
(m x change in vel.)/(time of change in vel.),
or for the present case,
0.5 N/m2 x 0.1 m x 0.2 m = (0.1 kg x v')/(5/1000 second),
where it has been assumed in taking the camera's effective mass to
be 0.1 kg (instead of 1 kg) that the camera is merely twisted and
not translated. (It is known from the laws of rotation and
translation that a force acting on a camera-shaped object which is
rotating about a preferred axis can be rough twelve times more
"effective" than when it is translating the object; for this reason
we have taken the mass to be 0.1 kg instead of 1 kg.) For the
right- and left-hand sides of this last equation to be equal, v'
must be equal to 0.0005 meter per second, or equivalently 0.5
millimeter per second. As discussed previously, a motion of one
end of the camera with a velocity of this magnitude is sufficient
to cause detectable streaking of the individual frames. This is
especially true for Zapruder frames before 160 when the limousine
was about twice as far from Zapruder's camera as it was at frames
in the general interval between 290 and 340; that is, for these
earlier frames the same angular velocity will produce streaks about
twice as long as those in the later frames. In this last example,
the calculated pressure is the average pressure over the entire 5
millisecond time duration of the muzzle blast; this is in contrast
to the values of pressure used in the previous examples where the
peak pressures such as those at the maxima of the pressure peaks in
Figure SSS. This explains why the pressure in this last example is
somewhat less than in the previous examples. In this last example
of a muzzle blast produced about 30 feet (about 10 meters) from the
camera, the estimated velocity is sufficient to produce observable
streaking in the case where the motion of the camera is primarily
rotational motion and not translational motion.
Thus, the streaks noticed by Luis Alvarez on Thanksgiving
weekend in 1966 were indeed of roughly the right length to have
been caused by shock waves "pushing" Mr. Zapruder's camera. This,
of course, does not prove that a particular jerking episode was in
fact caused be a direct interaction with the bow shock or muzzle
blast. It does, however, alert us to the fact that A. Zapruder's
camera may have experienced rapid jerking motions from causes other
than his neuromuscular reactions to bullets being fired or to the
sight of President Kennedy being struck in the head by a bullet.
Lack of definite association of the camera motion with muzzle
blasts or bow shocks does not negate the Alvarez analysis since the
neuromuscular reactions to bullets still provide important insights
concerning the timing of the bullets --- especially when considered
in conjunction with other visual evidence as illustrated in Chapter
3. However, lack of a definite causal linkage between the camera
motion and the muzzle blasts or bow shocks does make it impossible
to use the camera motion alone to determine the directions from
which the bullets were fired.*

---

* The author is indebted to Prof. Peter Franken of the University
of Arizona for cautioning me concerning the quoted strengths of bow
shocks; based on his insights this appendix was revised to its
present form.
About the author ...

Dr. Michael A. Stroscio earned a Ph.D. in Physics from Yale
University and held research positions at the Los Alamos Scientific
Laboratory and the Johns Hopkins University Applied Physics
Laboratory, before moving into the management of federal research
and development at a variety of U.S. government agencies. Dr.
Stroscio has served as a policy analyst for the White House Office
of Science and Technology Policy, and as Vice Chairman of the White
House Panel on Scientific Communication. He has taught and
lectured on Physics and Electrical Engineering at several
universities including Duke University, the North Carolina State
University and the University of California at Los Angeles. He has
authored over 350 publications, presentations and patents covering
an exceptionally wide variety of topics in the physical sciences.
His professional publications have appeared in over 20 different
journals including a large number of those covering topics in the
areas represented in this book. The author is a Fellow of the Yale
Science and Engineering Association as well as of the Institute of
Electrical and Electronics Engineers. He is a member of the Phi
Beta Kappa honorary society and a long-time member of the American
Physical Society.