Chemical and forensic analysis of JFK assassination bullet lots: Is a

arXiv:0712.2150v1 [stat.AP] 13 Dec 2007

The Annals of Applied Statistics

2007, Vol. 1, No. 2, 287–301

DOI:

10.1214/07-AOAS119



Institute of Mathematical Statistics, 2007

CHEMICAL AND FORENSIC ANALYSIS OF JFK ASSASSINATION

BULLET LOTS: IS A SECOND SHOOTER POSSIBLE?

By Cliff Spiegelman, William A. Tobin, William D. James,

Simon J. Sheather, Stuart Wexler and D. Max Roundhill

Texas A&M University, Forensic Engineering International,

Texas A&M University, Texas A&M University,

Hightstown High School and Chem Consulting

The assassination of President John Fitzgerald Kennedy (JFK)

traumatized the nation. In t his paper we show that evidence used

to rule out a second assassin is fundamentally ﬂawed. This paper

discusses new compositional analyses of bullets reportedly to have

been derived from the same batch as those used in the assassination.

The new analyses show that the bullet fragments involved in the

assassination are not nearly as rare as previously reported. In par-

ticular, the new test results are compared to key bullet composition

testimony presented before the House Select Committee on Assassi-

nations (HSCA). Matches of bullets within the same box of bullets

are shown to be much more likely than indicated in the House Select

Committee on Assassinations’ testimony. Additionally, we show that

one of the ten test bullets is considered a match to one or more assassi-

nation fragments. This ﬁnding means that the bullet fragments from

the assassination that match could have come from three or more

separate bullets. Finally, this paper presents a case for reanalyzing

the assassination bullet fragments and conducting the necessary sup-

porting scientiﬁc studies. These analyses will shed light on whether

the ﬁve bullet fragments constitute three or more separate bullets.

If the assassination fragments are derived from three or more sepa-

rate bullets, then a second assassin is likely, as the additional bullet

would not easily be attributable to the main suspect, Mr. Oswald,

under widely accepted shooting scenarios [see Posner (1993), Case

Closed, Bantam, New York].

1. Introduction. The assassination of President John Fitzgerald Kennedy

(JFK) was arguably the most traumatic event to the nation in the early

Received October 2006; revised May 2007.

Supplementary material available at http://imstat.org/aoas/supplements

Key words and phrases. Forensic, CABL, heterogeneity, bullet.

This is an electronic reprint of the original article published by the

Institute of Mathematica l Sta tistics in The Annals of Applied Statistics,

2007, Vol. 1, No. 2, 287 –301. This reprint diﬀers from the original in pagination

and typographic detail.

2 SPIEGELMAN, TOBIN, JAMES, SHEATHER, WEXLER AND ROUNDHILL

1960s. The assassination precipitated much scientiﬁc investigation and con-

sequent testimony before Congressional subcommittees. The scientiﬁc inves-

tigations included a National Academy of Science Committee on Ballistic

Acoustics report, forensic evidence on bullet fr agment matching by the FBI

crime lab and by Dr. Vincent P. Guinn, as well as more typical forensic evi-

dence such as ﬁngerprints, ballistic evaluations and simulations, crime scene

investigations and reconstructions, and autopsy. The House Select Commit-

tee on Assassinations [U.S. Cong. House (

1979)] concluded that there was

a probable conspiracy, but one in which an additional shooter (likely ﬁring

from the Grassy Knoll) missed all limousine occup ants. The evidentiary an-

chor for the second part of that conclusion—that any additional shot must

have missed—was Dr. Vincent P. Guinn’s comparative bullet lead analy-

sis [U.S. Cong. House (

1979)]. It demonstrated to the Committee, with the

added insights from ballistics testing, that all of the recovered ballistics ma-

terial had only one common origin, Mannlicher–Carcano rounds ﬁred from

Oswald’s riﬂe.

The +/− numbers in Table

1 represent standard deviations based upon a

single observation using Poisson counting statistics. The exception is th e last

row of the table where 3 fragments constitute sample CE 840, and Dr. Guinn

(

1979) analyzed all of them. In that case, the standard deviation measure-

ment was constructed from 3 replicate measurements. Dr. Guinn grouped

the bullet fragments listed in Table

1 [Guinn (1979)] into two groups. Frag-

ments CE 399 and CE 842 form ed one group and fragments CE 567, CE

843 and CE 840 formed the second group. Guinn testiﬁed [U.S. Cong. House

(1979)] that only two bullets represented the sources of those fragments.

We compare data from our studies of other JFK assassination-related

batch bullets to selected contextual excerpts of Dr. Gu inn’s House Select

Committee on Assassinations’ testimony [U.S. Cong. House (

1979)] to the

recent National Research Coun cil (NRC) report Forensic Analysis: Weighing

Bullet Lead Evidence (

2004) and, also, to author experience in compositional

analysis of bullet lead. We will show that Dr. Guinn’s most important testi-

mony to the House Select Committee on Assassinations [U.S. Cong. House

Table 1

Guinn’s NAA results for silver and antimony in bullets and fragments

Specimen Description Silver, ppm Antimony, ppm

CE 339 (Q1) Bullet from stretcher 8.8 ± 0.5 833 ± 9

CE 842 (Q9) Largest metal fragment from Connally’s arm 9.8 ± 0.5 797 ± 7

CE 567 (Q2) Bullet fragment from front seat cushion 8.1 ± 0.6 602 ± 4

CE 843 (Q4) Larger metal fragment from the 7.9 ± 0.3 621 ± 4

President’s head

CE 840 (Q14) Metal fragments from rear ﬂoorboard carpet 8.2 ± 0.4 642 ± 6

JFK ASSASSINATION AND BULLET EVIDENCE 3

(1979)] is unlikely justiﬁed. In particular, we shall show that random matches

to assassination fragments of bullets from the same box are not as rare as

Dr. Guinn testiﬁed. Most importantly, our studies and analyses of in divid-

ual bullet compositions, bullet lead source compositions and compositional

mixtures in packaged retail boxes show that Dr. Guinn ’s statements about

the uniquen ess of individu al bullets from the brand of bullets believed to be

used in the assassination are seriously ﬂawed.

2. Forensic issues.

2.1. Deciding whether bullets “match.” Before describing the experimen-

tal technique used for our study, we ﬁrst explain how bullet compositions

are associated as forensic “matches.” A match criterion establishes a rule

for declaring bullet compositions close enough to be considered analytically

indistinguishable. Typically, a “match” criterion is established, such as conﬁ-

dence interval overlap between mean analyte levels (chemical element levels

in the lead matrix) measured in two diﬀerent specimens. The conﬁdence

intervals are typically based upon multiples of estimated standard devia-

tions from replicate measurements (called a multiple of sigmas method ).

Since 1993, the analytes of two or more b ullet specimens were compared

as described below. A typical analysis, which we consider here, compares

the “questioned” or crime scene evidence of “unknown” origin with samples

“known” to have been in the suspect’s possession. Th e chemical elements

present in bullet lead that were most frequently analyzed after approxi-

mately 1989 and used for forensic comparisons were antimony, copper, ar-

senic, bismuth, silver, tin and cadmiu m. In earlier years (roughly from the

1960s to 1993), only antimony, copper, arsenic and sometimes silver were

characterized. The fewer elements that are used to declare a match the

more likely that matches, including coincidental ones, will occur [see NRC

report (

2004)]. When an analyte concentration in bullets from a crime scene

specimen and in those from a suspect bullet were compared and the concen-

trations fell within the established “match” criterion range, that p articular

elemental comparison was declared a “match.” If all the remaining elemental

comparisons between th e crime scene specimen and “known” specimen also

fell within the established “match” criterion, the two bullet specimens were

then declared to be analytically “indistinguishab le.”

2.2. The brand of bullets believed to be used in the Kennedy assassination.

In the House Select Committee on Assassinations hearing [U.S. C on g. House

(1979)], Dr. Guinn testiﬁed about the brand of bullets believed to be used,

namely, Winchester Cartridge Company Mannlicher–Carcano bu llets, and

about the ﬁve bullet fragments of forensic interest in the assassination. In

particular, he concluded that “This great variation from bullet to bullet f rom

4 SPIEGELMAN, TOBIN, JAMES, SHEATHER, WEXLER AND ROUNDHILL

the same box thus indicated that, for this unusual kind of ammun ition, it

would be possible to distinguish one bullet (or bullet fragment) from another,

even though they both came from the same box of Mannlicher–Carcano

cartridges” [U.S. C ong. House (

1979)].

The authors purchased 2.5 boxes of Winchester Cartridge Company Mannli-

cher–Carcano bullets from 2 of the only 4 separate lots ever produced. One

box came from lot 6000, and one and a half from lot 6003.

We then ana-

lyzed 10 bullets from each box. Th e measurement approach was similar to

that used by Dr. Guinn except that we used more appropriate standards,

a known quality control procedure, and analyzed physical samples having

a known geometry. One of the bullets analyzed matched an assassination

fragment. We also found that many bullets in the same box have match ing

antimony and silver levels; this discovery is contrary to Dr. Guinn’s testi-

mony that based on these two elements virtually every bullet of this type is

unique. Peele et al. (1991) found similar supporting evidence of many bullets

matching within boxes of bullets, in cluding those of other large US b ullet

manufacturers. Further, we have found th at about 14 percent of b ullets

in the “1837” bullet FBI empirical compilation reported in Spiegelman and

Kafadar (2006) from murder cases have antimony concentrations at or below

those of the assassination fragments. Approximately the same percentage of

bullets is at or below the antimony concentrations of the Western Cartridge

Company bullets measured by Dr. Guinn. The percentages vary somewhat

with diﬀerent FBI empirical compilations. For the other (non-“1837”) FBI

bullet compilations, it is not clear which case entries (samples) correspond

to bullets rather than buckshot, other irrelevant entries and/or null cell val-

ues. Regardless of assumptions used to interpret various FBI bullet datasets,

low antimony bullets are not rare. Our ﬁnd ings also call into question other

aspects of Dr. Guinn’s testimony [U.S. Cong. House (

1979)], such as the

following exchange that followed Dr. Guinn’s testimony about the low anti-

mony content of Western Cartridge Company Mannlicher–Carcano bullets:

Mr. Wolf: In your p rofessional opinion, Dr. Guinn, is the fragment removed

from General Walker’s house a fragment from a Western Cartridge Company

Mannlicher–Carcano bullet?

Dr. Guinn: I would say that it is extremely likely that it is, because there are

very few, very few other ammunitions that would be in this range. I don’t know

of any that are speciﬁcally this close as these numbers indicate, but somewhere

near them there are a few others, but essentially th is is in the range that

is rather characteristic of Western Cartridge Company Mannlicher–Carcano

bullet lead.

Preliminary background investigation revealed some uncertainty as to the source of

10 of the bullets that were purchased as a half box. After additional investigation and

information from the bullet supplier (including photos), it is concluded likely that the 10

originated from lot 6003, and we den ote this lot as 6003P.

JFK ASSASSINATION AND BULLET EVIDENCE 5

There has never been a comprehensive or forensically meaningful statisti-

cally based sampling study of bullet composition by manufacturer, location

or epoch.

Assuredly, the passage of time has allowed a more sophisticated analysis

of the data obtained by Dr. Guinn. Our ﬁnal point will be that it may

be possible to provide substantial evidence of a third assassination bullet

by following the guidelines in the NRC report (2004) and reanalyzing the

assassination fragments. In any case, we believe that there is no scientiﬁc

basis from the fragment matching performed by Dr. Guinn to conclude that

only two bullets were the sources of the assassination fragments [U.S. Cong.

House (1979)]:

Mr. Wolf: What is t he number of bullets, in your opinion?

Dr. Guinn: These numbers correspond to two bullets. Two of the samples

have indistinguishable compositions, indicating that they came from the same

bullet, and the other three particles are evidently samples from another bullet.

Mr. Wolf: So it is your opinion that the evidence specimens represent only

evidence of two bullets, is that correct?

Dr. Guinn: Yes, sir, there is no evidence for three bullets, four bullets, or

anything more than two, but there is clear evid ence that there are two.

Dr. Guinn may have been correct or incorrect about the number of bullets

originating from the J FK fragments; the state of knowledge even today, but

deﬁnitely about 30 years ago, remains too uncertain.

Finally, we note that much has been written about the JFK assassina-

tion, but most of the results such as th ose in Rahn and Sturdivan (

2004) and

Sturdivan and Rahn (

2004), are based upon historical data using what we

feel are inadequate models for bullet distribution and sample sizes that are

too small. It is our belief that the lognormal model used by these authors

to model antimony concentrations is one of a large set of reasonable models

that might have been used. For example, the “distﬁt” command from the

PLS

Toolbox for MATLAB ranks best-ﬁtting distributions to the data us-

ing p-values from a chi-squared goodness-of-ﬁt test. For the 14 data values

that were used by Stur divan and Rahn (2004), the exponential, Weibull,

gamma, triangular an d chi-squared distributions had p-values that were

0.71,0.71,0.70,0.58 and 0.54, respectively, while the lognormal distribution

had a p-value of 0.54. Many other distributions, as well, are realistic possibil-

ities f or modeling th e data, including Gumbel (p = 0.45) distributions. Based

on the lognormal d istribution, Sturdivan and Rahn (

2004) concluded that

there was a 2%–3% chance of a coincidental match. This result is clearly

dependent on distributional assumptions and, hence, we believe that the

2%–3% ﬁgure is questionable. Stur divan and Rahn (

2004) are f ocused on

chance matches within th e whole population of Western Cartridge Com-

pany Mannlicher–Carcano bullets. We think a more relevant population for

consideration is that consisting of bullets within the same box of Western

6 SPIEGELMAN, TOBIN, JAMES, SHEATHER, WEXLER AND ROUNDHILL

Cartridge Company Mannlich er–Carcano bullets. Comparing the composi-

tion of diﬀerent bullet fragments is based on the assumption that diﬀerent

fragments from the same bullet are compositionally similar at all levels of

sample size. With this issue in mind, Rahn and Sturdivan (

2004) discuss

fragment h eterogeneity, based upon historical data from both Dr. Guinn

and the FBI. Based on the FBI data, Rahn and Sturdivan (

2004) found

little heterogeneity between bullet fragments.

In our compositional analysis of 30 bullets, we found marginally detectable

heterogeneity, which can be taken into account when matching b ullets. We

believe we have struck a good balance between the considerations adversely

aﬀecting compositional accuracy and precision relating to specimen size.

Specimens that are too large result in s elf-absorption problems during anal-

ysis by NAA; specimens that are too small can result in analyses that may

not be r ep resentative of the overall (bulk) composition, as demonstrated by

Randich and Grant (2006).

The description of our measurement experiment can be found in the

Appendix.

3. Statistical analysis of Dr. Guinn’s data. Dr. Guinn grouped the bul-

let fragments show n in Table

1 into two groups. Fragments CE 399 and CE

842 formed one group and fragments CE 567, CE 843 and CE 840 formed

the second group. Guinn testiﬁed [U.S. Cong. House (

1979)] that only two

bullets represented the sources of th ose fragments. It is clear that CE 567

and CE 840 antimony measurements are ±4 estimated stand ard errors (of

the mean) apart. Thus, we consider here a ±4 standard error method in or-

der to remain consistent with Dr. Guinn’s testimony. [A r ecent NRC report

(2004) found that the stand ard procedure used by the FBI to match bullet

fragments or bullets was based on ±2 standard deviations. When there are 4

replicate measurements the ±4 standard error matching method is the same

as that used by the FBI.] Later in this paper we also consider a ±2 stan-

dard error matching criteria for matching our bullet measurements to Dr.

Guinn’s bullet fragment measurements. As Rahn and Sturdivan (2004) indi-

cate, with the exception of C E 840, Dr. Guinn’s measurements involved only

one measurement of each specimen, so the estimated standard deviations and

estimated standard errors are the same and are based upon Poisson counting

statistics. The NRC report (

2004) also discusses other matching techniques

such as the equivalence t-test and a multivariate Hotelling’s T

test.

Bias associated with any measurement system changes with time. To min-

imize this bias, it was common for th e FBI crime lab to measure bullets or

bullet fragments obtained from the crime scene and from a suspect within

a short time frame. Dr. Guinn’s measurements were made over a short time

period and, hence, bias is not an issue for grouping h is measurements. In

JFK ASSASSINATION AND BULLET EVIDENCE 7

Fig. 1. ( a) Boxplots for silver and antimony measurements for lot 6000; ( b) boxplots

for silver and antimony measurements for lot 6003P; ( c) boxplots of silver and antimony

measurements for lot 6003.

this report we included a bias correction for time as an additional com-

ponent to the bullet comparisons. Based upon measurements on our three

“standards,” we have a mean oﬀset from the certiﬁed values between 2%

and 5.4%. Therefore, a bias correction to the antimony measurements that

adds 2% to 5.4% is appropriate. This results in a match with one of our

bullets with CE 567 that we will describe below. For the same reasons for

silver, we added 5.5% to our measurements. As a result, th e same bullet

8 SPIEGELMAN, TOBIN, JAMES, SHEATHER, WEXLER AND ROUNDHILL

matches CE 567 at ±2 standard errors. Alternative approaches based on

components of error adjustments are problematic, since Guinn’s standard

error estimates do not h ave traditional degrees of freedom associated with

them. Dr. Guinn’s uncertainty estimates do not take into account many

sources of error, such as repositioning of samples, biases or instrument ab-

normalities. We invite readers who wish to u s e a diﬀerent method for bias

correction to consult our measurements on standards available in the online

supporting material. Given the overlap in the boxplots in Figure

1 below, it

is clear that many fragments corresponding to diﬀerent Western Cartridge

Company Mannlicher–Carcano bullets match on the two elements antimony

and silver.

The NRC report (2004) recommends that seven elements be us ed for

matching, and it is clear that many fragments that match on two elements

may not match on th ree or more elements.

Of particular note is ou r bullet number one from lot 6003. We compare the

outer, middle and inner fragments as well as the combined measurements to

Guinn’s measured fragment CE 567 (see Table

2), where means and standard

errors are given.

Applying the criterion of ±4 standard err ors , both the identiﬁed f rag-

ments and combined measurements from bu llet 1 in lot 6003 would belong

to Group 2 of Guinn’s classiﬁcation of fragments. The ±2-standard error

match criterion fails, but that ignores the fact that there likely are biases in

both Guinn’s measurements and ours. As previously discussed, our biases

are assessed to be approximately −5% to a positive 9.8% relative bias for

silver and from −5.4% to −2% r elative bias for antimony (data available

within the online supporting documents). Once the adjustment for bias is

performed, we can see that all fragments, labeled or not, have a ± two stan-

dard error match for antimony, but only the fragments labeled by position

have a two standard error match for silver.

If every bullet ever manufactured, or if every bullet in a local geographic

area, was of the same composition, there would be little or no forensic value

of a claimed “match” or “nonmatch.” As discussed in Tobin and Thompson

(

2006),

Assuming you are satisﬁed that . . . specimens were properly characterized

as indistinguishable ( therefore a “match” or “inclusion”), the next step for

assessment of forensic signiﬁcance involves estimation of probabilities for de-

termination of probative value. . . . there are two crucial questions: (1) how

likely are the observed results if the samples had a common source; and (2)

how likely are the observed results if the samples did not have a common

source? Without valid answers to both questions, there is no way to assess the

probative value of the forensic evidence for proving that the “matching” items

had a common source.

JFK ASSASSINATION AND BULLET EVIDENCE 9

Table 2

Bullet # 1 lot 6003 measurements by radial location and combined giving summary statistics for antimony and silver

Degrees Degrees

of freedom Silver, ppm of freedom Antimony, ppm Antimony

Location (silver) (Mean ± standard error) Silver bias range (antimony) (Mean ± standard error) bias range

Outer fragment 3 6.30 ± 0.13 −5.5% t o + 9.8% 3 578 ± 9.75 −5.4% to − 2%

Middle fragment 2 6.66 ± 0.05 −5.5% t o + 9.8% 2 585 ± 6.97 −5.4% to −2%

Inner fragment 3 6.35 ± 0.14 −5.5% t o + 9.8% 3 581 ± 7.56 −5.4% to − 2%

All measurements 19 6.30 ± 0.06 −5.5% t o + 9.8% 17 576 ± 3.47 −5.4% to −2%

for this bullet

including

unlabeled

measurements

10 SPIEGELMAN, TOBIN, JAMES, SHEATHER, WEXLER AND ROUNDHILL

Table 3

Summary statistics for bullets 1, 8, 9 and 10 from lot 6003 by radial location for

antimony and silver

Outer N Middle N Inner N Whole bullet N

Antimony (Sb)

1 578 ± 19.5 4 585 ± 12.1 3 581 ± 15.1 4 576 ± 3.47 18

8 957 ± 4.86 3 952 ± 17.4 3 963 ± 16.3 3 966 ± 7.32 12

9 1829 ± 61.4 3 1806 ± 18.1 3 1869 ± 13.4 3 1834 ± 14.3 9

10 260 ± 10.0 3 262 ± 0.180 3 258 ± 4.69 3 260 ± 1.93 9

Silver (Ag)

1 6.30 ± 0.26 4 6.66 ± 0.09 3 6.35 ± 0.27 4 6.30 ± 0.06 20

8 6.90 ± 0.14 3 6.79 ± 0.16 3 6.73 ± 0.18 3 6.81 ± 0.04 18

9 8.71 ± 0.38 3 8.51 ± 0.28 3 8.68 ± 0.42 3 8.66 ± 0.08 18

10 5.04 ± 0.25 3 5.21 ± 0.09 3 5.14 ± 0.16 3 5.04 ± 0.05 18

Some of the information needed to properly assess the value of Dr. Guinn’s

data an d testimony r elate to both compositional homogeneity and compo-

sitional uniqueness (individuality) of the Mannlicher–Carcano bullets. For

example, how compositionally homogeneous (uniform) was each batch of

bullets made by Mannlicher–Carcano (homogeneity), how compositionally

homogeneous are the individual bullets d erived from each batch (homogene-

ity), and how f requently do Mannlicher–Carcano bullets and bullets from

other manufacturers “match” in composition (uniqueness).

Dr. Guinn testiﬁed about the homogeneity of Western Cartridge Company

bullets to the House Select Committee on Assassinations [U.S. Cong. House

(1979)], “One can only show what information we do have, and that is that

you simply do not ﬁnd a wide variation in composition within individual

Western Cartridge Company Mannlicher–Carcano bullets, but you do ﬁnd

wide composition diﬀerences from bullet to bullet for this kind of bullet

lead.” This section further investigates this claim with regard to our study.

4. Bullet homogeneity. In our study we sampled the outer, middle and

inner radial regions of each of four bullets. The four bullets were chosen

based on preliminary measurements that best matched the assassination

fragments. Table

3 gives the means and standard errors of antimony and

silver measurements for the four bullets. Results in Table

3 are given at

the radial portion of the bullet at which measurements were recorded. In

addition, summaries for the entire bullet (which include measurements both

labeled and unlabeled in terms of radial position) are reported in Table

The diﬀerences in composition within a bullet are m arginally detectable

even with the small sample sizes used in our study. Our working hypothesis

for this study is that bullets can be m odeled as reasonably homogeneous

JFK ASSASSINATION AND BULLET EVIDENCE 11

in composition. However, in part because of variations in fabrication prac-

tices, and in light of the recent ﬁndings of Randich and Grant (

2006), some

bullets may not be homogeneous, disallowing homogeneity as a universal as-

sumption. For example, when we compare silver from the middle and outer

fragments of our bullet one from lot 6003, the p-value for comparing means

using a pooled t-test (Fisher’s LSD) is just less th an 0.08 and when com-

paring arsenic f or the middle and inner fragments for arsenic from the same

bullet, the p-value is about 0.06. (Log-transformed data analysis produce

similar p-values.) When a two-way multivariate analysis of variance on log

silver and log arsenic with interaction term (factors “bullet” and “location”)

test is run using the three bullets from lot 6003, with replicates for both log

silver and log arsenic, the p-value for bullet homogeneity is 0.04 (using Wilk’s

lambda; it is slightly lower using Hotelling–Lawley). These tests should be

considered exploratory because of the small sample sizes and because other

hypotheses were evaluated that did not show extraordinarily s tr ong diﬀer-

ences in homogeneity.

5. Using the compositional bullet evidence. To decide whether the com-

positional bullet lead evidence sup ports one shooter or more than one shooter,

it is useful to use the ratio of pr ob abilities

Pr(T |E)

Pr(

T |E)

, where T den otes two bul-

lets used in the assassination,

T denotes its complement (in this case three

or more bullets since at least two bullets were involved in the assassination),

and E s tands for evidence. As in Carriquiry (

2006), Bayes theorem can be

used to obtain the equation

Pr(T |E)

Pr(

T |E)

Pr(E|T )

Pr(E|

T )

Pr(T )

Pr(

T )

The ratio on the left-hand side of th e equation is a ratio of the probabilities

for two bullets as the sou rce for the ﬁve JFK fragments in question versu s

more than two bullets being the source for the ﬁve JFK fragments. The

ﬁrst ratio on the right-hand side is the ratio of probabilities f or th e evidence

given two bullets versus having more than two bullets. This ratio allows us

to decide whether, given the evidence, two bullets or more than two bullets

is more likely.

Supporters of the lone-assassin interpretation, including Gerald Posner

(

1993), insist that Oswald missed the limousine occupants entirely with one

of three shots, leaving only two of Oswald’s bullets to wound President

Kennedy and Governor Connally; therefore, a third shot s tr iking both vic-

tims would require an additional shooter. Under this scenario, the second

ratio on the right-hand side of the equation represents a ratio of the prior

probabilities that we believe that there was a single shooter versus the fact

that there are multiple shooters. This ratio is assessed independently of the

12 SPIEGELMAN, TOBIN, JAMES, SHEATHER, WEXLER AND ROUNDHILL

compositional bullet measurements. In assessing the value of the evidence,

characterizing the number of distinct compositional bullet groups in a box

is important. To illustrate this point, we consider a situation similar to the

outcome of our measurements from the ten bullet measurements fr om lot

6000. (These measurements are provided in the online supplemental materi-

als.) To keep calculations as simple as possible and to emphasize that what is

assumed about the number of m atching bullets in a box matters, we assume

no measurement error and no heterogeneity issues in the following calcula-

tion. We illustrate the calculation of the probability ratio by considering that

the evidence of two bullets making up the ﬁve assassination fragments came

from two or three bullets. We assume that there are two distinct groups of

bullets from among ten measured bullets. This is similar to the groupings

obtained for lot 6000 bullets using the ± four s tandard error criteria. We

assume that there are six bullets in one group and four bullets in the other

group. The hypergeometric distribution is an appropriate model distribution

to use. If only two bullets were chosen, from our 10 b ullets then there would

be a 53.3% chance that two of them would come from two diﬀerent groups .

If three bullets were chosen, then there would be an 80% chan ce that they

came from two groups. Thus, the critical ratio

Pr(E|T )

Pr(E|

T )

0.53

0.80

. Since this ratio

is less th an 1, Dr. Guinn’s testimony that the evidence supports two and

only two bullets making up the ﬁve JFK fragments is fundamentally ﬂawed,

unless one places a very strong prior probability on T .

Dr. Guinn testiﬁed that essentially every bullet in a box of Mannlicher–

Carcano bullets is unique and un der that assumption, his conclusions are

more logical. Our measurements on three diﬀerent boxes of these bullets in-

dicate a great many bullets have two element matches within a box. If more

elements are measured and then compared for each bullet, there may be

fewer within box matches. Also, if m ore elements are chemically analyzed,

the JFK fragments may reasonably be placed into more th an two groups.

It is not known whether or not there was a second shooter. However, if

there was a second shooter, the possibility exits that the bullets came from

diﬀerent boxes. The calculations above show that it is n ot possible from

the compositional bullet lead analysis to conclude that there were only two

bullets as the source of the ﬁve assassination fragments as Dr. Guinn tes-

tiﬁed. The answer could change dramatically depending upon assumptions.

By r eanalyzing the JFK bullet fragments to measure more elements, it may

be possible to provide substantial evidence of more than two bullets as the

source of the assassination fragments if there were, in fact, more than two

bullets used. However, if bullets came from the same box, clear evidence of

more than two bullets may not be present because many bullets in the same

box typically have similar chemical compositions.

JFK ASSASSINATION AND BULLET EVIDENCE 13

6. Summary and conclusions. We presented results from a study where

ten bullets from each of three boxes of Mannlicher–Carcano bullets were

analyzed for chemical composition. Compositional data from the ten bullets

sampled from each box were compared to Dr. Guinn’s testimony before the

House Select Committee on Assassinations [U.S. Cong. House (

1979)] re-

garding assassination bullet f ragment compositions and also to the ﬁndings

of the NRC in their report “Weighing Bullet Lead Evidence” (2004). We

found that many bullets within a box of Mannlicher–Carcano bullets have

similar composition. Further, we found that one of the thirty bullets ana-

lyzed in our study also compositionally matched one of the fragments from

the assassination analyzed by Dr. Guinn [U.S. Cong. House (1979)]. If we

allow for the bias associated with Dr. Guinn’s measurements, it is possible

that there would be even more matches among our bullets with the JFK

fragments. We have shown that two-element chance matches to assassina-

tion fragments are not extraordinarily rare. Further, we have shown that if

bullets come from the same box, they are even less rare. Given the signiﬁ-

cance and impact of the JFK assassination, it is scientiﬁcally desirable for

the evidentiary fragments to be reanalyzed. The reanalysis should include

at least the seven elements id entiﬁed in the NRC r eport (

2004), should es-

tablish the scientiﬁc basis for matching f ragments originating from a single

bullet, and should address the critically important issues of b ullet and source

heterogeneity.

APPENDIX: EXPERIMENTAL DETAILS

The analyses performed in this study were designed to be comparable to

the 1977 Neutron Activation Analysis (NAA) work of Guinn (1979). Vari-

ations in protocol were made to accommodate diﬀerences in reactors and

counting instrumentation used by the diﬀerent research teams. In the sub-

sequent 30 years, signiﬁcant advancements in detectors and electronics have

occurred. Modern computing has f acilitated rigorous peak extraction meth-

ods and analytical corrections. Still, the basic method used in both cases

was very similar, and no development discounts the quality of the Guinn

data.

The bullet lead matrix poses special concerns durin g NAA due to its heavy

mass. The neutrons used as the analytical probe in th is method ﬁnd th e lead

sample to be fairly transparent, but the gamma-ray which is emitted from

the subsequent decaying nuclide of the element of interest is likely to be

attenuated. The issue is to ensure that any s elf-absorption [Knoll (

1979)]

of the gamma-rays is minimized and, if possible, corrected for. Since the

likelihood of absorption is based on the path length of the emission through

the sample as well as the absorption coeﬃcient in lead, it is b en eﬁ cial to use

small samples.

14 SPIEGELMAN, TOBIN, JAMES, SHEATHER, WEXLER AND ROUNDHILL

Guinn used sample masses ranging from 1 to 50 mg, sizes dictated by the

fragments available. The bullet r ecovered f rom Governor Connelly’s stretcher

(the “stretcher” bullet) was drilled and the resulting d rillings/powder ana-

lyzed. In Guinn’s study (

1979), correcting f or sample self-absorption because

of variable geometry was diﬃcult. In our study we used fragment ch ips pre-

pared from the bullet lead m aterial weighing 15 to 20 mg that had maximum

linear dimensions between 0.1 mm and 1.5 mm, averaging 0.4 mm. Loss of

gamma intensity by absorption should average about 2.47% to 3.34% for

the range of gamma energies used at this average distance. Rather than risk

inaccurate adju s tments due to irregular specimen geometries, we included

credible ranges for self-absorption in the calculation of the bias contribution

to our uncertainty estimates.

Sample positioning in the neutron ﬂux and counting positions is critical.

The use of small samples to minimize self-absorption resulted in the n eed

for additional measures to ensure that the sample was held at a precise

location in the sample irradiation package. Sample portions were selected

from the test bullets according to three diﬀerent protocols. Three samples

were prepared for each of 10 bullets from lot 6000 and a putative 6003 lot,

for a total of 60 samples. We r efer to this later set of bullets as coming from

lot 6003P. Eﬀorts were made to maximize the spread of locations samp led

within a bullet. Additionally, ten bullets known to be fr om lot 6003 were

sampled in a similar fashion, except three samples were removed fr om each

of the three locations chosen for a total of nine samples per bullet, or 90

for the lot. Finally, several bullets (bullet numbers 1, 8, 9 and 10) from lot

6003 were sampled a second time. At each of the three sampling locations

of these bullets, the three samples were taken fr om an interior slice with one

sample representing the radial center of the bullet (inside), one representing

the middle and one near the outside surface of the bullet (outside). Samples

were prepared following Guinn’s procedure (

1979) and packaged into pre-

cleaned polyethylene vials.

Standardization—Commercial plasma solutions were used for comparator

NAA standards.

Standards were prep ared by depositing, and then drying,

weighed portions of liquid solutions of know n concentrations of the elements

of interest into irradiation vials prepared exactly as for the bullet samples.

Silver standards were prepared separately with approximately 2 micrograms

of element deposited into each standard. Composite standards were prepared

for arsenic, antimony and copper by depositing about 6, 19 and 12 micro-

grams respectively.

Quality material selection—Standard Reference Material Bullet Lead,

SRM C2416 produced by the National Institute for Standards and Tech-

Alfa Aesar, Specpure Plasma Standards, Ward Hill, MA.

JFK ASSASSINATION AND BULLET EVIDENCE 15

nology (NIST )

is intended for use as a composition standard for optical

emission spectroscopy (OES). The standard is not sectioned, but rather a

newly exposed surface is presented to the instrumentation for analysis. Al-

though NIST does not certify the homogeneity of the bulk standard nor

provide a “minimum sample mass” as they do with standards intended for

sub-sampling, and since no other reference material of similar matrix to our

samples was available, the C2416 standard was the only feasible selection.

We included three analyses of NIS T SRM 1571, Orchard Leaves for arsenic,

as well as three analyses of a second independ ent set of plasma standards

(referred to here as Tr ace Element Research Laboratory standard s )

from a

diﬀerent manufacturer for silver, and six analyses for the other elements.

Irradiations and Counting—All ir radiations were perf ormed at the Texas

A and M University’s Nuclear Science Center 1 MW T.R.I.G.A. research

reactor. The irradiation positions include a pneumatic tube and rotisseries,

both with nominal neutron ﬂuxes of 1 × 10

−2

−1

Silver was determined using the p neumatic facility by sequentially irra-

diating standards, unknowns and quality materials for 60 s (T

), followed

by a 30 s delay (T

) and a 180 s count period (T

). The

109

Ag(n, γ)

110

reaction induced by thermal neutrons dur ing the irradiation gave rise to the

657 keV gamma line (E

) from

110

Ag which decays with a 24 s half-life

1/2

). Measurements were taken us ing standard gamma-ray spectrometer

protocols.

Arsenic, antimony and copper were each determined using longer-lived

isotop es; therefore, a rotisserie irradiation of two hours was employed. Neu-

tron capture reactions were responsible for production of indicator isotopes

As (t

1/2

= 26.4 h, E

= 559 keV),

122

Sb(t

1/2

= 2.70 d, E

= 564 keV) and

Cu(t

1/2

= 12.7 h, E

= 511 keV). Samples were counted in irradiation

batches with each irradiation can being pr ocessed in consecutive counts on

a single detector system.

Details of quality contr ol material analyses are in supporting material but,

in each case, the standard deviation of measurement distributions overlaps

with the quoted uncertainty of NIST values. NIST speciﬁes that the uncer-

tainties for their certiﬁed standard values are not statistically derived mea-

sures of variability but rather are “based on judgment.” Tabulated r esults of

Tr ace Elements Research Lab standards are available in online supporting

material.

National Bureau of Standards, Certiﬁcate of Analysis, Standard Reference Material

C2416, Bullet Lead, February 16, 1988, Gaithersburg, MD.

National Bureau of Standards, Certiﬁcate of Analysis, Standard Reference Material

1571, Orchard Leaves, January 28, 1971, revised August 15, 1976, Gaithersburg, MD.

Trace Element Research Laboratory Standards (TERL), Inorganic Ventures, Lake-

wood, NJ.

16 SPIEGELMAN, TOBIN, JAMES, SHEATHER, WEXLER AND ROUNDHILL

Acknowledgments. The authors are grateful to the Editors and an As-

sociate Editor for many helpful comments that led to an imp roved paper.

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C. Spiegelman

S. J. Sheather

Department of Statistics

Texas A&M University

3143 TAMU

College Station, Texas 77843-3143

USA

E-mail:

cliﬀ@stat.tamu.edu

W. A. Tobin

Forensic Engineering International

2708 Little Gunstock Rd.

Lake Anna, Virginia 23024-8882

USA

W. D. James

Center for Chemical Characterization

and Analysis

Texas A&M University

3144 TAMU

College Station, Texas 77843-3144

USA

S. Wexler

Humanities and Advanced

Placement Government

Highstown High School

25 Leshin Lane

Hightstown, New Jersey 08520

USA

D. M. Roundhill

Chem Consulting

13325 Black Canyon Drive

Austin, Texas 78729

USA