Resolving the logical incompatibility

      We can now restate the logical incompatibility more simply: the tight groups and their physical meaning are incompatible with strong heterogeneities in Sb. One or the other has to give. Since neither the analyses of the fragments nor the analyses of heterogeneity in quarters of WCC/MC bullets are wrong, and the tight groupings and physical meaning of the groups could not have arisen by chance, one or the other must be inappropriate. The only possible inappropriateness is the large heterogeneities of Sb in quartersthey must not apply to the fragments from the assassination. The effective heterogeneity of these fragments (both small and large) must be much smaller than indicated by Guinn’s samples over quarters.

The fact is more important than the explanation
    As critical thinkers, we are duty-bound to seek explanations for important facts such as the tightness of the two groups of fragments that could not have arisen by chance. But in this case we must be clear that the reason for the small heterogeneities and the consequent tight groupings is less important than the million-to-one probability that these groupings are real, and hence that some organizing force lies behind them. We can profit from the the fact while we are working out the reason for it.

Is the organizing force natural or sinister?
    The organizing force behind the groupings could be natural (something related to bullets fragmenting) or sinister (bullets and fragments with the right concentrations of antimony being carefully planted to hide the fact of a different shooter or multiple shooters). Which was it? From the earlier discussion of chains of custody and the near-impossibility of anticipating the details of the firing, it is easy to conclude that the fragments were not planted. Thus the organizing force was something natural.

The FBI’s NAA data hold the key
What natural process could produce such small heterogeneities from bullets that have large heterogeneities? (They are so small as to approach the analytical uncertainties, i.e., to represent no real variations in Sb.) An important clue, and the only one we have so far, comes from the FBI's data. The FBI did an extremely valuable thing back in 1964, something that I don’t think they realized would 35 years later prove to be so important to this case. In distinction to Dr. Guinn, who analyzed whole fragments of a single piece from larger fragments, the FBI took 25 little subpieces from these fragments and analyzed them individually. You can see the results in the previous Table 13 and on Figure 21 belowfour aliquots from the end of the stretcher bullet (Q1), three from the fragment from the front seat (Q2), three from the fragments from Kennedy’s brain (Q4, 5), three from Connally’s wrist (Q9), and three pieces from the rear carpet (Q14). This information has proved to be a gold mine because each of the five groups of subfragments proved to be practically homogenous—the tiny replicates of every fragment gave essentially identical results. Gone was the variability of the whole bullets and of the quarters, and in their places appeared a tightness that is very similar to that of the two groups of fragments from the crime scene. The critics who have been so fixated on Guinn’s data have ignored the rest of the story, to the detriment of all concerned.

Figure 21. The characteristic heterogeneities of antimony in WCC/MC bullets, quarters, within fragments, and the two actual groups of fragments.

      The two groups and five fragments from the crime scene have in essence been trying to tell us that they do not represent pieces taken randomly from Mannlicher-Carcano bullets, or else they would have been spread out like the 12 individual bullets on the left side of Figure 21. They are also trying to tell us that they don’t represent pieces taken at quarter intervals down a bullet, or they would have varied the way those quarters do (groupings second from left). They are trying to tell us that they look like those subfragments tested by the FBI and forgotten about by all of us in the face of Guinn’s more publicized analyses. In other words, these groups of fragments represent little pieces that have come from locations within each bullet that are very near one another.
Figure 22 summarizes this message more clearly, in a simple way that needs no abstruse mathematics to understand. The heterogeneities of antimony over “whole” bullets (really single quarters from 12 bullets) are 90%. Over quarters within three individual bullets, the heterogeneities drop to 24%. Next come the FBI’s groups of samples within fragments5%. Then come the two groups from the assassination3%. The graph concludes on the right with typical analytical uncertainties of Sb in fragments2%3% in general. Thus the fragments from the assassination are barely more scattered than expected from the analysis, which means that they are practically homogeneous and that they originated very close to each other.


Figure 22. Numerical heterogeneities for antimony in WCC/MV bullets, quarters, within fragments, the two actual groups of fragments, and the uncertainties from NAA.

      The point is that Figure 22 has two high numbers and three very low numbers. The highly variable fragments are from whole bullets and quarters only. The fragments from the assassination, in the low group, are not from random bullets or quarters. Rather, they represent closely allied subfragments. The heterogeneities that should be attached to them are of the scale displayed by the three other groups of fragments, somewhere between 2% and 5%. It is wrong to attach 24% heterogeneities to them.
A graph of the two groups of assassination fragments with 3% uncertainties attached sends a very clear message, even at the 95% confidence limits (Figure 23). No serious mathematics or statistics is required to understand such a clear-cut graphthe groups are distinct and not the product of chance. We have now moved beyond the gloom and doom offered by Wallace Milam and the other critics. I applaud Milam for taking the first step of drawing our attention to the potential problem. But then he got lost, I got lost, everybody else got lost along the way. Now we know how to take the next step(s) and remove this problem.

Figure 23. The two groups of assassination fragments, with uncertainties of 3% and confidence limits of 95%.

      Is there a plausible way for groups of tiny subfragments to arise so close to one another? Yes. For CE 399 and the wrist fragments, it’s easy to explainthe tiny fragments were sheared off the end of the lead extruded from the deformed bullet, and then the sample from the bullet was also taken from the exposed end of the core, the only place available if the bullet were not to be torn apart. Thus the pieces from Connally’s wrist and from the bullet came from right next to one another.
But what about the general case? How could typical fragments from a fractured bullet originate so close to one another? One simple possibility exists. When bullets shatter, their Pb cores do not break into smithereens—the system does not possess enough energy or time for that. (This is analogous to the limits of comminuting rocks and seawater into aerosols, where the extent of subdividing the large starting material is ultimately limited by the surface free energy possessed by the finest particles.) So bullets and their cores might well break in only one or two places, and these few irregular surfaces will shed all the little particles that are later analyzed. Thus the many little fragments from a single break would have originated from very near each other, and would be expected to have very similar compositions (concentrations of antimony) in most of the cases. The more one thinks about this mechanism, the more reasonable its general principle seems.
    Larry Sturdivan, the HSCA's ballistics guru, has endorsed this general mechanism and has kindly provided a more detailed explanation for its realization with WCC/MC bullets. Here is what he had to say, edited only slightly:

      When a fully jacketed bullet breaks up in a target, whether it is simulated tissue or a human body, it does so in a very consistent manner, even though the sizes and shapes of the resulting fragments are unique to each case. A WCC/MC bullet will not break up in soft tissue alone. It must strike a bone early in the penetration process in order to break After it has penetrated several centimeters of soft tissue, it may deform on bone, but will not fracture (as CE 399 did not fracture when it hit Connally’s rib). The WCC/MC bullet that hit Kennedy’s head would not be deformed as it penetrated hair and scalp, but would be badly deformed as it penetrated the entry table of the skull. Tissue penetration is a bit more complex than air penetration, but the law of aerodynamic drag gives the first-order effects that dominate the initial part of the penetration, during which the bullet may (or may not) break apart. The drag law states that the retarding force (proportional to the deceleration) is proportional to the square of the velocity and to the density of the material being penetrated. Thus for a given velocity, the force is twice as great in bone as in soft tissue because bone is twice as dense. This is why bullets break up in bone (where the pressure exceeds the yield strength of gilding metal) but not in flesh. When the velocity has dropped by half, the retarding force has decreased by three-quarters. This is why CE399 did not break when it struck rib.
As the bullet is shattering a plug of bone and penetrating the skull, the force on its nose is tremendous. The jacket begins to flatten as it decelerates faster than the aft portion of the bullet, and the nose begins to skew sideways. Extremely high pressure is created inside the jacket. Although the lead has a yield strength much smaller than the gilding metal jacket, this pressure cannot be relieved by pushing the lead out the opening at the tail of the bullet because the decelerating mass of lead is pushing forward to create the pressure. Consequently, the deforming nose tries to skew sideways and the aft portion of the bullet tries to push straight ahead, and the jacket is ruptured by the combination of bending stress and internal pressure. Almost like snapping a cylinder filled with liquid, the rupture relieves the pressure by releasing a fine spray of lead just as the bullet passes into the skull. The higher the pressure (i.e., the greater the velocity), the greater the spray. This is why faster bullets produce more small fragments than those that barely splits, but remain in one piece.
Once the internal pressure is relieved, the lead core does not continue to break into small pieces, but rather stretches like a piece of taffy as the jacket continues to split. The “local” lead that gave rise to the spray of fragments remains on the exposed surface in the “crack.” Depending on where the jacket ruptures, a piece of the jacket may be torn off by itself or with a portion of the core inside it. If the core separates from the jacket, it can remain in one badly deformed piece or can be further torn into two or more large pieces by the retarding force of the tissue. All the large pieces will retain their forward momentum, however, and will exit through the same hole in the opposite table of the skull. If exposed lead contacts bone at this point, a fragment can be sheared off (as with the tail of CE399 on Connally's wrist bone). The size of the fragment depends on the orientation of the core and the jacket. It can be considerably larger than the small fragments from the spray, or may be thin like a smear of lipstick. Since the new fragment comes from the exposed and stretched taffy-like surface, it would likely have originated near the origin of the spray. Likewise, any samples taken from the exposed surface (for NAA, for instance) are likely to have a composition similar to the composition of the small fragments. Quarter-bullet heterogeneity is quite irrelevant here.
The JFK head shot gave rise to at least three bullet fragments large enough to exit: one piece of core and jacket that was recovered, one piece of jacket from the nose that was recovered, and probably only one other large piece of core originally associated with the nose, which flew over the windshield and the trim that stopped the other two. A forward extension of the trajectory of this fragment lines up very well with the smear of lead on the curb near James Tague. [See section on Tague below—KAR] If a piece of the lead core that hit Tague’s cheek had been recovered, the quarter-bullet heterogeneity would have been relevant, because that fragment would have had to come from the interior of the splattering core fragment.
Incidentally, simulations at Edgewood showed that the exiting fragments were still traveling at nearly half the muzzle velocity of the bullet. Thus, a large piece of core would have maintained enough energy to splatter into a spray of small fragments when it hit the curb near Tague. The early missed shot would have had hit the street so steeply that it would have disintegrated into a spray of lead and bronze particles rather than ricocheting and retaining its identity. None of these particles would have been able to reach Tague, much less with enough energy to cut his face. Alignment would not have been a factor, however, as the particles would have splattered in a broad band of forward directions.

    Fortunately, this mechanism is testable in two stages. One would first test the general idea by breaking Pb cores from WCC/MC bullets, scraping little particles from both surfaces, and seeing whether their compositions are comparably similar to those from the two groups of JFK fragments. One could then test Sturdivan's detailed mechanism by shooting WCC/MC bullets into something that would shatter them in the same way as Kennedy’s head did.
    Martin Fackler has also provided some experimental justification for the idea that the lead core jacketed bullets breaks into only two or three pieces as the bullet shatters. He has constructed a very informative illustration that shows how jacketed bullets of the general WCC/MC type deform and eventually fragment when shot into gelatin at speeds of 15563204 ft s-1, equivalent to 474–977 m s-1 (Figure 24). At the lower energies (speeds of 2139–2650 ft s-1), the bullets shed one or two large pieces of lead and 0–4 tiny fragments. Only at higher energies did multiple large fragments appear. Thus the idea of one or two surfaces shedding essentially all the tiny fragments seems to be seen in practice for speeds only somewhat higher than those of the Mannlicher-Carcano. Of course, a bullet entering a cranium will fragment at slower speeds than a bullet entering gelatin. This makes the analogy to Figure 24 even closer than it might appear from speed alone.)

Figure 24. Deformation and fragmentation of jacketed bullets when entering gelatin. [Martin Fackler, as reproduced in Sellier and Kneubuehl, Wound Ballistics and the Scientific Background, Elsevier, 1994].

Benefits of this new explanation
This powerful new explanation settles (proves) several important issues from the assassination.

  1. Every fragment recovered and tested came from Oswald’s rifle to the exclusion of all other rifles (combination of ballistic and chemical evidence, each of which is essentially absolute).
  2. There is positive evidence for two and only two bullets, both WCC/MC.
  3. Both bullets were fired that day. (None of the fragments found in the limousine or on the stretcher could have been planted because they matched the tiny fragments from the men’s bodies, which had to have entered that day. In particular, CE 399 was not planted on the stretcher.) This is the only way to prove that the “external” fragments could not have been planted.
  4. All of the fragments are genuine (because none of them could have been planted). Thus we need not worry about supposed weaknesses in chains of custody, as has been claimed. (But the chains of custody are strong enough to stand on their own, anyhow. This is a good example of the redundancy of the physical evidence.)
  5. The close match between the stretcher bullet and the fragments from Connally’s wrist is consistent with the SBT but does not prove it. It lends strong support to it.
  6. If JFK was hit by a shooter from the right front, none of those fragments were ever found or tested.
  7. Therefore, anyone who speaks of another shooter is doing so in the complete absence of physical evidence. Such sheer speculation is, of course, logically indefensible. The hypothesis of a second shooter does not survive its very first testthe need for physical evidence specifically for it.
  8. And last but not least, Dr. Guinn was right, even if he didn’t fully justify his conclusions.

Broader implications for the assassination
The fruits of the NAA data do not stop with the eight conclusions above. They extend into broader areas of the assassination. Here are four of the major implications:

  1. With a chance of roughly one in a million of being wrong, the NAA evidence may be the strongest of the entire assassination.
  2. The sense of the simple two-bullet, one-rifle result for the fragments agrees with the sense of the two-motion, one-bullet result for physical analysis of JFK’s motions. This crime, complex as it often made out to be, was really very simple.
  3. We no longer need to analyze quarters of additional “background bullets” to check Guinn’s heterogeneities because those results are not relevant to the undisputed homogeneities of the two groups of fragments actually found. Instead, we should analyze tiny particles shed from the irregular surfaces of breaks in lead cores.
  4. The NAA results allow us to work around certain troublesome problems of evidence, and in so doing turns them from essential to inessential. Two example as the height of the back wound and the exact locations of the entrance and exit wounds to the head. With the NAA, none of these things needs to be know precisely. This removes the continuing confusion and debate over the exact position of these wounds.
        I understand that these are strong statements. The way in which this process of working around operates is shown in the next section. Basically, it works by tying a fragment on one side of the body through a wound in the body to Oswald's rifle on the other side. Since the process proves that the bullet in question started at a known place, passed though a known part of the body, and was retrieved from a known location on the other side, the exaction location and nature of the wounds to the body are no longer central because they must have allowed the bullet to pass through. 

Examples of the workaround procedure allowed by the NAA data

    The location of the rear head wound (entrance). Students of the assassination argue incessantly about the height of the entrance wound at the rear of his head. One group, composed mainly of nonconspiracists, accepts that it is just above and to the right of the EOP, as reported by the three autopsy physicians and reproduced in the warren Report. Another group, composed mostly of conspiracists, claims that it is four inches higher, near the cowlick. They follow the report of the HSCA. Each group claims photographic evidence for its position.
    Neither group is willing to budge about the height of the head wound. Even though there is persuasive evidence that the high position is the correct one and that the autopsy physicians made a mistake, let us assume for the sake or argument that we cannot know. The following chain of logic shows that this intractable problem can indeed be worked around, that is, the height doesn't really matter in getting to the right answer about the assassination.

  1. The bullet entered somewhere in the rear of JFK's head.
  2. The bullet did not stay in his head.
  3. The bullet exited somewhere on the right side of his head.
  4. Two large fragments of one or two bullets, a base and a tip (Q2,3), were found in the front seat of the car.
  5. Two pieces of damage to the inside of the windshield area (chrome strip and windshield proper) were found.
  6. The lead fragments retrieved from JFK's brain (Q4,5) were tied compositionally to the front-seat bullet (Q2) by NAA.
  7. Q2 was tied to Oswald's rifle (C2766) by ballistics.
  8. Therefore the bullet whose fragments hit the windshield area came unambiguously from Oswald's rifle and passed through JFK's head, where it left telltale fragments.
  9. Once this three-point trajectory is established, the details of passage through the head become inessential. Therefore we don't need to know exactly where the bullet entered the head.

    The three-point path of the bullet through the head is shown in Figure 25 below. The fragments from JFK's brain effectively tie the rifle behind to the fragments ahead, thus making details of the entrance and exit wounds interesting rather than critical.

Figure 25. The three-point path of the head shot from Oswald's rifle to the fragments recovered from the car, as fixed by the NAA.

    The location of the forward head wound (exit). The logic for the forward head wound is the same as for the rear wound, but with "forward wound" replacing "rear wound." Figure 25 applies to it as well.

    The height of the back wound. It is a bit more involved to establish the inessentiality of the height of the back wound because the bullet left no analyzable fragments as it passed through JFK's back and neck. Nevertheless, it can still be done. This issue is contentious because the high position leads to a downward trajectory through the neck and out the throat, and a logical connection to Connally's back and thereby to the single-bullet theory (SBT), whereas the low position leads to a horizontal or slightly upward track that is often said not to hit Connally or create the SBT. Here is the logical train of evidence without the height of the back wound or the inclination of the trajectory through the neck:

  1. Bullet A passed from the back to the throat and out.
  2. Bullet B (nonpristine) entered Connally's back well below Kennedy's throat and on a downward course.
  3. Bullet B was fired from Oswald's rifle because the wrist fragment was linked chemically (by NAA) to the stretcher bullet (CE 399), which was linked ballistically to Oswald's rifle.
  4. If Bullet A did not become bullet B, we have four problems: (a) A must have disappeared out of the car without a trace; (b) A must have been fired horizontally or upward so as to miss the car, which means from a ground-level position near the corner of Elm and Houston (i.e., near the motorcade and the crowds); (c) B had to conveniently appear at the same time to replace A; and (d) in order for B to be nonpristine, it must have hit something (the live oak tree?) between the sixth floor and Connally's back. These four problems make a very complicated scenario, indeed.
  5. But if Bullet A became Bullet B, these problems disappear: (a) A didn't disappear because it passed into Connally as B; (b) A, becoming B, was traceable to Oswald's rifle up high rather than being fired from ground level in a crowd; (c) no second bullet B had to conveniently appear; and (d) B was nonpristine because it had (as A) passed through Kennedy. This amounts to the single-bullet theory.
  6. Simplicity, even common sense, demands that we go with step 5 and the SBT—the choice isn't even close.

   This simple line of reasoning shows how the SBT flows naturally from the evidence with or without the the height of the back wound. Thus, that height is not needed to understand the assassination properly. The three-point path of the bullet through the bodies is shown in Figure 26 below. The fragments from Connally's wrist effectively tie the rifle behind to the thigh/stretcher bullet ahead, thus rendering details of the entrance wound in Kennedy's back interesting rather than critical.

Figure 26. The three-point path of the body shot from Oswald's rifle to the thigh bullet CE 399 recovered from the stretcher in the hospital, as fixed by the NAA.

    There's more, though. Once the conclusion in step 6 is granted, the downward trajectory through the neck follows automatically, and from it follows the high position of the back wound.

The missing lead, the Tague fragment, and the missed shot
Surprising as it may seem, the idea of the head bullet breaking into only two or three large fragments may tie together several other puzzling aspects of the assassination that have resisted satisfactory explanation. Three of these unresolved questions are the missing lead, the Tague shot, and the missed shot.
First, why is so much lead from the head shot missing? To address this puzzle, we may begin with another one—the strange observation that the fragments from the head shot, with their disparate origins (JFK’s brain, the large fragment in the front seat, and the three tiny fragments on the rear carpet), all cluster together remarkably tightly. A core that broke only once could explain this, for all its tiny particles would have to be shed from a single surface and would therefore emerge with a single composition. A core that broke only once would also be easy to get rid of—its one big piece (besides the one from the front seat would just have to fly out of the car somewhere. Additional evidence for minimal breakup comes from the line of tiny lead fragments that extends from the top back of the head (the point of entrance) to the front right side of the head (presumably the point of exit). Dr. Michael Baden, medical consultant to the HSCA, noted in his testimony that the collective mass of these fragments was so small that the bullet had broken up only minimally as it passed through JFK’s head. This means that nearly all the lead left the head. This is also consistent with all the fragments coming from a single break and its two surfaces.
if that missing mass of lead flew out somewhere as a single unit, where did it go?
A large piece of Pb core did indeed show up outside the car at the time of the assassination. It hit the curb of Main Street down near the triple underpass, where James Tague was standing, with enough force to shatter the curb and break off a piece (of curb or lead) that evidently flew upward and hit him in the cheek, for after the shots a bystander told him that his cheek was bleeding. He then noticed the fresh curb below, with some discoloration from the object that hit. Eventual spectrographic analysis of a piece of that curb by the FBI revealed that the slight marking on the curb was lead plus a trace of antimony—either from a hit by a lead core or by a copper-lead bullet from whose remnants the copper had leached completely. The simpler explanation of a lead fragment would fit with the missing core from Kennedy’s head shot. It also fits the geometry of the situation, for a line from the sixth-floor window extended through Kennedy’s head comes within a few degrees of Tague’s position (Figure 27). The core could have simply continued in a straight line out of Kennedy’s head and hit the curb by James Tague. Such a fragment from the head shot could well have emerged with enough speed to carry it over to Tague, for the two other large fragments had enough energy to dent the chrome strip and nearly penetrate the windshield. That means velocities of hundreds of feet per second, which would probably allow the big lead fragment to go the extra distance to Tague and still retain enough momentum to damage the curb and send a fragment of curb or lead up high enough to hit Tague’s cheek. Tague’s being hit by a large fragment from the head shot offers two additional benefits—(1) it frees up another bullet for a missed shot, probably early; and (2) in so doing it relieves an early miss of the difficulty of having to bounce high enough to reach Tague but be low enough to the ground to hit the curb. This feat is handled much more naturally by a fragment leaving Kennedy’s head, where starting well above the ground would allow it to more horizontally near the ground and strike the curb more forcefully than a bullet bouncing off the pavement would probably do, especially if it came from an early miss.[1] The other explanation for Tague, that the curb was hit by the rebound of a missed shot early in the sequence, has always been problematic because an early bullet would have gone well to the left of Tague (to the south). It is also rendered improbable by the observation that bullets hitting concrete don’t bounce very high, even if they are jacketed (previous footnote).

Figure 27. Map of Dealey Plaza showing the close alignment of Oswald’s rifle, Kennedy’s head, and James Tague at the moment of the fatal head shot. [From page 230 of Josiah Thompson's Six Seconds in Dallas, 1967, Bernard Geis Associates.]

      So we have at least five points of logic all converging on the missing lead from the head shot hitting James Tague: (1) the minimal breakup in the head and the extreme similarity of all the fragment from the head shot suggest strongly that the breaking of the head bullet released a large fragment of lead; (2) the natural path of that fragment would have been directly toward Tague; (3) judged by the other large fragment from the head shot, the large lead fragment would have had enough energy to break off part of the curb and sent it to nick Tague’s cheek; (4) the curb was probably hit by lead because it contained lead and antimony but no copper from a jacket; and (5) Tague’s being hit by a fragment of one of the two major shots would free up a third bullet for an early miss.

Getting the fragment over the windshield but down to Tague's curb
    Even though the web of evidence is strong that a large fragment of lead from the third shot flew down and hit the curb near James Tague, it is important to show that the fragment could actually cover that path. (We need not show, however, that it actually did take that route, for that requirement is patently impossible. A plausibility argument is the best we can do with the available evidence.) The conceptual problem in a nutshell is getting the fragment over the windshield but down to Tague. One is tempted to think that the angle needed to get the fragment over the windshield would cause it to hit the ground far past Tague, who was downhill from the car.
    This problem can be resolved quickly by some simple angles and physics. The angles are shown in Figure 28, which is a side view of the presidential limousine taken from Figure 33, page 118, in Robert B. Cutler's The Umbrella Man: Evidence of Conspiracy (Bett's and Mirror Press, Danvers, MA, November 1975).

Figure 28. Side view of the presidential limousine at Zapruder frame 313.

Note that the three-degree upward angle needed for a fragment exiting from the front of the head to clear the windshield just cancels the three-degree downward inclination of Elm Street and produces a horizontal path for the fragment as it clears the windshield. This simplifies the physics calculations to come.
    Once past the windshield, the fragment must fly 270 feet to Tague. How far must it drop? The answer is shown in Figure 29, which is based on part of Cutler's Figure 34, page 122. It shows a vertical section from the Dal-Tex Building past the Texas School Book Depository and the limousine and on to Tague's curb. I have superimposed a horizontal line just touching the top of the windshield. Tague's curb (the end of the three arrows on the lower left of the diagram) falls 15.5 feet below the line from the limo. Although the uncertainty in my line where it passes over Tague is probably at least a foot, elevations provided by Mr. W. Anthony Marsh gave a drop of 16 feet. Thus the two approaches agree within the uncertainties. For simplicity, we will use a drop of 16 feet.

Figure 29. Vertical section through Dealey Plaza from the Dal-Tex Building to James Tague.

    To determine the conditions that would allow the fragment to fall 16 feet while traveling 270 (i.e., the maximum speed when released from the head, ignoring for the moment the effects of air resistance), one uses the acceleration of gravity (32 feet per second per second) to derive a relationship between horizontal velocity, horizontal distance, and vertical distance. This relationship can be obtained by two successive integrations of the equation for acceleration a = dv/dt. When the initial position and velocity are set to zero, the simple result is:

Vb = D(16/H)½

where Vb is the average horizontal velocity of the bullet in feet per second, D is the horizontal distance covered by the bullet (270 feet in this case), and H is the vertical drop (16 feet in this case). When the values for D and H are inserted, Vb becomes about 270 feet per second.
    While this speed appears large enough to do the observed damage to the front of the car and to carry the fragment across the remaining part of the plaza to Tague, it may not be enough to damage the curbstone there, especially when air resistance is considered. (See below.) It is also considerably less than the 800–1000 fps that fragments emerged with from the test skulls used in the Warren Commission's re-creations run at the U.S. Army's Aberdeen Proving Ground, Maryland. At a velocity of 800 fps, for example, a fragment would fall only 1.8 feet by gravity as it traversed the 270 feet to Tague.
    Conversations with Larry Sturdivan, formerly of APG, have revealed that the Army used Asian skulls for their tests. These skulls would have been thinner than typical American skulls, and so would have produced higher exit velocities than might be expected with American skulls. The latter Mr. Sturdivan estimates at closer to 700 fps. But even with those velocities, a fragment would drop by only about 2.4 feet. When air resistance is taken into account, the final velocity of a 700-fps fragment would be about 300 fps, and it would be expected to drop by 4.5–5 feet, which is still shy of the 16 feet required.
    The resolution of the problem seems to lie in the nonballistic motions of bullet fragments. This means that every bullet fragment leaving a wound follows a curved trajectory over and above the gravitational effect. Some trajectories are even composed of multiple curved parts in different directions. This curvature is caused by spinning and irregular surfaces. Several such curving trajectories (in gelatin) were presented by Mr. Sturdivan in his testimony to the HSCA, and are shown in pages 389–392 of HSCA Volume I. Because the curvature is effectively random and unpredictable, it may appear to be left, right, up, or down. As a rough rule of thumb, the extent of the curvature could equal that from gravity. Thus the fragment that hit Tague could have obtained its new rightward deflection by curving rather than by emerging rightward from the head, and it could have also curved downward. One needs an average speed of about 400 fps to drop 8 feet by gravity on the way to Tague. Since not all multiple fragments will emerge from a wound with the same speeds, a speed of 400 fps for one fragment seems compatible with an average of 700 fps or so for multiple fragments. When air resistance is considered, a particle could have begun at roughly 600 fps and hit the curb at 200 fps.
    Detailed calculations by Mr. Sturdivan have confirmed this basic conclusion and refined it. His results, shown in Table 22 below, give the exit velocity of fragments with mass between 3.0 and 6.0 g that are required for them to fall gravitationally by either 8 or 16 feet as they travel the 270 horizontal feet to Tague's curb, assuming that they begin with zero absolute elevation from the head. (The first value represents half the fall to Tague's curb, the second the full fall. The half fall
represents the minimum fall that could be expected to be deflected down to the curb by unpredictable spinning and irregularities of shape.) MPA stands for "mean predicted area" of the fragment, "residual velocity" refers to that at Tague's curb, and E/MPA is the kinetic energy per mean presented area of the fragment, which is a measure of the penetrating power of the fragment. The last column shows the probability that such a fragment could break the skin at Tague's location.
    As the mass increases, the allowable velocity (exit velocity) decreases, but not by much (from 515 to 480 fps for the half fall and 360 to 340 fps for the full fall). The residual velocity and energy per unit area increase, and raise the probability of breaking the skin. The latter may also increase the energy of fragments splattered from the curbstone. Depending on mass, fragments with exit velocities of about 500 fps could have fallen halfway and been deflected the other half. Without deflection, exit velocities down to 350 fps would have been required in order for the fragments to drop the entire distance by gravity. Although exit velocities of 500 fps are smaller than the 800
–1000 fps observed in the Army's tests, there are certainly not out of line with thicker American skulls and some variation about the mean exit velocity.

Table 22. Detailed ballistic calculations for fragments from the head shot.
Mass, g Drop, ft MPA, cm-2 Exit velocity, fps Residual velocity, fps E/MPA, J cm-2 Prob. of breaking skin
3.0 8 0.61 515 238 12.9 0.81
4.0 8 0.74 500 248 15.4 0.88
5.0 8 0.86 488 255 17.5 0.91
6.0 8 0.97 480 260 19.5 0.93
3.0 16 0.61 362 169 6.5 0.36
4.0 16 0.74 352 176 7.8 0.49
5.0 16 0.86 344 181 8.9 0.59
6.0 16 0.97 339 186 9.9 0.66

    What kind of fragment could have wounded Tague? An interesting conundrum arises if we grant that nonballistic deflection would have been required for particles to sink the full 16 feet. The heavier particles retain more kinetic energy and so have a higher probability of breaking the skin. But the lighter particles can be deflected more. The information in Table 22 does not allow us to determine which size of particle most likely hit Tague.
    In summary,
the path over the windshield and down to Tague seems entirely plausible from all that is known about Dealey Plaza, the limousine, head wound, and the travel of lead fragments through air. One certainly cannot say that it could not have happened.

Potential problems with this Tague scenario

  1. Could the missing part of the core have been able to fly all the way to Tague and still have enough energy to break off a piece of curb and deflect it up to his cheek? Probably yes, if we take the other two pieces of the bullet (Q2,3) as a guide. They flew out of the head with enough energy to dent the chrome strip and nearly penetrate the windshield. A lead core with this kind of energy could probably fly down to Tague and still have enough velocity to fly off the curb.
  2. Does the position of Kennedy’s head allow the lead to fly out in that direction? This is an easy one. If Kennedy's head allowed Q2 and Q3 to fly out and hit the center and left parts of the windshield area, it could certainly allow another large fragment to more in the same general direction in which Tague was.
  3. Tague insisted, at least later, that he was hit by the second shot because he heard a shot after he was hit. But this seems inconsistent with his not knowing he was hit until afterward. His original testimony makes in plain that he wasn't sure which shot hit him. Only later did his story evolve into the second shot's hitting him.
  4. There still should be two or three basic levels of Sb if a bullet breaks in to 23 pieces. We don’t know how many pieces there were. We have two large fragments, one with Pb and one without. Therefore, there is no evidence for more than two pieces of lead, or a single break in the core. So we must start with the assumption of a single break and a single basic concentration of Sb.
  5. Does this interpretation necessarily mean only two bullets? Why not two zones from the same bullet but with different levels of Sb? Why not more than two bullets and a coincidental matching or two? Need to consider these intermediate solutions as well.

The missed shot
    The third question enlightened by the new explanation for the NAA is the missed shot, because in allowing Tague to be hit by a fragment from the third shot, it removes a separate "Tague shot" from the mix and opens the way for an early clean miss. Is there evidence for an early, clean miss? Yes. The best report I have seen is that written by Stavis "Steve" Ellis, solo motorcycle officer of the Dallas Police Department, in Larry A. Sneed's valuable book No More Silence [Three Forks Press, Dallas, 1998]. Ellis was in charge of the motorcycle escort for the motorcade through Dallas, and rode between Curry's car and the president's. On pages 144–145 of No More Silence he writes:

    We came west on Main Street to Houston Street and took a right, facing right into that building [the depository]. The building with the window was looking right at us as we came up to Elm Street and made a left, heading back toward the triple Underpass. Midway down Elm I remember waving at my wife's niece and nephew, Bill and Gayle Newman, who had apparently come out to see the President. About the time I started on a curve on Elm [near the knoll], I had turned to my right to give signals to open up the intervals since we were fixing to get on the freeway a short distance away. That's all I had on my mind. Just as I turned around, then the first shot went off. It hit back there. I hadn't been able to see back where Chaney was because Curry was there, but I could see where the shot came down into the south side of the curb. It looked like it hit the concrete or grass there in just a flash, and a bunch of junk flew up like a white or gray color dust or smoke coming out of the concrete. Just seeing it in a split second like that I thought, "Oh, my God!" I thought there had been some people hit back there as people stated falling. I thought either some crank had thrown a big "Baby John" firecracker and scared them causing them to jump down or else a fragmentation grenade had hit all those people. In any case, they went down! Actually I think they threw themselves down in anticipation of another shot.
    As soon as I saw that, I turned around and rode up beside the chief's car and BANG!…BANG!, two more shots went off: three shots in all! The sounds were all clear and loud and sounded about the same. From where I was, they sounded like they were coming from around where the tall tree was in front of that building. Of course, I'm forming an opinion based on where I saw that stuff hit the street, so I knew that it had to come from up that way, and I assumed that the others came from the same place.

    Thus Ellis is reporting that the first shot hit on or near the south curb of Elm Street about the time he reached the knoll. It sounds as if he was ahead of Chief Curry's car at that time, which would put the president's car far enough back up Elm for the shot to have come before it passed under the live oak tree. This would put the missed shot in the rough vicinity of Z 160, where many students of the assassination feel it had to have been.

The final shooting scenario
    Adding the neutron activation to the ballistics and the autopsy allows us to recreate the sequence of shots with considerably greater reliability that has been possible before. Here is a summary of that sequence, with the appropriate source of evidence placed in parentheses after each main point.
    Three shots were fired (three empty cartridge cases; most witnesses heard three shots). All came from the sixth floor of the depository. The second and third came from Oswald's rifle (NAA and ballistics), and the first one probably did, as well (no evidence for another rifle or shooter).
    The first shot missed and hit the street or the grass (Officer Ellis). It was an early shot, probably somewhere around Z160 to Z180. Presumably it was a rushed shot fired just before the president's car passed under the tree. This shot was made more difficult than often realized by the steep angle, the partially closed window, and the rapid and changing relative motion of the motorcade.
    The second shot was fired somewhere around Z220 to Z230. It entered the upper right part of Kennedy's back, passed at a downward angle through both men, left fragments in Connally's wrist, and was recovered as CE 399 (the stretcher bullet (autopsy, ballistics, NAA).
    The third shot was fired at Z313. It entered the right rear of Kennedy's head, left a trail of fragments through the head, and exited through the right side as three large fragments, two of which were recovered from the front seat of the car (autopsy, ballistics, NAA). The third large fragment, a sizeable fraction of the lead core, flew just over the top of the windshield, continued over the interior grass of Dealey Plaza, hit and marked the curb near where James Tague was standing (NAA, ballistics), sprayed up fragments of the curb and its lead, and disintegrated or flew far enough away that it was never recovered.
    No physical evidence for a fourth shot, a second shooter, or a shooter from any other location has been found to this day. The actual scenario was thus very simple.

[1] Vincent J.M. DiMaio, in Gunshot Wounds: Practical Aspects of Firearms, Ballistics, and Forensic Techniques (Elsevier, 1985, p. 90), give a table that shows that most bullets hitting smooth stone at angles of 1030 degrees ricochet at angles of only 12 degrees, which are generally not enough to allow them to avoid hitting curbs. Only .30 MI Carbine bullets weighing 110 grains were able to ricochet at 728 degrees when impacting at 2030 degrees. In other words, an early miss makes the bullets ricochet at a bad angle for hitting Tague.

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