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Kilner-Walter: Mathematician review (Step 2)

Reviewer role: PhD mathematician. I check logic, derivations, units, hidden assumptions and the numbers. Physics and physiology judgements belong to the Physicist; where I need them I tag them [memory] and say how sure I am.

Source: Walter J. Kilner, The Human Atmosphere (Rebman, 1911), read here as the extracted text (PDF page = printed page + 19) [read]. I read myself: PDF pp.24-27 (screens), 80-81 (Tables I and II, as page images), 109-132 (Chapter III: forces, magnets, how the screen works), 321-323 (Case 40). I also used the Step 1 deep reads (Chapter IV and the Appendix) and the Investigator's notes. The book has no equations. Its mathematics is the logic of its inference, its classification scheme, its tables and its few numbers, so that is what I check.

Web checks (budget about 6; 2 used): the BMJ replication claim and Kilner's death were checked on Wikipedia [web: https://en.wikipedia.org/wiki/Walter_John_Kilner]. It says BMJ scientists "attempted to replicate" and got negative results, and quotes the 1912 review ("failed to convince us that his 'aura' is more real than Macbeth's visionary dagger"). That is a secondary source and I did not read the BMJ review itself (the Investigator also could not). A search for the dicyanin absorption spectrum returned nothing usable; I rely instead on Kilner's own pocket-spectroscope observation of the screen (p.131) [read].

Corrections to Step 1

Claim 4 overstates Case 40. claims.md lists "a dead foetus" among conditions the C.C. band signals. In Case 40 the text says "The C. C. band showed nothing unusual" [read: p.322]. The dead-foetus diagnosis rested on the texture of the Inner Aura (coarsely granular in the lower abdomen) plus the history (movement stopped three weeks before, abdomen shrinking, patient "thinking the child was dead"). Palpation later found a soft uterus and no heart sounds; she delivered a dead infant two months later [read: p.321-323]. So Case 40 is evidence offered for claim 3 (texture), not claim 4 (band). The Step 1 deep read of Chapter IV already says the cases were not read fully, so this is a gap, not an error of the deep read.
Claims 1-2 hide a contradiction that Step 1 did not flag. See claim 2, question a.
Step 1 did not tabulate the heredity data (claim 3), the one place in the book with countable data. I did (below). Step 1's statement that "no counts" exist is right for the C.C. band and the disease cases, but Tables I and II are counts.
Step 1's note that the Appendix subject "G.2" is B.G. is an inference (as the deep read says). I agree it is plausible: Table II lists B.G., 20, "Not fully developed, backward", with footnote "May be wide in two or three years' time. See Appendix" [read: page image p.81]. One small tension: the Appendix gives her aura as "quite nine inches", which is inside Kilner's own "average" band of 8 to 10 in for women (p.78-79), and Table II lists her as A (average) [read]. Table II shows "Wide" for her sister N.G. (23). Nothing is wrong here, but the footnote predicts a later reclassification the book never reports.
Number of experiments: the Step 1 deep read correctly found six, not five. I confirm that in the Appendix text as summarised there; I did not re-read the Appendix pages beyond the passages listed above.
Otherwise I found Step 1's quotations and page references consistent with the text I re-read (pp.109-132, 321-323), including the Chapter III passages on 1 aF and 2 aF and the statement that the Aura is invisible in the dark.

What the claims depend on, in mathematical terms

Every claim rests on a judgement of "visible or not", "wider or narrower", or "lighter or darker" made by one unblinded observer with no recorded counts of failures. The book has no measurement with an uncertainty, no repeated trial with a denominator, and no control condition (a person or object with nothing to see). I note where numbers exist and test them.

Claim 1: A faint structured haze (the aura) surrounds every human body and is visible after viewing through a dicyanin screen

a. Internally consistent? Partly. - The book says the aura "has been searched for constantly in the dark without the slightest sign" and is therefore "not luminous"; it is seen by "reflection of light from some extraneous source", best in diffused daylight, and can be seen "through red, yellow, green, and blue screens" [read: p.109]. Reflected visible light seen through ordinary coloured filters is a visible-wavelength phenomenon. That sits badly with claim 2's "outside the ordinary visible spectrum" (see claim 2a). - It also says the aura would have been noticed long ago "if the rays lay within the visible spectrum" [read: p.110]. That is an argument from absence (it was not noticed, so it is not visible), and it ignores a simpler explanation Kilner records himself: the effect needs dim light, a prepared eye and a trained observer. - Kilner's account of the screen's action is explicitly "completely hypothetical and without proof" [read: p.131]. The spectroscope observation he gives is that the dicyanin screen removes orange entirely, much of the yellow, slightly diminishes blue and violet, and leaves red unaltered [read: p.131]. A filter that only subtracts wavelengths cannot add a new band of light. So whatever it does, it does it by changing the state of the eye (adaptation), which is what his rhodopsin hypothesis says. Taken together his explanation is coherent in structure but is a hypothesis he flags as unproven.

Chromatic-focus paper (Investigator lead, Kilner 1911-12, Archives of the Roentgen Ray). This is Kilner's only quantitative measurement, and I checked its arithmetic as reported in the Investigator's note (I could not open the paper itself: HathiTrust served a bot challenge to scripted access; Chrome reading was the Investigator's, so these numbers are [web, via the Investigator's note] and I cannot see the full table). - Units: one fine-adjustment division = 1/1000 in = 25.4 micrometres (µm). Observer A's white-light focus moved by +2.5 divisions = about 64 µm after viewing through dicyanin. The largest, in a clairvoyant, was +6.5 divisions = about 165 µm. - Scale check. A shift of the microscope's best focus Δz (at the object) corresponds to a change of vergence at the eye of about ΔV = M²·Δz / fe², where M is the objective magnification and fe the eyepiece focal length. With a 1/4-in objective (M about 25 to 40 on a 160 to 250 mm tube) and a low-power eyepiece (fe about 25 to 50 mm), 1 dioptre (D) of change at the eye corresponds to only about 0.4 to 4 µm of object focus. [This is my calculation, with those assumed instrument values; the paper's exact objective and eyepiece are not given in the Investigator's note.] So 64 µm would be 16 to 160 D, and 165 µm would be larger still. The eye's total accommodation is about 10 to 15 D in the young [memory, high] and its chromatic spread across the whole visible range is about 2 D [memory, high]. A true refractive change of that size is not credible. - The more likely reading is that the number is dominated by the microscope's own depth of focus, which for NA about 0.17 is roughly λ/NA² about 20 µm plus an eye-resolution term of a few µm. Kilner's own filter spread before dicyanin (red -1, violet +3 divisions, i.e. 100 µm) is far larger than the eye's chromatic aberration would give in this geometry, so it must come mostly from the objective's own chromatic aberration. That tells us the instrument's colour error is larger than the effect looked for, and the eye's contribution is a small difference of large numbers. No repeat readings, spread or blinding are reported (as far as the Investigator's note shows), so a shift of 2 to 3 divisions is about one depth of focus and cannot be separated from judgement drift after a minute of staring at a bright light through a dark screen. - Conclusion on this lead: it is a real attempt to quantify, with 12 observers, but the effect size in eye units is implausibly large if read as a change in the eye, and small if read against the instrument's depth of focus. It does not show the aura band moves beyond violet. I flag that the full paper should be read before this is treated as settled.

b. Consistent with experiment? Mixed. The independent trial by H. C. S. and Dr Goodspeed found "a physical phenomenon" observable but stronger around an inanimate hand towel than a human [read via the Investigator: Archives v.16 pp.199-200]. Kilner's own reply says he has never seen a haze around an inanimate object except a magnet or a radioactive substance, and he suspects the correspondent's sight [Investigator note A5]. These are two opposed first-hand statements. I keep both. Surya's two Graz observers and the Paris failures (de Rochas, de Fontenay, Roux) are in the record too (see the Investigator's leads); none was blinded in any way the sources describe.

c. Tested? By Kilner himself (many cases, no counts), by H. C. S. and Goodspeed (reported in a letter), by Surya and two of his subjects (published in a journal from the same publisher as the book), by the Paris group (negative, "a reservation, not a denial"), and a BMJ review that Wikipedia says involved failed replication (unverified: I did not read it). No test with a hidden target, a sham person or independent scoring is on record in the sources I have.

d. If true: a faint structure near the skin visible to a primed normal eye in dim light would be an ordinary optical phenomenon (a scattering or emission layer, or a visual effect). It would need a stated mechanism and would not by itself require new physics. The physicist must say whether it is more likely scattering, thermal convection, retinal adaptation or afterimage.

Quantitative check I can add (visibility by scattering). Kilner says the aura is visible only by reflected light and is not auto-luminous (p.109). If so it must scatter light like a thin haze. Suppose the background is black cloth of reflectance ρ about 0.03, and a haze is just visible at a contrast of 2% (a typical threshold, [memory, medium]). For a layer of thickness L = 0.25 m (the Outer Aura, 10 in), single scattering gives radiance ratio about τ·P where τ is the optical depth and P the phase factor (about 1). Need τ ≥ 0.02 × 0.03 = 6×10⁻⁴, so the scattering coefficient is about 2.4×10⁻³ per metre. Clear air scatters at about 1.4×10⁻⁵ per metre at 500 nm (Rayleigh) [memory, high]. So the aura would have to scatter about 170 times as much as air, comparable to a light mist (visibility about 1.6 km by Koschmieder's rule V = 3.9/α, [memory, high]). That requires real particles or droplets (order 10⁷ to 10⁸ per m³ of micrometre-scale droplets [my rough estimate]). Kilner rejects vapour on the grounds that the aura does not move with draughts or warm air (p.91-92). That is his reason to call it a force; it is also a reason his observation does not behave like matter, and the Physicist should weigh it. This calculation is only a plausibility bound under my assumptions; it does not test his claim.

Verdict: Never properly tested (the observation that something is seen). Split: the strong form (a body-specific, structured aura seen by normal eyes through the screen) has had no blinded or instrumented test on record; the weak form (a screen-primed eye sees some haze in dim light) is plausible and is compatible with the H. C. S. report. The dye's effect on the eye has never been measured in a way that separates it from visual adaptation.

Claim 2: The aura is a force acting on the ether, lies outside the visible spectrum, and has counterparts around magnets, uranium and galvanic circuits

a. Internally consistent? No, on several points. 1. Visible by reflection yet outside the visible spectrum. The aura "is not luminous"; it is seen by reflected light and through red, yellow, green and blue screens [read: p.109], yet its "vibrations lie outside the ordinary visible spectrum" [read: p.110]. If it reflects or scatters visible light it is, as an optical object, a visible-light phenomenon; if it emits or responds only beyond the visible range, the reflection argument does not apply. He needs the aura to be both. (In 1920 he writes "an ultra-violet phenomenon", per the Investigator's note; this narrows the claim but does not remove the problem, because then the aura could not be seen by reflection of visible light at all.) 2. "Auto-luminous" axiom. He states that a substance whose force makes ether vibrations at visible wavelengths is auto-luminous, and that invisible-wavelength vibrations may be seen by "persons gifted with some peculiar sight, or by others by means of Instrumental Aid" [read: p.125]. The screen is the "instrumental aid", but his own spectroscope reading (p.131) shows the screen only removes light. The two statements are not reconciled. 3. No quantity is defined. "Force", "vibrations corresponding in number and wave length" and "action on the Ether" are never given units, magnitudes or equations. The 1 aF and 2 aF forces are inferred from appearance (a structured Inner Aura with rays and a nebulous Outer Aura that grows in women) [read: p.99-101]. The step from two textures to two forces is an inference with no measurement. He says "if, however, there be only one force... it will be advantageous to treat the subject as if two forces were present" [read: p.101]; that makes the two-force statement a bookkeeping device, not a result. 4. Magnet analogy. He admits the magnet haze "does not exactly follow the magnetic lines of force" and hopes the discrepancy "will vanish" when the haze is seen more clearly [read: p.94]. A hypothesis that predicts agreement and finds disagreement is stated as expected to resolve later. 5. Photography failed (p.91), and the 1920 preface says it succeeded "to a slight extent" [Investigator]. These are different statements in different years, not a contradiction, but nothing in the record reconciles them. 6. Ether. The 1911 text uses "the Ether" as a medium that carries visible vibrations. Whether this is internally consistent is the Physicist's question (the ether concept was dropped from physics after special relativity, 1905, but was still in use in medicine and popular physics in 1911 [memory, high]).

b. Consistent with experiment? The classical result that a screen-primed observer sees structure near a magnet or conductor is not established anywhere I have; the Investigator found no independent replication. H. C. S. and Goodspeed's stronger haze around a towel is more consistent with a general visual or lighting effect than with a body-specific force. The 1915 static-charge experiments in the 1920 edition (aura vanishes, returns 3 in wider, per the Investigator) are in the record; I cannot check the numbers (12 in to 15 in is a 25% change, reported as an eyeballed estimate).

c. Tested? Only by Kilner and by those who read the screens. No instrument measured the "force".

d. If true: a new field or ether-like medium coupling to living bodies and to magnets, one that is visible to the eye but invisible to every photographic and spectroscopic instrument of the era, would need a mechanism for coupling to the retina. Mainstream electromagnetism would not need to change if it is an ordinary scattering or perception effect.

Verdict: Internally inconsistent for the combined statement (visible by reflection, but outside the visible spectrum; a "force" with no quantity). The magnet, uranium and galvanic "hazes" are Never properly tested. The "two forces" statement is Not testable as stated.

Claim 3: Aura size, shape, texture and colour reflect sex, age, heredity, temperament and disease

a. Internally consistent? The scheme is flexible rather than inconsistent. - Classification defined after the fact. Kilner says the thresholds (women 8 to 10 in "average"; men 3.5 to 4.5 in; children 2.5 to 3 in) "have been decided on by experience only, and not by any scientific plan", with "no hard and fast rule" for adolescents and ambiguous cases judged "on its own merits" [read: p.78-79]. Infants, whose auras he gives as about 1 in, have no stated scale. So the class of any case, especially an unusual one, is chosen with the answer in view. - Hysterical "type" aura is defined as wide at the trunk and narrow at the legs (p.79-80), so a mismatch in one measurement can be assigned to a type rather than counted as a deviation.

Heredity tables: my check (the one place with counts). I read Tables I and II as images [read: page images pp.80-81] and counted each pair as concordant if both are in the same class (W = wide, A = average, N = narrow). - Table I (parent-child), 18 parent-child pairs: 16 same class (89%). The two exceptions are in the F.X family: G.X is A and E.X is W, with the parent N. - Table II (siblings), 9 pairs: 5 same class (56%). Discordant: N.D./E.D. (W,A), L.N./Q.N. (A,W), G.B./I.B. (A,W), N.G./B.G. (W,A). - Chance agreement if classes were unrelated to family: using the pooled class frequencies in the tables (A 25, W 15, N 14 out of 54 entries), the chance of two random people agreeing is about 0.36. Under that null, 16 or more agreements out of 18 has a probability below 0.0001; 5 or more out of 9 has about 0.19 (not unusual). All 27 pairs: 21 agree, below 0.0001. If each family counted once (13 families in Table I, 12 concordant) the Table I result is still far below 0.001. My calculation, assuming independent pairs, which they are not (one parent appears with several children), so the p-values are only indicative. - Reading the result: the parent-child agreement is much higher than chance, but the sibling agreement is not, even though siblings share as much ancestry as parents and children. That asymmetry is hard to explain by heredity alone. A method effect is a candidate: the observer knew the relationship, classed infants (for whom there is no stated scale) and children by an age rule he describes as unscientific, and tended to assign the child the parent's class. Two of the four sibling mismatches are explained away in footnotes ("Not wider than usual for her age"; "May be wide in two or three years' time"; the other note says she is "backward"), which is a post-hoc handling of mismatches. Against that, the 16/18 figure is a real pattern in the record and the Physicist or a later tester could check it with a blind classifier. I state both. - Selection: the tables say they contain "all the examples which have been investigated of two or more individuals of the same family up to date" [read: p.79], which is a point in their favour (no stated cherry-picking). Sample size is small (13 + 9 families).

Other claims in this group. Large-sample statements ("the most intelligent people have the finest Auras", dull people have smaller auras, grey colour marks a duller mind [read: digest p.72-78]) have no counts and rest on Kilner's own judgement of intelligence and aura together. The case-by-case disease statements (epilepsy, hemiplegia, hysteria) are single cases with narrative description; no denominator.

b. Consistent with established results? There is no established measurement of "aura size" to compare with. Observer-dependent width estimates in inches, to the nearest half inch, are plausible only as visual estimates of a faint edge.

c. Tested? No blind test. No second observer on the width classifications.

d. If true: a body-fluid or field-like feature correlated with heredity and temperament would be a new, measurable biological variable; it would be most easily tested by blind photography or radiometry, not by new physics.

Verdict: Never properly tested. The family-concordance table is the best-quantified item in the book and should be kept: parent-child agreement (16 of 18) is far above chance and sibling agreement (5 of 9) is not; a method artefact (unblinded, post-hoc thresholds, no scale for infants) is a stronger explanation than a hidden variable, but the data cannot decide. The disease and temperament parts are Not testable as stated until the classes are defined in advance.

Claim 4: C.C. (afterimage) band darkening or lightening over a patient diagnoses disease, tenderness, menstruation, pregnancy

a. Internally consistent? The Step 1 deep read of Chapter IV is thorough and I agree with its main findings, which I re-checked against the text of pp.150-163 as quoted there. 1. Every outcome is assigned a cause. Same change in all bands means granular aura; opposite changes means colour; no change means granularity "at times has no effect" or a conical gap that blurs too much; a light spot means a gap; a dark spot means a small gap or a dense surround [Step 1 deep read, pp.150-163]. So no pattern of band results can count against the aura explanation, which is a falsifiability defect in the logic itself, apart from any physics. 2. The list of causes leaves out the observer. The four candidate agencies (skin, thickness, texture, colour) are all properties of the patient. Kilner's own text records that eye movement changes the afterimage (p.134), that it drifts to purple and vanishes (p.139), that it is "more readily" seen "when the colour is fading" (p.147-148) and that the observer's eye fatigues quickly (p.149) [Step 1 deep read]. The observer's retina is not tested as a cause. 3. "Lighter" and "darker" are not defined. The text does not say whether darker means lower luminance, higher saturation or a different hue. This matters for his sign rules. Adding a coloured light to a surface can only add luminance, so a "darker" patch from an added tint can only arise by contrast or adaptation effects in the observer, not by additive mixing. His rules (a yellow ray looks darker on the blue band and lighter on the yellow; a red ray darker on both blue and yellow and lighter on red [Step 1 deep read, pp.158-159]) are stated, not derived. In a standard opponent-colour picture (blue-yellow and red-green are independent axes, [memory, high]), a red tint would act mainly on the red-green axis and would not be expected to darken both the blue and the yellow band. I cannot say these rules are wrong, but they are not implied by anything in the book. 4. Sign flip with fatigue. In Experiment 1 the red band showed the willed side "at first darker, and, as the patient became a little fatigued, it appeared lighter" [Step 1 deep read, p.334]. The sign of the effect changed with time. Kilner takes this as consistent. It also shows the reading depends on the state of the observer's eyes or of the subject. 5. The "turn the patient round" control is real but limited (a good control for room-fixed light, not for body-fixed features or expectation), as the deep read states. I agree.

Case 40 correction (above): the dead-foetus diagnosis did not use the C.C. band.

Predictions with outcomes. Menstrual timing: Case 18 (predicted 4 days), a 38-year-old (predicted 6 to 7 days, occurred 7 days later) and a young woman (expected 3 to 4 days, "no C.C. change, period occurred week late"), Case 21 (ruled out pregnancy; menstruation 7 days later) [read: digest pp.252-254, 318-319]. Of the few outcomes reported, some are hits, some misses; Kilner reports the misses, which counts in his favour. With a cycle of about 28 days, any prediction "in about a week" has a high chance of being roughly right by luck, and there are no denominators (how many women were examined). The pregnancy cases are small in number (Cases 89, 21, 40) and no false positive or false negative rate is given.

b. Consistent with established results? Afterimage colour and brightness are known to depend on adaptation time, background, fixation and lighting [memory, high]; the band is a subjective construct (Kilner: "entirely subjective", p.140). That a patient's skin, clothing, posture or reflected light would produce a darker area beside the body is a candidate physical cause the book dismisses as "negligible" without a described test (p.150-151).

c. Tested? By Kilner only. No second observer, no sham patient, no blind reading.

d. If true: a physiological state would imprint a visible-light-neutral signal on air near the skin that modifies afterimage tint. Visual science would have to accept an external, patient-linked modulation of afterimages. Simpler: it would be an unmodelled effect of skin colour and reflected light, requiring no change.

Verdict: Never properly tested. The method as described is unfalsifiable in its decision logic (every outcome has an assigned cause) and has no blinding; I would call the logical structure Internally inconsistent only for the combination "darker if small gap, darker if dense surround, lighter if gap, no change if blurred, sign set by colour". As a diagnostic claim with no controlled trial, Never properly tested is the accurate verdict.

Claim 5: C.C. band changes arise, where texture does not explain them, from the aura's colour, which the naked eye cannot see

a. Internally consistent? Not as stated. - Kilner introduces colour as "the only [agent] that will explain all the remaining cases" and says it "may be problematic" [Step 1 deep read, p.156]. A hypothesis introduced as the remainder after other candidates fail is not tested by its own definition: it cannot be wrong. - His evidence is the assertion of unnamed clairvoyants, one finger ray, and a thought experiment ("we have not the slightest doubt") [Step 1 deep read, pp.156-159]. - The Appendix is his offered test. In Experiments 1 to 3 the willed colour was visible to the naked eye (he saw grey-red in Exp. 1), which is the opposite of the premise (colour not distinguishable by the naked eye). In the "crucial" Experiments 4 to 6 the target colour is declared invisible because the ray points at the observer, which he asserts but did not test. - Experiments 5 and 6 (the only trials where the observer did not know the location) used only the blue band. By his own rules both a red and a yellow ray appear dark on the blue band (p.158-159), so these trials cannot discriminate colour. They test only whether a dark spot appeared where she was willing [Step 1 deep read].

Chance check on Experiments 5 and 6 (my calculation). Assume the abdomen search area is about 80 to 120 square inches and the thorax about 150 square inches, and call a "hit" a finger within 0.5 in of the willed centre (area 0.8 sq in). A single random guess lands inside with probability about 0.7% to 1% (abdomen) and 0.5% (thorax). Kilner did not guess at random: he looked for dark patches on the band, which are common ("small patches... almost invariably" mark tenderness, p.147; D. already had a dark sacral patch, p.332 [Step 1 deep read]). If there were N plausible candidate patches on the field and he picked one, the chance of a hit is about N times the figure above (for N = 5, about 4% on the abdomen). Two reported trials, one exact and one 0.5 in off, give a joint chance of order 10⁻⁵ if one random pick each, and of order 10⁻³ to 10⁻² if several candidates and some cueing are allowed. The subject said when the spot was ready, could see the observer and knew the search region; no cue channel was excluded. The number of unreported trials is unknown ("No more experiments of this nature were possible", p.338). Two trials cannot support a statistical claim either way.

b. Consistent with established results? No experiment replicating the colour-specific pattern with a blind observer is on record. The one pattern in the Appendix that does carry colour information (Exps. 1 and 4) had the observer knowing both colour and site.

c. Tested? Kilner only; one subject (D.), one session, one observer.

d. If true: the aura would carry a spatially resolved visible-colour signal that normal eyes cannot see directly but can read from afterimages. That would require an account of why the afterimage is sensitive to it while direct vision is not.

Verdict: Never properly tested. The hypothesis is also not falsifiable in its structure as presented (the remainder explanation). Logically, the Appendix experiments do not test the colour claim because the only blind trials do not discriminate colour.

a. Internally consistent? Mostly yes within its own terms. The Chapter III statement ("1 aF is, to a certain extent, under the influence of the will", p.101) is the stated premise, and the Appendix matches it. Tensions: - Case 41 conclusion that the will acts "more easily on the Aura in front of protuberances" is accompanied by Kilner's own note that concentrating on a distinct part is easier (p.329), a confound he names but does not remove [Step 1 deep read]. - The willed colour never matched the cue (Exp. 1 and 3), and the subject "could see plainly" a colour the observer saw differently (Exp. 3). Those mismatches reduce the claim to "some change", as he reports it. - Observer-willed rays by Kilner himself ("he must then will that a ray should extend from the end of his finger", p.106) are described but have no counts.

Additional note. The experiment on p.104-105 (a hand held near the patient makes a ray appear between the hands) states that the "minds of the two persons should be... as passive a state as possible"; the effect is thus conditioned on mental state. A procedure whose result depends on the observer's and subject's unmeasured inner state, judged by the observer, has a high risk of expectation effects.

b. Consistent with experiment? The 1915 Wimshurst charging experiment and the Graz observers' report of rays (Surya) are the nearest others; Surya's second subject saw rays at the observed person's ears and a band between fingertips, and he recommended using naive observers [Investigator note]. No blinded trial of willed rays is on record.

c. Tested? By Kilner with one willing subject (G.2, D.) and an unnamed second observer for one phenomenon. Not replicated.

d. If true: conscious intention would modulate a visible emission or scattering structure near the skin. This would link intention to a physical field on a timescale of seconds (they report "within a minute", "instantly"), which is a mind-body coupling absent from current physiology.

Verdict: Never properly tested. Split: the willed-ray claim (Case 41, with the subject knowing the site and the observer judging by eye) is Not supported by any controlled test and cannot be separated from suggestion; the "located two blind spots" claim is Never properly tested (two trials, no control for cues or candidate patches, location not colour).

Cross-cutting points for the Arbiter

The strongest items are small and checkable: the heredity tables (parent-child 16 of 18, sibling 5 of 9), the two blind location trials, the chromatic-focus paper. Each has a design that a later tester could repeat with a blind classifier or an independent scorer. I computed rough chance levels; the tables above show where the real uncertainty lies (non-blind classification; hidden number of candidate patches; instrument depth of focus).
Evidence kept: the contrary and supportive accounts (H. C. S., Goodspeed; Surya; de Rochas, de Fontenay; Boddington on the post-1914 dye supply; the BMJ review as reported by Wikipedia) are cited above in the claims they bear on. The silence after 1920 is explained in the Investigator's notes by several competing causes (wartime dye loss, Kilner's death in 1920, commercial failure, professional rejection). I cannot add to those; none is a mathematical question.
What would settle the logical defects: a protocol with a pre-registered hit criterion, an observer blind to site and colour, several C.C. bands per trial, sham trials (no one willing anything), a second independent scorer, and counts of misses.
Source gap: none for the book's text, which is clean. The 1920 edition and the Archives papers were read through the Investigator's notes and saved OCR, not by me in full; where I rely on them I say so.