Using chemical data to determine origins

      Chemical analysis is frequently used in forensic science to help determine origins of objects related to a crime. Chemical analysis is also used in areas such as geology, oceanography, and air pollution to help determine origins of rocks, aerosol particles, and air masses. In order to understand how chemical was used in the JFK assassination, it is helpful to briefly review some basic principles of determining origins from elemental data. This section restricts itself to the general approach, whose principles hold for any analytical technique and any set of objects. Their realization in the JFK case is treated in subsequent sections.
      In all chemical studies of origins, the chemical composition of the object in question is compared to the compositions of possible sources. From similarity or dissimilarity in compositions, the appropriate conclusions about origins are drawn. I have chosen the wording of this last sentence very carefully, because terms like “appropriate” and “conclusions” contain shadings of meaning that must be understood before the analyst can deduce the correct information about origins, or before the reader can properly evaluate whether the analyst got it right.
      There are two basic working principles for assessing origins: (1) two objects have the same origins when their chemical compositions are the same and different from all other possible sources; and (2) two objects have different sources when their compositions are different. “The same composition” and “different composition” are defined operationally, and are always relative to the suite of source materials. These principles are described in the rest of this section.
      We consider only the simplest case, where a single chemical property of a substance, such as the concentration of an element, is used to assess origins. The “composition” of the object in question is then expressed operationally as the mean concentration and the standard deviation of that element determined from replicate analyses of the object. For example, if four analyses of the concentration of antimony in the lead core of a bullet gave results of 21, 28, 24, and 30 ppm (parts per million by mass), the concentration of antimony in the bullet is said to be 26±4 ppm. This is the “composition” of the bullet for purposes of assessing its source.[1] Note that the standard deviation of 4 ppm includes variations within the bullet (which show up as variations among the four samples taken from the lead core), as well as variations from the analysis of each sample of the core. It is important to determine how much of the 4 ppm comes from real heterogeneities within the core, and how much is just analytical scatter. (In this simple case, the information provided does not answer this question.) This means that wherever possible, samples of bullets or fragments should be analyzed in replicate. Unfortunately, many fragments of bullets are too small to allow replicate analyses. Strictly speaking, then, only part of the needed information is provided by single analyses. The situation is not as bleak as it may appear, however, for experience with typical heterogeneities within bullets can be tapped as needed. This problem arose in the JFK case in a way that could not be resolved by general experience. The problem and its resolution are described at length near the end of this manuscript.
      More is needed than just analyzing objects in replicate, however. Enough subsamples of the bullet must be taken to define its heterogeneity properly. Statistical tests are available to determine the number of samples needed to define the standard deviation to any desired limit of accuracy. My rule of thumb is that at least four replicates are desirable. The more, the better, of course. Four hundred replicates is obviously better than four replicates, but not one hundred times better.
      If the source of this bullet is to be assessed from its concentration of antimony, potential sources (different types of bullets) must be analyzed similarly. The analyst assembles bullets of various types and analyzes them, always in replicate, for antimony. The mean and standard deviation of the bullet are compared to the means and standard deviations of potential sources, and the appropriate conclusions are drawn.
      A full study of sources will involve multiple specimens from all possible sources, each specimen being analyzed in replicate. If subunits of sources exist, such as multiple production lots of a given type of bullet, each lot must be considered as a different source unless or until the resulting data demonstrate to the contrary. It is easy to see how a “simple” study of sources can turn into a major effort. For example, suppose 50 types of bullets could be the source of a particular core of lead found at a crime scene. If each type of bullet were produced by a single manufacturer in an average of five production runs, fully characterizing the sources would require the analysis of at least 50 types x 5 production runs each x 4 bullets per production run x 4 samples of each bullet, or 4000 analyses! Should the bullets prove to be heterogeneous, another factor of something like 4 would be added (for replicates of each subsample), to give 16,000 analyses. Clearly, compromises must be made when designing such studies. Unfortunately, compromises inevitably degrade the resolving power of the results. Great care is required to find the least-disruptive compromise. Few actual studies of this type can be considered ideal.
      We now consider how a simple set of hypothetical results is interpreted. For the bullet described above, suppose four potential sources (types of bullets) were analyzed appropriately (taking a reasonable number of bullets from the various lots, and running reasonable numbers of replicate analyses on each bullet), and gave the following overall results:

Table 2. Hypothetical concentrations of antimony in one test bullet and four possible sources.

      The source in this simple example is obviously #2, because it matches the bullet (overlaps its concentration of antimony) and the other sources don’t. We must be careful here, however, for all conclusions about sources are probabilistic, not absolute. The uncertainties shown here represent the ranges of only 68% of the expected values from each analysis (the so-called 1–s ranges, where s represents the standard deviation). This means that 32% of the analyses may fall outside the 1-s range. To be more cautious, the 95% limits are often used, which correspond to about 2 s. The 2-s version of the Table 2 is:

Table 3. The 2-s version of Table 2.

      At this level, the origin of the bullet is less clear, for it could be either source 1 or source 2. This very simple demonstration shows how the interpretation of analytical data depends on the level of confidence that we associate with it. At the 68% confidence level, the bullet can come from only source 2, whereas at the 95% confidence level, the bullet can come from either source 1 or source 2. Very seldom do scientists accept levels of confidence less than 95% (2 s). Sometimes they even choose 99%, which is about the 3-s level.
      But even this simple interpretation is potentially wrong, for it assumes that sources 1–4 are the only possible ones. Suppose that there were another source 5 that we had missed, whose concentration of antimony was 18±6 ppm at the 2-s level. It could also have been the source of the bullet, as seen from Table 4 below:

Table 4. Hypothetical concentrations of antimony in one test bullet and five possible sources.

      In practice, it is very difficult to be sure that all possible sources for an object have been tested. Thus from these data we may conclude only that the source of the bullet could be sources 1, 2, or 5. The real source might have been another type of bullet that we didn’t know about, or even a bullet from source 3 or 4 that deviated greatly in composition from their norms. In other words, equality of composition does not necessarily mean identity of origin. That is the bad news. The good news is that differences of composition can show differences of origin, within the statistical limits discussed above, because there is no question of similar sources slipping in. Thus we are allowed to say from Table 4 that the source of the test bullet could not have been source 3 or 4 (within reasonable limits).
      As you read below about how chemical techniques were applied to the JFK assassination, keep these principles in mind, and use them as a benchmark against which to judge the sufficiency of the procedures that were actually used.

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