Chapter 24: Gunshot Residue, Paint, Glass, and Soil: The Microscopic Evidence

"The dust of a man's clothing is often a more eloquent witness than the man himself — provided we do not ask the dust to say more than it knows." — constructed teaching epigraph, in the practitioner voice of this book, after the long tradition that runs from Edmond Locard to the modern trace laboratory.

Overview

Four materials — a smear of metallic particles from a fired gun, a chip of layered paint, a scatter of glass fragments, a crumb of soil from a boot tread — share a chapter for one reason: each is transfer evidence in the purest sense, Locard's exchange principle (Chapter 3) made literal, and each is, almost always, class evidence whose value is a probability rather than a proof. None of them, on its own, names a person. All of them, read honestly, can place an object in a category, associate it with an environment, or — most powerfully and most cleanly — exclude a suspected source outright. The whole craft of this chapter is holding each of these materials to the exact strength it can bear, no more, because the temptation to overstate microscopic evidence is older than forensic science itself and has put innocent people in prison.

So we begin where the book always begins: with the question the evidence is being asked to answer. Did this person fire a gun? is what an investigator wants from gunshot residue — but residue can only tell you that particles characteristic of a discharge are present on a surface, and particles travel, settle, and contaminate with an ease that should make you cautious before they make you confident. Did this paint come from that car? is what a hit-and-run case asks — but paint answers in layers, and a single common layer says little while a matching sequence of many layers can say a great deal. Did this glass come from that window? turns on a physical property — the refractive index — measured precisely, but shared by enormous quantities of ordinary glass. Was this person at that place? is the soil question, and soil answers it the way pollen did in Chapter 13: by association with an environment, scaled by how distinctive that environment is.

This is also a chapter with a particular debt to the one before it. The instruments that turn "looks like" into "is" — above all the scanning electron microscope with elemental analysis (SEM-EDX), which Chapter 23 introduced — are what let a modern laboratory identify a gunshot-residue particle by its shape and its elemental composition rather than by a chemist's hopeful eye. Where Chapter 23 gave you the instruments, this chapter puts four difficult materials in front of them and asks the harder question: granting that the instrument measured what it measured, what may we honestly conclude? The answer, four times over, is the answer of the whole book. These methods exclude well, associate honestly, and prove almost nothing by themselves — and the analyst's discipline is to say exactly that, on the page and on the stand.

In this chapter, you will learn to:

• Say what gunshot residue (GSR) and primer residue actually are, what their particles can establish, and why contamination and transfer make the evidence weaker than its reputation.
• Read a paint-layer comparison — why the sequence of layers, not any single layer, is where the probabilistic weight lives.
• Define the refractive index of glass and explain how it and fracture analysis compare fragments and reconstruct a break, and where the "match" stops.
• Explain how soil comparison associates an object with a place, why it is class evidence, and what makes one soil association strong and another worthless.
• Apply the honest verbs to all four materials, and refuse the slide from consistent with to proves.
• Locate gunshot residue, paint, glass, and soil on the NAS 2009 / PCAST 2016 validity spectrum and write each conclusion at its true strength.

Learning Paths

🔎 Investigator/CSI: Collection decides everything here, and most of it cannot be undone. Weight §24.1 (the GSR contamination problem starts at the scene and in your own squad car), §24.3 (collecting glass and reference fragments without cross-transfer), and §24.4 (where and how to take soil control samples — the edge of the lot, not the center). A trace you contaminate or a control you fail to collect is a result the lab cannot rescue. 🧪 Lab analyst: Weight §24.1–§24.4 throughout. The SEM-EDX particle criteria for GSR (§24.1), the layer-by-layer paint examination (§24.2), refractive-index measurement (§24.3), and the soil-profile comparison (§24.4) are your bench. §24.5 is where you decide how strong to call an association, and §24.6 is the language discipline that keeps your report defensible. ⚖️ Law/courtroom: Sections §24.5 and §24.6 are the chapter for you — the probabilistic nature of all four materials, the specific overstatements to attack on cross, and the difference between "consistent with" and the certainty a jury will hear if you let them. The GSR transfer problem (§24.1) is one of the most fruitful cross-examination openings in forensic science. 👥 General reader/juror: §24.1, §24.5, and §24.6 are your antidote to the television "gunshot residue test" that proves the suspect fired the gun. Learn why "his clothes had gunshot residue" can mean he fired a weapon — or stood near someone who did, or sat in the back of a patrol car, or shook hands with an officer.

24.1 Gunshot residue: what it is, what it proves, and the contamination problem

Start with the moment a gun fires, because the evidence is born in it. When a cartridge is discharged, the firing pin strikes the primer — a small charge of pressure-sensitive chemicals at the base of the cartridge whose job is to ignite the main propellant. The primer detonates, the propellant burns, and in the few thousandths of a second the weapon is in operation, a cloud of vaporized and particulate material erupts from every gap in the firearm: the muzzle, the ejection port, the gap between cylinder and barrel on a revolver. That cloud is gunshot residue (GSR) — the particulate and chemical debris produced by the discharge of a firearm, deposited on the shooter, on nearby surfaces, and on the target. It is composed of two broad ingredients: burned and unburned particles of the propellant (organic residue — nitrocellulose, nitroglycerin, stabilizers), and inorganic particles condensed from the vaporized primer — the part that matters most for identification.

That primer-derived fraction is the heart of GSR analysis, and it deserves its own name: primer residue — the inorganic particulate component of gunshot residue, formed when the metallic compounds in the primer are vaporized by the discharge and condense into tiny spherical particles. In the most common traditional primer chemistry, those compounds contain lead, barium, and antimony, and the diagnostic particle is one that contains all three of these elements fused together in a single particle with a characteristic morphology — typically a spheroid, formed by molten material cooling in flight. It is this combination — the right elements and the right shape, in one particle — that the modern laboratory looks for, and the instrument that finds it is the one Chapter 23 built toward: the scanning electron microscope with energy-dispersive X-ray analysis (SEM-EDX), which images a particle at high magnification (revealing its shape) and simultaneously reads its elemental composition (revealing what it is made of). A chemist's color test ("does this swab turn pink for lead?") can tell you an element is present somewhere on a surface; only the particle-by-particle SEM-EDX examination can say this single spheroidal particle contains lead, barium, and antimony together, which is a far more specific finding.

🔬 At the Bench Why morphology and elements, and not either alone? Because the world is full of lead, and full of barium, and full of antimony, separately. Lead is in old paint, fishing weights, and wheel weights; barium and antimony appear in brake linings, certain lubricants, and industrial dusts. A swab that simply shows "lead present" proves almost nothing. What is rare in ordinary life is a single microscopic particle that fused lead, barium, and antimony together while molten and cooled into a sphere — that specific combination, in that specific form, is what the discharge of a firearm produces and what most everyday sources do not. SEM-EDX examines a sample particle by particle, automatically locating candidate particles by their brightness (heavy elements scatter electrons strongly), then confirming each one's elemental spectrum and shape against established criteria. The honest output is a count: how many particles consistent with primer residue, of what confidence class, were found. That is a defensible, instrument-grounded statement — and it is a much narrower statement than "this person fired a gun."

Here is the first hard limit, and it is the one the whole section turns on. Finding GSR on a person establishes that GSR is present on that person — not that the person fired a weapon. The gap between those two statements is filled by every way a primer particle can reach a surface other than by that surface's owner pulling a trigger, and the ways are many. A GSR particle is tiny, light, and indifferent to how it got where it is. It cannot tell you whether you fired the gun, stood next to the person who did, handled a fired weapon, touched a contaminated surface, or were placed in the back of a police car where a hundred armed officers and arrestees have shed residue before you. This is the contamination and transfer problem, and it is not a minor caveat — it is the central reason GSR sits where it does on the validity spectrum and the reason a thoughtful laboratory states its conclusions with deliberate restraint.

Walk through the transfer routes, because each is a real cross-examination and each has changed real verdicts:

• Secondary (and tertiary) transfer. GSR moves by contact. A particle on the hand of a shooter transfers to anything they touch — a doorknob, a handshake, a steering wheel — and from there to the next person who touches it. A non-shooter can acquire GSR simply by being handcuffed by an officer who fired at the range that morning, or by sitting where a shooter sat. The particle does not record its own history.
• Environmental and occupational background. People who are routinely around firearms — police officers, range workers, some military personnel, hunters — carry background GSR as a matter of course. Their cars, clothing, and hands are part of the residue's environment. A particle "found on the suspect" found its way there in a world already dusted with the stuff.
• Police-transport and booking-area contamination. This is the most insidious route, because the very system that collects the evidence can deposit it. Patrol-car back seats, interview rooms, holding cells, and the hands and uniforms of arresting officers are reservoirs of GSR. A suspect sampled after a ride to the station and a few hours in a contaminated environment may carry residue that has nothing to do with any shooting. The countermeasure — sampling at the scene before transport, controlling for officer contamination, documenting the chain of every surface the suspect contacted — is exactly the kind of discipline that is easy to skip and impossible to recover later.
• Loss over time. Running the other direction, GSR also falls off. Particles on hands are lost within hours through ordinary activity — wiping, washing, putting hands in pockets. A negative GSR result on a person sampled many hours after a shooting therefore proves very little: the absence of residue is consistent with not having fired a gun and with having fired one and then washed, sweated, and moved through the day. GSR's absence is weak evidence in both directions.

🧠 Cognitive-Bias Watch GSR is unusually vulnerable to a bias the analyst never sees coming, because the contamination happens before the sample reaches the lab. The examiner at the SEM-EDX is doing honest, instrument-grounded work — counting particles that genuinely meet the criteria — and can be entirely correct that "three particles consistent with primer residue were present on the sample" while the investigative inference built on top of that finding ("the suspect fired the murder weapon") is contaminated by a transfer the examiner had no way to detect. The danger compounds when the analyst is told why the sample matters: an examiner who knows the detective is sure this is the shooter may, at the margins, resolve an ambiguous two-component particle generously, or report a borderline result with less hedging than it deserves. The safeguards are the book's usual ones — keep the case narrative away from the particle examiner, document every contamination opportunity at collection, and report the count and its limits rather than the conclusion the detective wants (context management, Chapter 31). The cleanest GSR statement is the most modest one, and modesty here is not timidity; it is accuracy.

What, then, can GSR legitimately do? More than the criticism above might suggest, provided the claims stay narrow. GSR distribution can help reconstruct muzzle-to-target distance: the density and spread of residue around a bullet hole in clothing, calibrated against test-fires of the same weapon and ammunition, can distinguish a contact shot (heavy soot, searing) from a close shot (a tightening pattern of particles) from a distant one (no residue on the target at all) — a genuinely useful, physics-grounded determination shared with the forensic pathologist (Chapter 11). GSR on a garment is also generally more probative than GSR on hands, because clothing holds particles longer and is less exposed to the casual transfer that hands suffer. And a well-documented, particle-confirmed GSR finding, presented as "particles consistent with primer residue were present, in this quantity, with these limits on what that implies," is real evidence — evidence a jury may weigh alongside everything else. What is not legitimate is the television sentence: "the gunshot residue test proves he fired the gun." It proves the particles were there. How they got there is the case's problem, not the particle's answer.

⚖️ In the Courtroom The reckoning over GSR contamination has reached the institutions, not just the textbooks. The U.S. Federal Bureau of Investigation Laboratory, by its own account, discontinued routine gunshot-residue examinations in 2006, citing in part the contamination and interpretation problems described here; other laboratories continue the work under increasingly cautious interpretive guidelines, and standards bodies have pressed for explicit treatment of transfer and background in every report. For the courtroom reader, the lesson is concrete: the most effective cross-examination of GSR evidence rarely attacks the instrument (the SEM-EDX is sound and the particle criteria are well established); it attacks the inference — Where was the suspect sampled, and when? Who handcuffed him, and had they fired a weapon recently? What was the GSR background of the patrol car? Was a control sample of the transport environment taken? Each question targets the gap between "particles were present" and "this person fired this gun," which is precisely the gap the science cannot close on its own.

24.2 Paint: layer structure and comparison

Paint is the quiet workhorse of trace evidence, and it teaches the chapter's central lesson — that the weight of class evidence scales with its complexity and rarity — better than almost any other material. A single drop of paint is rarely impressive. A multi-layered chip, read in cross-section, can be one of the more powerful associations a trace laboratory produces, short of DNA. The difference is entirely a matter of structure, and structure is where we begin.

Consider where paint evidence most often arises: a hit-and-run collision, where a vehicle leaves a smear of its paint on a victim, a garment, a bicycle, or another car, and carries away a smear of the struck object's paint or coating in return (Locard, both directions). Modern automotive paint is not one substance but a layered system, applied at the factory in a defined sequence: typically an electrocoat primer (for corrosion resistance, bonded directly to the metal), one or more primer-surfacer layers, a colored basecoat (the pigment that gives the car its color), and a clearcoat (the glossy protective top layer). Each layer has its own chemistry — binder type, pigments, additives — and its own thickness, and the sequence and composition of the whole stack is characteristic of a manufacturer, a model range, a production period, and sometimes a specific assembly plant. A repainted vehicle adds still more layers (the refinish coats over the original factory system), multiplying the structure and, with it, the potential for a distinctive comparison. This brings us to the method's defining term: a paint-layer comparison — the examination and comparison of the number, sequence, color, thickness, and chemical composition of the individual layers in a questioned paint sample against those in a known sample, to assess whether they could share a common origin.

🔬 At the Bench The examination is patient, sequential, and mostly about not destroying the structure. A paint chip is first examined intact under a stereomicroscope and then prepared as a thin cross-section — embedded, cut, and polished — so the examiner can see the layers edge-on, like the rings of a tree or the strata of a cliff face. The comparison then proceeds layer by layer: Do the questioned and known samples have the same number of layers? In the same order? Of matching color and thickness in each layer? Microscopy handles the visible structure; the chemistry of each layer is probed with the instruments of Chapter 23 — infrared spectroscopy (FTIR) to identify the binder and some pigments in each layer, SEM-EDX for the elemental composition of pigments and fillers, and pyrolysis gas chromatography–mass spectrometry for the organic polymers. The principle throughout is the trace examiner's first principle: look for differences. A single reproducible difference in any layer — a pigment present in one and absent in the other, a layer in one sample with no counterpart in the other — excludes a common source, cleanly. Agreement across every layer does not prove a common source; it fails to exclude one, and the weight of that non-exclusion depends entirely on how unusual the matching sequence is.

The probabilistic logic here is worth making explicit, because it is the model for the whole chapter. One layer of common white automotive paint is shared by millions of vehicles; a match on that layer alone is weak. But each additional matching layer multiplies the rarity, because the probability that two unrelated vehicles share layer one and layer two and layer three and the exact thicknesses and the refinish history shrinks with every independent feature. A questioned chip that matches a known vehicle across six or seven layers — factory system plus a non-standard repaint, in the same order, with the same chemistry at each level — is a strong association precisely because the coincidence has become implausible. This is class evidence the honest way: not a leap to "this car," but a sober assessment that the more complex and unusual the matching structure, the less likely the match is coincidental. The examiner who can articulate that — "the agreement spans seven layers including an unusual aftermarket coat, which makes a coincidental match with an unrelated vehicle unlikely, though I cannot exclude every similarly repainted vehicle" — is doing the method right.

🔬 Read the Evidence

```text FIGURE 24.1 — "A paint chip in cross-section" [constructed teaching example] THE ITEM A flake of paint, ~2 mm across, recovered from the clothing of a pedestrian struck in a hit-and-run, examined as a polished cross-section beside a known sample lifted from a suspect vehicle's damaged fender. THE CONTEXT Recovered with clean tools into a paper fold (not tape, which can distort soft layers); the known sample was taken from an undamaged area adjacent to the impact, with a substrate note recording exactly where on the vehicle it came from.

     CROSS-SECTION (schematic — not to scale; top = outermost)
     ┌───────────────────────────┐
     │  clearcoat        (gloss) │  ← layer 1
     ├───────────────────────────┤
     │  red basecoat             │  ← layer 2  (color the eye sees)
     ├───────────────────────────┤
     │  gray primer-surfacer     │  ← layer 3
     ├───────────────────────────┤
     │  BLUE refinish basecoat   │  ← layer 4  (an earlier color — vehicle was repainted)
     ├───────────────────────────┤
     │  factory e-coat primer    │  ← layer 5  (bonded to metal)
     └───────────────────────────┘

WHAT IT SHOWS Five layers in the questioned chip, in this order, with these colors and thicknesses; the known sample shows the same five layers, same order, same colors, and FTIR identifies the same binder chemistry in each. The buried BLUE refinish layer (layer 4) means the vehicle was repainted from blue to red — an uncommon, individualizing-ish history. WHAT IT DOESN'T It does not name THIS vehicle to the exclusion of all others; any vehicle repainted the same way in the same sequence would match. It does not say WHO was driving or WHEN the transfer occurred. A single chip cannot date itself. THE INFERENCE The five-layer agreement, INCLUDING the unusual buried repaint, STRONGLY SUPPORTS a common origin — coincidence across all five layers and the repaint history is unlikely — stated as "strongly supports," not "came from this car and no other." THE LESSON The weight is in the SEQUENCE, not any one layer. One common layer proves little; a long, unusual stack makes coincidence implausible. Rarity and complexity are what turn class evidence into strong evidence — and even strong class evidence is not individualization. ```

Two further points keep paint honest. First, architectural and tool paint — the paint on a pried windowsill, a forced door, a safe — works the same way and arises constantly in burglary cases: a pry bar carries away paint from the surface it forced, and that paint can be compared, layer by layer, to the scene. The logic is identical; only the substrate changes. Second, a physical fit trumps everything. If a paint chip from a scene can be physically reassembled with the damaged area of a suspect vehicle — the broken edges interlocking, the layers continuous across the join — that is no longer class evidence but a near-individual association, the same jigsaw-match logic Chapter 1 met with duct tape and Chapter 19 met with a torn edge. A fracture match reconstructs a unique break; it is the one circumstance in which paint approaches "this object and no other." Absent that physical fit, paint speaks in the probabilistic register of every other material in this chapter: it excludes cleanly, it associates by the rarity of a matching sequence, and it never, by composition alone, individualizes.

24.3 Glass: refractive index and fracture analysis

Glass is everywhere a crime can happen — windows, bottles, headlamps, eyeglasses, vehicle glazing — and it breaks, scatters, and clings. A burglar who breaks a window is showered with a fine spray of fragments that lodge in clothing, hair, and shoe soles and persist for hours to days; a hit-and-run shatters a headlamp and leaves fragments at the scene and on the victim. The forensic questions are two: could this recovered fragment have come from that broken source? (a comparison question), and what does the pattern of breakage tell us about how and from which side the glass was broken? (a reconstruction question). Glass answers the first through measured physical properties and the second through fracture mechanics — and, like everything in this chapter, it answers both as class evidence with honest limits.

Begin with the property that does most of the comparison work: the refractive index (RI) — a measure of how much a material bends (slows) light passing through it, expressed as a number that, for ordinary glass, falls in a narrow band around 1.52. Refractive index is a bulk physical property determined by the glass's composition and manufacture, it can be measured very precisely on a fragment far too small to do anything else with, and — crucially — two pieces of glass with different refractive indices cannot have come from the same source. That makes RI a superb exclusion tool. The catch, and it is the whole catch, is that float glass — the modern process by which nearly all flat window glass is made — produces enormous quantities of product within a very tight RI range. Two fragments with matching refractive index are therefore consistent with a common source but also consistent with two entirely unrelated panes off the same vast production stream. RI excludes powerfully and associates weakly, and the honest examiner says so.

🔬 At the Bench Refractive index is measured by a clever trick of disappearance. A glass fragment is immersed in a special oil whose own refractive index changes predictably with temperature, and the preparation is viewed under a microscope while the temperature is slowly varied. When the oil's RI exactly equals the glass's RI, the fragment's edges vanish — light passes from oil to glass to oil without bending, so there is no contrast — and the temperature at that match point, read against the oil's calibration, gives the glass's refractive index to several decimal places. (The modern automated version of this is called GRIM — glass refractive index measurement — which images the edge and finds the match-point temperature automatically.) The measurement is precise, reproducible, and objective, which is exactly what makes it valuable: unlike a subjective pattern comparison, two competent analysts measuring the same fragment will get the same number. Density (whether a fragment sinks or floats in liquids of known density) and elemental composition by SEM-EDX or, increasingly, by laser-ablation mass spectrometry add further comparison points — and, like added paint layers, each independent property that matches makes a coincidental common source less likely while any single decisive mismatch excludes.

Now the second question — breakage — and here glass earns a different kind of keep. When glass fractures, it does so according to mechanics that leave a readable record, and the most useful pattern arises in a pane broken by an impact, such as a thrown object or a bullet. The fracture propagates as two families of cracks: radial cracks that run outward from the point of impact like spokes from a hub, and concentric cracks that form rings around it. The order in which they form, and the microscopic stress marks on the broken edges, can reveal which side the force came from — a determination with obvious investigative value (was the window broken from outside, consistent with a break-in, or from inside, consistent with a staged one?). For a bullet hole specifically, the glass also records direction of travel through the shape of the hole (a cone that widens in the direction the bullet traveled) and, when there are multiple holes, the sequence of shots (a later fracture's radial cracks terminate where they meet an earlier fracture's cracks — the break that stops at another break came second).

🔬 Read the Evidence

```text FIGURE 24.2 — "Reading a broken pane" [constructed teaching example] THE ITEM A window pane broken by a single impact (e.g., a thrown object), photographed in place and then reconstructed on a light table from recovered fragments. THE CONTEXT Documented before collection; fragments kept oriented (which face was the exterior was marked) so the fracture geometry could be read.

     PLAN VIEW OF THE BROKEN PANE (schematic — not to scale)

               radial crack
                   │   ╱ radial
            ╲      │  ╱
             ╲     │ ╱        ● = point of impact
       ───────●───────────    ─── concentric rings around impact
             ╱  │  ╲╲
            ╱   │   ╲ ╲ concentric
           ╱  radial  ╲

     EDGE OF A RADIAL CRACK (microscopic stress marks — schematic):
        exterior face  ┃▏▏▏▏▏▏▏  ← stress marks ~perpendicular to the
        interior face  ┃ ╲╲╲╲╲      face the force came from

WHAT IT SHOWS Radial cracks running outward from the impact point and concentric cracks ringing it. The stress marks on the radial-crack edges are near-perpendicular to one face and curved on the other — the classic signature read to determine which side the force was applied to. WHAT IT DOESN'T It does not identify WHO applied the force, WHAT object did it, or WHEN. It tells you about the mechanics of the break, not the identity of the breaker. THE INFERENCE The fracture pattern is CONSISTENT WITH a single impact from the [exterior/interior] face — a directional, mechanical conclusion, stated as "consistent with," that bears on whether a break-in or a staging is more plausible, without naming an actor. THE LESSON Glass fracture answers "from which side" and "in what order," which is real and useful — and it stops there. Mechanics, not identity; sequence and direction, not a suspect. ```

The prose walkthrough of Figure 24.2 is worth doing slowly, because the diagram compresses two separate readings. The plan view shows the gross pattern — radials out, concentrics around — which tells you there was a single point of impact and lets you locate it. The edge view is the finer and more powerful reading: when a pane bends under impact, it stretches on the face opposite the force and the radial cracks open there first, leaving stress marks (sometimes called rib marks or hackle) that run roughly perpendicular to that opposite face. By examining which face the perpendicular marks sit against, the analyst determines the side from which the force came. This is genuine fracture mechanics, reproducible and grounded in physics — and notice what it does not do: it never names the person who threw the object or fired the shot. It establishes direction and sequence, which are facts about the event, not about the actor — exactly the reconstruction discipline Chapter 3 insisted on, that a reconstruction names a sequence, not a suspect.

⚖️ In the Courtroom Two honest sentences mark the boundary of glass testimony. The strong, defensible one is the exclusion: "The recovered fragment differs in refractive index from the known window; it did not come from that window." The associative one must carry its limits: "The recovered fragment is indistinguishable from the known glass in refractive index and density; this is consistent with a common source, but float glass of this refractive index is manufactured in very large quantities, so I cannot say the fragment came from this window to the exclusion of others." A jury that hears "the glass matched" without the second clause has heard an overstatement. And the fracture reading — "the window was broken from the outside" — is a statement about mechanics that an attorney should be careful to keep distinct from any claim about who broke it. The physics is solid; the identity is not in the glass.

24.4 Soil and geological evidence

Soil is the chapter's richest associative material and, not coincidentally, the one most directly tied to the cold case. It is also the one whose strength is most often misjudged in both directions — dismissed as "just dirt" by those who do not understand it, and overstated as a fingerprint of a location by those who understand it too little. The truth sits where the truth in this book always sits: soil is class evidence of unusual potential richness, capable of associating a person or object with an environment with real weight when the soil is distinctive and the comparison is properly controlled, and capable of proving nothing when it is generic or carelessly collected.

What makes soil potentially powerful is that it is not one thing but a composite — a mixture whose character comes from many independent components, each contributing a comparison point. This is the defining method: soil comparison — the examination and comparison of the physical, mineralogical, chemical, and biological properties of a questioned soil sample against known samples from locations of interest, to assess whether the questioned soil could have originated from such a location. The properties compared are layered, in a way that should by now feel familiar from paint:

• Color, assessed systematically (often against a standardized soil-color chart), and how it changes from moist to dry.
• Mineralogy — the kinds and proportions of mineral grains present, examined microscopically; the mineral assemblage reflects the local geology and can be highly distinctive in regions with unusual parent rock.
• Particle-size distribution (texture) — the relative proportions of sand, silt, and clay, which reflect how the soil formed and weathered.
• Density-gradient and other physical profiles — separations that produce a characteristic "fingerprint" pattern of the soil's components by density.
• Biological components — the pollen and plant material that Chapter 13 taught (palynology), plus fungal spores, diatoms in waterside soils, and other microscopic flora and fauna, which can tie a sample to a specific plant community and season.
• Chemical and anthropogenic components — pH, organic content, and human-introduced materials (a particular fertilizer, industrial particulates, fragments of a specific gravel or paint or glass) that can make an otherwise ordinary soil locally unique.

The power, and the honest limit, both follow from this composite nature. Power: because soil pools so many independent properties, a sample that matches a known location across color, mineralogy, texture, pollen assemblage, and an unusual anthropogenic component is associated with that environment by a coincidence that has become very unlikely — the same multiplying-rarity logic as the paint layers and the glass properties, with more dimensions to multiply. Limit: soil associates an object with a place of that character, not with one geographic point to the exclusion of all others, because environments are continuous and a distinctive soil type can extend across an area. And soil's value collapses entirely without the right control samples — which is where the investigator, not the analyst, determines whether the evidence will mean anything.

🔬 At the Bench The control-sampling discipline for soil is the make-or-break step, and it is the same lesson Chapter 3 taught about reference samples that represent the right place. To compare a suspect soil (say, from a boot tread) to a scene, you do not take one grab of dirt from the middle of the lot. You take multiple known samples that characterize both the specific spot of interest (where a body lay, where a vehicle parked — often the edge of a property, not its center, where the distinctive soil is) and the ordinary "background" soil of the surrounding area, so the comparison has a baseline that answers the only question that matters: is the questioned soil unusual relative to the background, or is it the generic dirt of the whole region? A match to a background soil that covers ten square miles is nearly worthless; a match to a distinctive soil that exists only in one small, unusual patch — and is different from the background a hundred yards away — is where soil earns its weight. The investigator who collects only one reference sample, from the convenient center of the scene, has often destroyed the evidence's value before the analyst ever sees it. Soil also carries a stratigraphy lesson: layers of different soils on a single boot or shovel can record a sequence of places visited, read like the layers of a paint chip.

Soil is, in this sense, the natural sibling of the pollen evidence in Chapter 13 — indeed, pollen is one of soil's components, and a serious soil examination often includes a palynological one. The cold case has already established (Chapter 13) that pollen on a vehicle floor mat is consistent with the cabin's distinctive flora, placing a vehicle in that environment. Soil extends the same logic to a person's belongings: the boots a person wears, the tools they carry, the vehicle they drive all pick up the ground they walk on, and if that ground is distinctive enough — and the controls show it to be distinctive — the association can place those belongings, and by reasonable inference the person who wore or carried them, in that environment. Place them there: not put a weapon in their hand, not establish a time, not prove a crime. The verb is places in the environment, and the strength is supports or, when the soil is genuinely distinctive and richly matched, strongly supports — climbing the ladder only as far as the distinctiveness and the controls allow.

🔬 Read the Evidence

text FIGURE 24.3 — "Soil in the boot tread" [the cold case] THE ITEM Soil recovered from the treads of a pair of work boots belonging to Roy Keller, a person of interest in the Mill Creek cabin case, submitted to the state laboratory's geology section with known soil samples collected from around the cabin and from several control locations elsewhere in Carrow County. THE CONTEXT The boots were seized under warrant and the tread soil removed and packaged dry, by layer where layers were visible; the cabin's soil was sampled at multiple points — including the distinctive area near the structure — and the county "background" soils were sampled to establish what is ordinary for the region. Chain of custody documented throughout. WHAT IT SHOWS The boot-tread soil corresponds to the cabin-site reference across color, mineralogy, particle-size distribution, and pollen assemblage, INCLUDING a mineral/pollen combination that the control samples show is UNCOMMON in the surrounding county — i.e., the match is to a DISTINCTIVE local soil, not the generic regional background. WHAT IT DOESN'T It does not establish WHEN Keller's boots acquired the soil (he is a co-owner of the property and had legitimate reasons to be there); it does not prove he committed any crime; it does not individualize the cabin clearing to the exclusion of every patch of similar soil; and it cannot, by itself, distinguish a guilty visit from an innocent one. THE INFERENCE The boots are CONSISTENT WITH, and — given the distinctiveness of the matched soil relative to the controls — STRONGLY SUPPORT, having been in the cabin's distinctive environment. This PLACES KELLER (via his boots) in that environment. It is a class/probabilistic association with a PLACE, not proof of guilt and not a time. THE LESSON Distinctive soil + good controls can place a person's belongings in an environment with real weight — and that is ALL it does. "Places him at the scene's environment" is the honest reading; "proves he was there when the crime happened" and "proves he did it" are leaps the soil cannot make. Resist them.

We will return to Figure 24.3 in the Case File, because it is the cold case's beat for this chapter and because it is the perfect specimen of the temptation §24.6 exists to resist. For now, hold the reading exactly as written: the soil strongly supports placing Keller's boots — and so, reasonably, Keller — in the cabin's distinctive environment, and it does so because the controls established that the matched soil is uncommon. That is a real and useful fact. It is also a class fact about a place, silent on time and silent on guilt, and the discipline of this chapter is to state it at that strength and stop. The instant "his boots carry the cabin's distinctive soil" becomes "he was there when Diallo died" or "he killed Diallo," the science has handed off to a story it has not earned — and that handoff is the subject of the next two sections.

24.5 The probabilistic value of class evidence

Step back from the four materials and look at what they have in common, because the commonality is the chapter's argument. Gunshot residue, paint, glass, and soil are all, with rare exceptions, class evidence: each associates an item with a category or an environment rather than with a single source to the exclusion of all others. None of them, by composition or property alone, individualizes. And yet they are genuinely valuable — not despite being class evidence, but in the specific, bounded way that honest class evidence is valuable. Making that value precise, and stating it correctly, is the skill this section teaches.

The value of class evidence is probabilistic, and it rests on a single question, the one Chapter 19 named for all trace evidence: what is the probability that this association arose by coincidence rather than by the contact alleged? Everything follows from that question. A common white paint, a float glass of ordinary refractive index, a soil that matches the dirt of half the county, three GSR particles on a person who lives among guns — each of these has a high probability of arising by coincidence, so the association is weak. A seven-layer paint match including an unusual repaint, a glass with both a rare refractive index and a matching unusual elemental profile, a soil distinctive in mineralogy and pollen and confirmed uncommon by controls — each of these has a low probability of arising by coincidence, so the association is strong. The material is the same kind of evidence in every case; what changes is the rarity, and rarity is what converts a class association from "consistent with" into "strongly supports."

Two factors drive rarity, and both should be in every assessment:

• Distinctiveness. How unusual is the matched feature? A rare custom paint, an uncommon mineral, a refractive index at the tail of the distribution — distinctive features are unlikely to be shared by chance. This is the rare-blood-type principle from Chapter 13: a rare type associates more strongly than a common one because fewer sources could account for it.
• Independence and number. How many independent features match? Each independent matching property multiplies the rarity, because the chance that two unrelated items share all of them is the product of the chances of sharing each. This is why layered, composite materials — multi-layer paint, multi-property glass, multi-component soil — can be strong: they offer many dice that must all come up the same way by coincidence.

🔬 At the Bench A word of honesty about numbers. The ideal of class evidence would be to attach an actual frequency to a match — "this paint system occurs in 1 in 50,000 vehicles" — the way DNA attaches a random match probability. For a few materials and questions, partial reference data exist (population studies of glass refractive index, paint databases that record manufacturers' formulations) and can support a qualified, data-grounded statement of how common a feature is. For most trace materials, however, no such validated population database exists, and any specific frequency an examiner recites is likely invented. The honest practice is therefore usually qualitative but disciplined: the examiner explains, in words, why a match is weak or strong — what makes the feature common or rare, how many independent properties agree — without manufacturing a false statistic. "I cannot give you a frequency, but this combination of an unusual mineral assemblage and a matching pollen profile, shown by the controls to be uncommon in the region, makes a coincidental match unlikely" is honest. "There is a one-in-a-million chance this soil came from anywhere else" is, absent a real database, a fabrication. Never invent the number; explain the rarity.

This probabilistic framing also clarifies the one move class evidence makes cleanly and powerfully: exclusion. Throughout this chapter, the surest statement has been the negative — these paints differ in a layer, these glasses differ in refractive index, this soil lacks the scene's distinctive mineral, this person's sample contains no primer-residue particles where a close-range shooting would predict them. A single decisive difference excludes a source; agreement only narrows. Class evidence is, in this respect, the book's first theme in concentrated form: its most reliable contribution is to rule sources out, and a great deal of the real-world value of the trace laboratory is exactly this — excluding a suspect's car as the source of the paint, a suspect's window as the source of the glass, a suspect's property as the source of the soil — quietly clearing the innocent, which is forensic science's finest and least televised hour.

🔍 Check Your Understanding 1. Two paint comparisons each "match." In the first, the agreement is a single layer of common black automotive paint; in the second, it spans six layers including an unusual aftermarket coat. Both are class evidence — so why is the second association far stronger? Name the two factors at work. 2. An examiner says a soil sample "could only have come from the crime scene." Using the idea of background and control samples, explain what would have to be true for any version of that statement to be defensible — and why it almost never is. 3. Why is a mismatch in refractive index a stronger and cleaner result than a match in refractive index?

Where, then, do these four materials sit on the validity spectrum? Not at the discredited end — there is nothing here like bite marks. The underlying measurements are sound and largely objective: SEM-EDX particle identification, FTIR layer chemistry, refractive-index measurement, mineralogical analysis are all real analytical science with reproducible results, much of it grounded in the instrumental methods PCAST and the NAS did not fault. The contested part is never "what did we measure?" but "what may we conclude from the match?" — and the answer the spectrum gives is consistent across all four: these are valid analytical methods supporting class-level (probabilistic) associations, strong for exclusion, honest for association when rarity is assessed candidly, and overstated the moment a class association is dressed as an individualization. They sit above the subjective pattern-comparison disciplines precisely because their core measurements are objective; they sit below DNA precisely because their associations are class-level and rarely come with a validated frequency. That is a respectable place on the spectrum — and keeping these methods in that place, rather than letting them drift upward into false certainty, is the entire subject of the section that follows.

24.6 Overstatement risks and honest reporting

We arrive at the section the whole chapter has been pointing toward, and it is less about technique than about language — because for class evidence, the difference between sound forensic science and a miscarriage of justice is almost always a sentence. The instruments rarely lie. The examiner rarely fakes a result. What goes wrong is the characterization: a true measurement, honestly obtained, described to a jury in words that claim more than the measurement supports. Overstatement is the failure mode of this entire family of evidence, and recognizing its specific forms — and the language that prevents them — is the most important thing you will carry out of this chapter.

Here are the overstatements, material by material, each paired with the honest version:

• Gunshot residue. The overstatement: "Gunshot residue on the defendant's hands proves he fired the gun." The honesty: "Particles consistent with primer residue were present on the sample; their presence is consistent with the person having fired, handled, or been near a discharged firearm, or with contact transfer from a contaminated surface or person — I cannot, from the particles alone, distinguish among these." The leap is from presence to action, and it ignores the transfer problem (§24.1) entirely.
• Paint. The overstatement: "This paint came from the suspect's car." The honesty: "The questioned and known paint are indistinguishable across [N] layers including [the unusual feature]; this strongly supports a common origin, but I cannot exclude another vehicle finished the same way." The leap is from a strong class match to individualization, dropping the unstated truth that other identically finished vehicles exist.
• Glass. The overstatement: "The glass on his clothes matches the broken window." The honesty: "The fragment is indistinguishable from the known glass in refractive index and density; this is consistent with a common source, but glass of this type is mass-produced, so I cannot say it came from this window to the exclusion of others." The leap is from indistinguishable to same source, ignoring the float-glass production stream.
• Soil. The overstatement: "This soil places the suspect at the murder scene at the time of the killing" — or worse, "proves he did it." The honesty: "The soil on the boots is consistent with, and given its distinctiveness strongly supports, having been in the scene's environment; it does not establish when the soil was acquired, and it associates the boots with a place, not with the crime." The leaps here are two — from a place to a time, and from association to guilt — and they are the exact leaps the cold case will tempt you to make in a moment.

⚠️ Junk-Science Alert The single most dangerous word in this chapter is "match," because it is doing two different jobs and a jury hears only the stronger one. When an examiner says two samples "match," they usually mean indistinguishable in the properties measured — a class statement. The jury hears the same object — an individualization. The word silently launders a probabilistic association into a certainty. The discipline, urged by the NAS 2009 report and echoed by standards bodies, is to retire the bare word "match" in favor of language that carries its own limits: "indistinguishable in [properties]," "consistent with a common source," "I cannot exclude," "strongly supports but does not individualize." This is not pedantry or lawyerly hedging; it is the difference between telling the jury what you found and telling them what you hope it means. Every wrongful conviction built on trace evidence has, at its core, a "match" that a jury heard as certainty and a witness let them.

There is a second, subtler overstatement that this chapter must name because it is the one a good analyst is most likely to commit: the fabricated frequency. Under cross-examination pressure to say how strong an association is, an examiner without a validated database may reach for a number — "one in ten thousand," "extremely rare" quantified — that has no empirical basis. As §24.5 insisted, this is a fabrication even when it is offered in good faith, and it is precisely the kind of unsupported precision the prosecutor's-fallacy discussions in Chapter 9 warn against. The honest analyst who is pushed for a number says: "I cannot give you a reliable frequency, because no validated population database exists for this material; what I can tell you is why this association is weak or strong, in terms of distinctiveness and the number of independent matching features." Refusing to invent a statistic is not weakness on the stand. It is the integrity the whole field depends on.

⚖️ In the Courtroom Notice that every honest version above shares a structure: a true positive statement ("indistinguishable in these properties," "particles were present," "strongly supports a common origin") immediately followed by its limit ("but I cannot exclude," "this does not establish when or who," "class evidence, not individualization"). That two-part grammar — finding, then limit, in the same breath — is the signature of competent forensic testimony across this entire book, and §1.4 first taught you to listen for it. The cross-examiner's job is to find the witness who gave the finding without the limit; the honest witness's job is to never make the cross-examiner's job that easy. If you remember one thing from this chapter when you are on the stand, remember to finish the sentence: the part after the comma is where the science lives.

The reporting discipline, finally, generalizes into a habit you can apply to any class evidence you ever meet, in any of the four materials or the dozens this chapter stands in for. State what you measured (objective, instrument-grounded). State what it is consistent with (the association). State its limits explicitly — what it does not establish about source, time, actor, or guilt. Assess its strength by distinctiveness and number of independent features, qualitatively if no validated frequency exists, and never with an invented number. Lead with exclusion where the evidence supports it, because that is class evidence's surest voice. And reserve "individualizes" and "proves" for the physical fit and the quantified DNA match, which are the only things in this chapter's neighborhood that earn them. Do that, and gunshot residue, paint, glass, and soil are exactly what they should be: honest, useful, bounded contributors to a case — bricks in a wall, never the wall itself.

🗂️ The Case File

The boots, the broken glass, and the test that came back negative. By the time the state laboratory's geology section took up the Mill Creek case, the investigation had already traveled a long way from the "accidental fire" that opened it (Chapter 1). The autopsy had established a homicide — blunt-force head trauma, no soot in the airways, dead before the fire (Chapter 11). The fire itself had been found incendiary, gasoline-fueled, on valid grounds (Chapters 22–23). Pollen on a vehicle floor mat had placed a vehicle in the cabin's distinctive environment (Chapter 13). Now three pieces of this chapter's microscopic evidence entered the file, and each must be read at exactly its strength — because this is the chapter where the temptation to overstate is sharpest, and resisting it is the lesson.

The soil — the chapter's beat. A pair of work boots belonging to Roy Keller — Diallo's business partner and co-owner of the property — was seized under warrant, and soil from the treads was submitted with known samples from around the cabin and from control locations across Carrow County. The geology section's comparison (Figure 24.3) found that the boot-tread soil corresponds to the cabin-site reference across color, mineralogy, particle-size distribution, and pollen assemblage — including a mineral and pollen combination the control samples show is uncommon in the surrounding county. The match, in other words, is to a distinctive local soil, not the generic regional background. State the conclusion precisely, in the chapter's verbs: the boots are consistent with, and — given the distinctiveness established by the controls — strongly support, having been in the cabin's distinctive environment. This places Keller, through his boots, in that environment. It is a real, useful, probabilistic association with a place.

Now the discipline, which is the whole point. Say what this soil does not establish, in the same breath, because every one of these limits is load-bearing. It does not establish when the boots acquired the soil — and here a fact cuts directly against overreading it: Keller is a co-owner of the cabin with legitimate, innocent reasons to have walked its ground many times. It does not prove he committed any crime. It does not individualize the clearing to the exclusion of every patch of similar soil. And it cannot, by itself, distinguish a guilty visit from an innocent one. The honest status line is therefore carefully bounded: Keller is physically tied to the scene's environment — a meaningful addition to the file — and that is all the soil says. It is one brick. The temptation to make it the wall — "the soil proves Keller was at the cabin, so Keller is the killer" — is precisely the §24.6 overstatement wearing the cold case's clothes, and we refuse it here, deliberately and on the record. Whether this association, combined with everything else, points to Keller is a question for the capstone (Chapter 39), assembled from all the evidence and stated with all its uncertainty. It is not a question the soil answers alone.

A glass item. Among the debris, a few glass fragments were recovered and compared — some from a broken window of the cabin, some found on items associated with the investigation. Read honestly, the glass does what glass does: refractive-index and density measurements can exclude sources cleanly and can find fragments indistinguishable from a known source (consistent with a common origin, but float glass of common type is mass-produced, so no individualization), and any fracture pattern on the cabin's broken pane speaks to how and from which side it broke, not to who broke it. The glass here is a supporting, class-level thread — useful for what it excludes and for the mechanics it can reconstruct, carrying its limits with it.

The GSR test — negative, and consistent. Finally, surfaces and items associated with the case were tested for gunshot residue, and the result was negative: no particles consistent with primer residue were found where a shooting would have produced them. Read this correctly, because a negative is as easy to misread as a positive. The negative GSR result is consistent with the autopsy's central finding — that Diallo died of blunt-force trauma, with no gunshot wound (Chapter 11) — and with the conclusion of Chapter 15 that the stray cartridge case in the inventory was a red herring, unrelated to the manner of death. There was no shooting; the GSR is negative; the autopsy says no one was shot. The three findings sit together cleanly. (Remember §24.1's caution that a negative GSR proves little on its own — but here it is not asked to carry weight alone; it simply corroborates a manner of death already established by the body.)

Running status. Keller is physically tied to the scene's environment by the distinctive-soil association — a genuine advance, stated at "strongly supports," bounded by every limit above and explicitly not converted into proof of guilt or of timing. The glass is a class-level supporting thread. The GSR is negative, consistent with a no-gunshot homicide. No person of interest is excluded by this chapter; Keller is associated with the environment, which is not the same as included as the killer and must not be written as if it were. Log the soil in the workbook (Appendix I) as a strong-but-class association with a place, with its caveats attached, and resist — as the chapter spent six sections teaching you to resist — the urge to let it say more than it knows. It is a capital mistake to theorize before one has data; it is an equal mistake to make the data confess to a theory. The convergence, if there is one, is for Chapter 39.

Conclusion

Four materials, one lesson, taught four times. Gunshot residue is real and instrument-grounded — a primer particle fusing lead, barium, and antimony in a characteristic shape, identified by SEM-EDX — and almost useless as proof that a particular person fired a gun, because the particles transfer, contaminate, and fall off with an ease that fills the gap between "present on the hands" and "fired the weapon" with reasonable doubt. Paint speaks in layers, and its weight lives in the sequence: one common layer proves little, a long and unusual stack makes coincidence implausible, and a physical fit — the rare exception — approaches individualization. Glass is compared through the precise, objective refractive index (a superb exclusion tool, a weak associator because float glass is mass-produced) and read through fracture mechanics that reveal direction and sequence of breakage but never the identity of the breaker. Soil is the richest associative material of the four — a composite of color, mineralogy, texture, pollen, and chemistry whose strength scales with distinctiveness and with the quality of control samples — capable of placing a person's belongings in an environment with real weight, and incapable of fixing a time or proving a crime.

The thread binding all four is the chapter's two central themes, lived rather than recited. Forensic science excludes; it rarely proves (Theme 1): every one of these materials is at its surest when it says no — different layer, different refractive index, absent mineral, no residue — and at its most honest when it states an association as a probability, "consistent with" or "strongly supports," never "proves." And not all forensic methods are equally valid (Theme 2): these sit in a respectable middle of the validity spectrum — objective measurements supporting class-level associations — above the discredited pattern disciplines because what they measure is sound, and below DNA because what they can conclude is a class association rarely accompanied by a validated frequency. The danger, every time, is not the instrument but the sentence built on it: the bare word "match" that a jury hears as certainty, the fabricated frequency offered under pressure, the soil that "places him in the environment" rewritten as the soil that "proves he did it." Keeping these methods at their true strength — finding, then limit, in the same breath — is the whole of honest trace reporting, and the cold case's soil is the chapter's standing reminder of how seductive, and how wrong, the overstatement would be.

We have now walked the chemical and toxicological evidence to its end — what the body absorbed, what the fire left, and the microscopic traces that transfer between people and places. In the next part we turn to the newest evidence and the newest claims: the digital forensics of phones and computers, where, in the cold case, Roy Keller's alibi will meet the one witness that keeps a timestamped record of where a person's phone has been.

Key Terms

• Gunshot residue (GSR) — the particulate and chemical debris produced by the discharge of a firearm (burned propellant plus condensed primer particles), deposited on the shooter, nearby surfaces, and the target; its presence on a person establishes presence, not that the person fired a weapon.
• Primer residue — the inorganic particulate component of gunshot residue, formed when the metallic primer compounds (commonly lead, barium, and antimony) vaporize on discharge and condense into characteristic spheroidal particles; the diagnostic particle contains the right elements in the right morphology and is identified by SEM-EDX.
• Refractive index — a measure of how much a material bends (slows) light passing through it; for glass it is measured very precisely on tiny fragments and is a powerful tool for excluding a common source, but only a weak associator because float glass is mass-produced within a narrow range.
• Paint-layer comparison — the examination and comparison of the number, sequence, color, thickness, and chemical composition of the individual layers of a questioned paint sample against a known sample; the probabilistic weight lies in the matching sequence, and a multi-layer match (especially with unusual layers) can strongly support a common origin without individualizing.
• Soil comparison — the examination and comparison of the physical, mineralogical, chemical, and biological (including pollen) properties of a questioned soil against known and control samples from locations of interest; class evidence whose strength scales with the soil's distinctiveness and the adequacy of control sampling, capable of associating an object with an environment but not of fixing time or proving guilt.

Spaced Review

1. A detective says, "We found gunshot residue on the suspect's jacket — that proves he's the shooter." Name two distinct transfer or contamination routes (from §24.1) by which GSR could be on the jacket without the suspect having fired a weapon, and state the honest version of what the finding establishes. (§24.1)
2. In the cold case, the soil on Roy Keller's boots strongly supports his boots having been in the cabin's distinctive environment. List two things this association specifically does not establish, and explain why "the soil proves Keller killed Diallo" is the exact overstatement §24.6 warns against. (§24.4, §24.6, The Case File)
3. (Chapter 13 → Chapter 24) Pollen on a vehicle mat (Chapter 13) and soil on a suspect's boots (this chapter) are both class evidence that "places" something in an environment. Explain how the two are related (what do they share?) and why neither, alone, can name a person or a time. (§24.4; Chapter 13, §13.6)
4. (Chapter 1 → Chapter 24) Recall the honest verbs excludes / consistent with / strongly supports / proves. For a glass comparison, explain why a mismatch in refractive index lets you reach the strongest of those verbs while a match leaves you near the weaker ones. (§24.3, §24.5; §1.4, §1.6)
5. Validity-spectrum question. Where do gunshot residue, paint, glass, and soil sit on the NAS 2009 / PCAST 2016 spectrum, and what single feature do they share that keeps them above bite-mark comparison (Chapter 16) yet below single-source DNA (Chapter 7)? (§24.5; the spectrum habit from §1.5)