I. Fragment Analysis

A. Introduction

One of the distinct differences between the "modified Waters" and "Riley frontal" interpretations is the relationship between the fragments on the lateral X-ray and the frontal X-ray.

• On the lateral X-ray, the two largest fragments are at opposite poles of the skull, one at the front and one at the back of the skull.
• On the frontal X-ray, the two largest fragments are on the right side of the skull, both roughly midway between the edge of the skull and the midline.
  • The most prominent fragment is nearly circular (with a small semi-lunar defect in the lower right) and is located in the supraorbital region.
  • The other large fragment is more linear, with the long axis oriented more or less up and down.
• The location and appearance of these fragments is shown in the following figure:

The "modified Waters" and "Riley frontal" interpretations are diametrically opposed in defining which fragment on the lateral X-ray corresponds to which fragment in the frontal X-ray.

• In the "modified Waters" interpretation:
  • The fragment at the back of the skull in the lateral X-ray corresponds to the circular fragment in the frontal X-ray.
  • The fragment at the front of the skull in the lateral X-ray corresponds to the linear fragment in the frontal X-ray.
• In the "Riley frontal" interpretation:
  • The fragment at the back of the skull in the lateral X-ray corresponds to the linear fragment in the frontal X-ray.
  • The fragment at the front of the skull in the lateral X-ray corresponds to the circular fragment in the frontal X-ray.

This difference in interpretation is easier to understand visually and is illustrated in the following figure (repeated from the article):

This distinct difference provides the opportunity for empirical tests between the two interpretations (in addition to those mentioned in the article).

B. Fragment Size

Simply put, how well do the fragments match in size between the two interpretations? The sizes of the fragments in the two interpretations are compared to the fragments in the frontal X-ray in the following figure:

• The "modified Waters" fragments are on the left, the fragments in the middle are from the frontal X-ray, and the fragments on the right are according to the "Riley frontal" interpretation.
• In the "modified Waters" interpretation, the fragments do not match in size. The rear fragment on the lateral X-ray is taller (y-axis) than the round fragment in the frontal X-ray and the frontal fragment in the lateral X-ray is shorter than the linear fragment in the frontal X-ray. (The results do not depend on the specific rotation used here -- the difference is distinct even at rotations which would invalidate the "modified Waters" interpretation, e.g., 15 degrees).
• In the "Riley frontal" interpretation, the fragments match in size. Within the limits of the methods employed, this match is exact.
• The conclusion, I hope, is obvious: in the "modified Waters" interpretation, the fragments do not match in size; in the "Riley frontal" interpretation, the fragments do match in size. I confess that this strikes me as compelling evidence in favor of the "Riley frontal" interpretation.

C. Fragment Alignment

In addition to comparing the sizes of the fragments, we can compare how well they align in the two interpretations. 'Alignment', as used here, refers to the vertical position of a fragment on the lateral X-ray compared to the vertical position on the frontal X-ray, i.e., do they have the same position on the y-axis in both the lateral and frontal X-rays.

• The points to be aligned are the two fragments and the top of the skull. The top of the skull serves as a common "point of origin".
• In the strictest sense, we already know that the "modified Waters" interpretation cannot produce an exact alignment because of the different "sizes" of the fragments in the lateral and frontal X-rays. As we shall see, such subtle differences are the least of the problems for the "modified Waters" interpretation. Whereas an exact alignment is not required (due to technical factors such as magnification differences, beam alignment, etc.), the alignment must be reasonably close.
• The general alignment can be seen in the following figure. (Subsequent figures are higher magnifications of the same figure.)

Note: the "modified Waters" angle has never been specified; "best fit" was obtained by aligning the fragments (see text for details). However, this relatively close alignment for the "modified Waters" interpretation ignores the fact that the tops of the skull do not align.

1. In the "modified Waters" interpretation, under no conditions do the fragments and top of skull align.

• This requires some elaboration. Since no specific angle has ever been specified for the so-called "modified Waters" interpretation, a variety of angles must be tested. Angles between 15-30 degrees (and the "modified Waters" angle must be much closer to 20 degrees) have been tested. The "best fit" results from aligning the two fragments and ignoring the alignment of the tops of the skull.
• It is clear that the tops of the skulls are not aligned (see top of figure). Even when the misalignment of the top of the skull is ignored, higher magnification shows that the fragments are only in rough alignment.

1. In the "Riley frontal" interpretation, the fragments and top of skull align exactly.

• As is said of good beer, "It doesn't get any better than this."
• A couple of comments:
  • It is not surprising that this misalignment has gone unnoticed. When "eyeballed", the fragments appear to be "roughly" in the appropriate position. However, when rigorous and objective techniques are used (computer images compared), it becomes clear that the fragments are not aligned in the "modified Waters" interpretation.
  • The statement that the fragments cannot be aligned in the "modified Waters" interpretation has a certain "trust me" element. Without resorting to a fairly complex topological argument, I simply point out that I've tried my best to get the best fit. What cannot be ignored, however, is that there is an exact alignment of fragments and the tops of the skull in the "Riley frontal" interpretation.
  • We now have two tests completed: the size and the alignment of the fragments in the X-rays. In the "modified Waters" interpretation, neither the size or alignment of the fragments is as predicted. In the "Riley frontal" interpretation, both the size and alignment of the fragments are exactly as predicted.
  • Alas, there is even more....

D. Optical Density Measurements

Dr. David Mantick has made optical density measurements on the original autopsy X-rays at the National Archives. [Making a long story short, optical density can be used as an indirect measure of "amount of material" present at the site of measurement. Also, it must be pointed out that Dr. Mantick accepts the "modified Waters" interpretation.]

When measuring the optical densities of the round fragment in the frontal X-ray (corresponding, in the "modified Waters" interpretation to the rear fragment), Dr. Mantick obtained values that indicate that there is more metal in the lower (ventral) part of the fragment than the upper part of the fragment. He considers these values to be anomalous since: (a) there is a semi-lunar defect in the lower region of the round frontal fragment; and (b) there is no indication in the lateral X-ray that the lower (ventral) part of the rear fragment is larger. Whereas these observations on the fragments are correct, there is another explanation that is possible.

The optical density measurements on the round fragment in the frontal X-ray are indeed inconsistent with the "modified Waters" interpretation. However, they are completely consistent with the "Riley frontal" interpretation. In the "Riley frontal" interpretation, the round fragment in the frontal X-ray corresponds to the frontal fragment in the lateral X-ray. As can be seen in the following figure, there is indeed more metal in the lower part of this fragment:

E. "Circumstantial Evidence"

The following points are not presented as empirical arguments. However, they are points that are worth considering.

• In the "modified Waters" interpretation, the round circular fragment in the frontal X-ray corresponds to the rear fragment in the lateral X-ray. Putting this into "real world" terms, this means that there is a disk of metal at the back of the skull below the HSCA's entrance wound. Consider how odd this is. It means (in this interpretation) that when the bullet entered the skull, a round fragment (presumably a cross-section of the bullet) broke off and somehow slid down the back of the skull. To put it mildly, this is an exceptionally odd way for a bullet to fragment.
• A round fragment on the back of the skull was not seen at autopsy.
  • Even though the prosectors examined the back of the skull thoroughly, they did not see such a fragment.
  • This conflict (between the HSCA's interpretation and the autopsy "non-description") has led some to suggest that the autopsy X-rays must not, therefore, be authentic.
  • It is quite clear that Dr. Humes equated the round fragment in the frontal X-ray to the frontal fragment in the lateral X-ray (got that? whew....). From Dr. Humes' interview with the HSCA forensics panel (HSCA, Vol. 7):

Dr. PETTY. Now, may I ask you one other question on this X-ray, Dr. Humes. Here is a view taken, I assume, with the radiation point above the face and the film behind the back of the head.

Dr. HUMES. Not being a radiologist, I presume that.

Dr. PETTY. If that's true, then the least distorted and least fuzzy portion of the radiopaque materials would be closest to the film, and we would assume then that this peculiar semilunar object with the sharp edges would be close to the film and therefore represent the piece that was seen in the lateral view-----

Dr. HUMES. Up by the eyebrow. [Emphasis added]

Dr. PETTY. No. Up by the--in the back of the skull.

II. On Lamboid Suture Visible in the Orbit

A. Overview

What follows is a fairly technical elaboration on a fine point in neuroanatomy. The heart of the matter is addressed in point B.; unless you eat this stuff up, you may wish to skip the remainder [and, no, dear reader, I am not trying to hide anything....]. There is a story behind this argument that won't be discussed in detail; to make that story short, what I perceived as an argument for my interpretation has come back at times as an argument against it. It is all the more frustrating because all the data are unequivocal.

Briefly put: suture is visible on the frontal X-ray in the orbit (crudely, one can "look through" the orbit and "see" suture). Assuming this to be lamboid suture (more on that at another time) the issue is, with which interpretation is this compatible?

Anatomical primer:

There's no way to get around some neuroanatomy, but I'll try to keep it short and simple. Two important things are (1) to understand the three-dimensional course of the lamboid suture and (2) know what the landmark "lambda" refers to.

The lamboid sutures (left and right) start out at the posterior ("back") side of the skull; they course upward and "backward", curving around the back of the skull.

"Lambda" is a skull landmark that refers to the point where the lamboid sutures intersect the sagittal suture. (Where the sutures join, they resemble the Greek letter lambda, hence the name; an inverted capital Y also works, but that's the origin of the use of lamboid suture.) A very important point: lambda makes the apex of the sutures -- all other lamboid suture will be in a horizontal plane below the level of lambda.

The following figure shows the location of lamboid suture that is visible in the orbit on the frontal X-ray.

The lamboid suture seen in the right side of the figure shows suture extending from 4 cm to 5 cm from the midline. This means that we are roughly half-way between the midline and the edge of the skull, a point where lamboid suture must be significantly below lambda.

C. Testing the "modified Waters" interpretation

Argument: Lamboid suture visible in lower orbit on the frontal X-ray demonstrates that the frontal X-ray cannot be a "modified Waters" projection.

The general principles are not difficult or complicated. In the "modified Waters" projection, a line passing through the lower orbit will not intersect lamboid suture. This point is illustrated below (note: Angel's diagram is used to illustrate the point and not for the actual data; we'll come to the "real stuff" shortly):

Since the lamboid sutures rise as they converge, the lamboid suture visible in the orbit must be significantly lower than lambda. So, the question is: does the "modified Waters" view through the orbit intersect lamboid suture? This is a testable question and the answer is unambiguous. So, let's take a look at JFK's normal lateral X-ray (as published by the HSCA; 8X10 glossy obtained from National Archives and scanned into computer format).

This is JFK's normal lateral X-ray superimposed on the HSCA drawing. Note that "the modified Waters" projection does not cross lamboid suture. It is debatable if it even passes below lambda, but that simply doesn't matter. Clearly, the line cannot pass significantly lower than lambda, certainly nothing even close to that required to see lamboid suture in the orbit.

C. Argument by Corollary

What we can see in the same figures is that the "Riley frontal" line passes through lamboid suture significantly below lambda. This is as predicted. There's really no point in going into great detail here. The important points are (1) the "modified Waters" interpretation doesn't work and (2) the "Riley frontal" interpretation does.

III. Focus of Image and Distance Estimates Argument

The following is a brief rebuttal to the argument that because the circular fragment in the frontal X-ray is in sharp focus, it must be located near the X-ray film and, therefore, must be the rear fragment on the lateral X-ray. As we shall see, as applied to the autopsy X-rays, this argument is specious.

• One thing to keep in mind is that the distance/focus relationship is a correlation, not a causal event. This point was discussed in the Third Decade article.[The distance/focus argument applies to biological tissue but breaks down when you're talking about radiopaque, sharp-edged metal. Location relative to the beam will be far more important in determining the focus of the image.]

• However, there is no need to bother with the description of factors since there is a very easy empirical check we can make to determine the validity of the argument. If the argument is valid, then the "other" fragment must be blurred. What's good for the goose is good for the gander. The argument is meaningful if and only if there is a measurable difference in "clarity" of the fragment images. But consider the two fragments on the frontal X-ray:

By what objective criteria can one be said to be in clearer focus than the other? Since the argument fails to distinguish between either interpretation, it is -- in the scientific sense -- meaningless.

To be continued ....

Technical Note:

Images were scanned on a Hewlett-Packard ScanJet Iicx. Scanned images included 8 x 10 glossy prints and 4x5 negatives of HSCA exhibits obtained from the National Archives.

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