Blondlot and N rays: a primer

Source gap (updated after QE). The project folder holds one document: a Google Books scan of the 1905 English translation of Blondlot's "N" Rays (a collection of his 1903-1904 notes to the French Academy of Sciences, plus his notes and observing instructions). The scan itself has no text layer, but the whole book has now been OCR'd (about 200,000 characters, Step 0), and the QE spot checks found it reads well. The reviewers first read it from page images, and the key pages were re-read for this primer (book pp.50, 58, 59, 60) [read: page images, PDF pp.75, 83-85]. So the book is fully available. What is missing lies outside the folder: the French originals in the Comptes Rendus (including his earlier notes on the speed of "X" rays), Robert W. Wood's 1904 report in Nature, the Berlin reports of Rubens and Lummer, and any later study. Everything said here about Wood's test and failed replications rests on one secondary source, [web] https://en.wikipedia.org/wiki/N_ray, as fetched by the arbiter. The calculations do not depend on that source: they use Blondlot's own printed numbers and measured data for aluminium.

Tags: [read] from the book; [web] with URL; [memory] from training, with confidence; [calc] computed in example.py (or by the arbiter, where marked).

Page numbers: "p.N" or "book p.N" is the printed page. "PDF p.N" is the scan page. The two differ by 23 to 33 pages, because unnumbered plates sit between pages (PDF p.55 = book p.30).

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1. The idea in one paragraph

In 1903 René Blondlot, a respected physics professor at Nancy in France, was studying X rays, which Röntgen had discovered eight years earlier. He saw a tiny electric spark near an X-ray tube appear to get brighter or dimmer as he turned it, and decided he had found a new kind of invisible radiation. He named it "N rays" after Nancy. Over the next year he reported that N rays come from gas lamps, the sun and hardened steel; that they pass through aluminium, wood and thick copper but are stopped by water; that prisms bend them and gratings diffract them, so that he could measure their wavelengths; and that bricks and stones soak them up in sunlight and give them out later. In his own observing notes he says that speaking aloud, whistling, or bringing a knife or a clenched fist near a dim phosphorescent screen makes its faint spots "more luminous" [read: book p.80, PDF pp.112-113]. His only detector was his own eye, judging whether a faint spark or a dimly glowing screen looked a little brighter. About 120 scientists, mostly French, published around 300 papers on N rays [web, N_ray page]. Physicists elsewhere could not see the effect. In 1904 the American physicist Robert Wood visited Blondlot's lab and secretly removed the prism from the apparatus in the dark. Blondlot went on reading the same spectrum. The episode is now the standard example of how an honest, skilled scientist can fool himself when his measuring instrument is his own expectation. This primer shows that Blondlot's numbers, taken seriously, rule themselves out. You can do the check yourself with undergraduate physics.

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2. What you need to know first

Electromagnetic waves and photons. Light, ultraviolet, X rays and radio are all electromagnetic waves. They differ only in wavelength λ (lambda, the distance between wave crests). Each wave also comes in packets called photons, each with energy E = hc/λ. Here h is Planck's constant and c is the speed of light. A handy form is E [eV] = 1239.84 / λ [nm], where eV is the electron-volt (the energy an electron gains crossing 1 volt) and nm is the nanometre (10⁻⁹ m). Yellow light (589 nm) has photons of about 2.1 eV. Read: any introductory modern physics text, e.g. Krane, Modern Physics, the photon chapter.

Diffraction gratings. A grating is a plate ruled with many parallel lines a distance d apart. Light of wavelength λ leaves it strongly only at the angles θ where d sin θ = mλ, with m = 0, ±1, ±2, ... (the "order"). Measure θ, know d, and you have λ. Because sin θ can never exceed 1, a grating cannot diffract a wavelength longer than d. Read: Hecht, Optics, the diffraction chapter; Halliday, Resnick & Walker, Fundamentals of Physics, the interference and diffraction chapters.

Refractive index and dispersion. The refractive index n of a material is the factor by which light slows down in it (speed c/n). Snell's law, n₁ sin θ₁ = n₂ sin θ₂, says how much a ray bends at a surface. A prism separates colours because n depends on wavelength; that dependence is called dispersion. In clear glass n falls as λ rises ("normal dispersion"). For X rays and extreme ultraviolet, n is very close to 1 and usually slightly below it. Read: Griffiths, Introduction to Electrodynamics, Chapter 9 (electromagnetic waves, including the section on absorption and dispersion).

Absorption: the Beer-Lambert law. When radiation passes through matter, a fixed fraction is absorbed in each thin layer. So intensity falls exponentially with thickness x: I = I₀ e^(−x/L). I₀ is the intensity going in, and L is the attenuation length, the depth at which the intensity has dropped to 1/e ≈ 37 %. Ten attenuation lengths let through e⁻¹⁰ ≈ 5 × 10⁻⁵. Many thousands let through nothing measurable. Read: Krane, Modern Physics, or any nuclear or radiation physics text, the section on attenuation of photons.

Thermal (blackbody) radiation. A hot body emits a broad spectrum set by its temperature T alone. Planck's law gives the number of photons per unit energy as proportional to E²/(e^(E/kT) − 1), where k = 8.617 × 10⁻⁵ eV/K is Boltzmann's constant. When E is much larger than kT, the factor e^(−E/kT) (the Boltzmann factor) makes emission collapse. A 2000 K lamp has kT ≈ 0.17 eV. It glows brightly at 2 eV and emits essentially nothing at 70 eV. Read: Schroeder, An Introduction to Thermal Physics, Chapter 7 (blackbody radiation).

Perception at threshold and blinding. Near the limit of night vision the eye is an unreliable photometer (light meter). A faint patch seems to brighten and fade over seconds, looks brighter when you look slightly to one side of it ("averted vision"), and seems to change when you expect it to [memory, high]. That is why careful experiments are blind: the person judging does not know which condition is in place. In a double-blind test, nobody in the room knows. No physics textbook covers this well. Read Irving Langmuir's lecture "Pathological Science" (see Further reading).

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3. The textbook view

Four pieces of standard physics are enough to test Blondlot's claims.

(a) Grating equation.

d sin θ_m = m λ

• d = spacing between grating lines (for a grating with N lines per mm, d = 1 mm / N)
• θ_m = angle of the m-th bright fringe from the straight-through direction
• m = integer order
• λ = wavelength

(b) Photon energy.

E = hc/λ, or E [eV] = 1239.84 / λ [nm]

(c) Refraction and absorption of extreme ultraviolet (EUV) light in a solid. EUV means wavelengths of roughly 10-120 nm. At these energies a material is described by a complex index n_c = 1 − δ − iβ. Its two parts are measured and tabulated for every element (the Henke/CXRO tables, Center for X-Ray Optics, [web] https://henke.lbl.gov/optical_constants/):

δ = r_e λ² N_a f₁ / (2π), β = r_e λ² N_a f₂ / (2π)

ordinary refractive index n = 1 − δ; attenuation length L = λ / (4πβ) = 1 / (2 r_e λ N_a f₂)

• r_e = 2.818 × 10⁻¹³ cm, the "classical electron radius", a constant that sets the strength of light-electron scattering
• N_a = atoms per cm³ (for aluminium, 6.03 × 10²² cm⁻³)
• f₁, f₂ = the measured "atomic scattering factors". f₁ controls bending (refraction). f₂ controls absorption.

These formulas are not exotic. They are what the Lorentz oscillator model in Griffiths Chapter 9 gives when the light frequency is far above most of the electrons' natural frequencies. The model treats each electron as a mass on a spring driven by the light's electric field. In that regime n is slightly below 1 and changes very little with wavelength. That is why EUV and X-ray optics use mirrors, not lenses or prisms [memory, high]. Near an absorption edge (an energy where a new group of electrons can just be knocked loose), f₁ can turn negative and n can rise a little above 1.

(d) Thermal emission. For a body at temperature T, photons of energy E ≫ kT are suppressed by about e^(−E/kT).

And one piece of experimental practice. A measured effect is believed when an instrument that has no expectations records it, or when observers who do not know the condition report it, and when another lab can reproduce it.

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4. Where Blondlot departs

Blondlot was no crank. He had measured the speed of electric waves along wires in 1891 to within about 1 % of the speed of light [web] https://en.wikipedia.org/wiki/Ren%C3%A9_Blondlot. He used the grating equation and Snell's law correctly: the reviewers rechecked his prism and fringe arithmetic and it holds [calc, arbiter]. His starting points were real physics too. X rays were new, radioactivity was new, and "a new invisible radiation" was a reasonable thing to look for in 1903. X rays can be polarized, as Barkla showed in 1904-05 by scattering [web] https://en.wikipedia.org/wiki/Charles_Glover_Barkla. And sparks really do respond to ultraviolet and X rays, which lower the voltage needed to break down the air in the gap [memory, high].

The departures:

An instructive twist: Blondlot first thought N rays had long wavelengths, like the far-infrared "residual rays" Rubens had found. He reported quartz indices of 2.93-2.29, which suit that reading. In January 1904 he switched to wavelengths about 6000 times shorter [read p.13 and note 7, per reviewers]. So the same radiation was said to behave like far infrared in one set of notes and like extreme ultraviolet in another. A real radiation cannot be both. The far-infrared phase has a loose end of its own. For the quartz lens the book prints one pair of distances: focal length 12 cm for yellow light, slit 26.5 cm from the lens, image at "about 13.9 cms" [read: book pp.14-15, PDF pp.37-38]. The lens formula 1/f = 1/l + 1/l' (f the focal length, l and l' the object and image distances) gives f' = 9.12 cm for N rays. A thin lens has 1/f proportional to (n − 1), so n' = 1 + (1.544 − 1) × 12 / 9.12 ≈ 1.72, using 1.544 for quartz in yellow light [calc, arbiter]. The quoted 2.93 is said to be "the mean value" of other pairs that are not printed, so the book's own example does not reproduce its own result.

A second reassignment shows the same habit. Some years earlier Blondlot had measured the speed of propagation of what he took to be X rays and found it equal to that of Hertzian (radio) waves, and so of light [read: book p.viii, PDF p.17]. The notes are in Comptes Rendus t.125, which is the 1897 volume [memory, medium], and they are not in the folder. In 1904 he wrote that those measurements "apply in reality not to 'X' rays, but to 'N' rays", and called the result "nothing more than a verification of an assured fact" [read: book p.viii]. A result that fits whichever radiation it is assigned to confirms nothing about the detector.

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5. Worked example: let Blondlot's own table rule on itself

This calculation uses only Blondlot's printed numbers and measured aluminium data. It needs neither Wood nor anyone's opinion. All numbers are reproduced by example.py [calc].

The data (book p.58, [read: page image PDF p.83]). Each wavelength was measured with three gratings of 200, 100 and 50 lines per mm. No unit is printed:

He measured the angle between the 10th fringe on the left and the 10th on the right [read p.58, page image].

Step 1: find the unit. A 200 lines/mm grating has d = 1 mm / 200 = 5 μm (micrometres). Suppose the unit were millimetres, so λ = 0.00815 mm = 8.15 μm. Then even the first order needs sin θ = λ/d = 1.63. That is impossible, so no fringes would exist at all. Now suppose the unit is micrometres, so λ = 0.00815 μm = 8.15 nm. Then the 10th order sits at sin θ = 10 × 0.00815 / 5 = 0.0163, or θ = 0.93°, and left-to-right is 1.87°. That is a reasonable angle for his mirror and telescope. His Newton's-ring cross-check says the same thing: he counts how many N-ray wavelengths fit in one wavelength of yellow light [read p.59, page image] and gets 0.589 / 0.0085 ≈ 69 per yellow ring, which only makes sense in micrometres. So the wavelengths are 8.15 to 17.6 nm. This is a deduction from his own method, not a guess.

Step 2: check his error claim. He writes: "I believe, nevertheless, that the relative errors do not exceed 4 per cent" [read p.60, page image]. Look at the n = 1.19 row: 0.0093, 0.0102, 0.0106. The mean is 0.01003. The full range is (0.0106 − 0.0093)/0.01003 = 13.0 %, so the values sit ±6.5 % about the mean. That exceeds 4 % even on the generous reading. The other rows are tighter (n = 1.04: ±2.7 %; n = 1.85: ±3.7 %). This is a small inconsistency, not a fatal one. It shows that his error estimate was a belief, not a calculation.

Step 3: photon energies. E = 1239.84 / λ[nm]:

These are 30 to 70 times the energy of a visible photon. This is the extreme-ultraviolet band, where chip makers now work at 13.5 nm, in vacuum [memory, high].

Step 4: can his sources make these photons? His main source is an Auer gas mantle, which runs at about 2000 K [memory, medium; the conclusion holds for any flame or lamp]. Then kT = 8.617 × 10⁻⁵ × 2000 = 0.1723 eV.

• At 70.4 eV: E/kT = 408.5, and e^(−408.5) = 10^(−177.4).
• At 152.1 eV: E/kT = 882.6, and e^(−882.6) = 10^(−383.3).

Now compare against yellow light from the same lamp, using the full Planck photon spectrum E²/(e^(E/kT) − 1). The lamp emits about 10⁻¹⁶⁹ times as many photons per eV at 70 eV as at 2.1 eV, and 10⁻³⁷⁴ times as many at 152 eV. For scale, there are about 10⁸⁰ atoms in the observable universe. A lamp emits none of these photons. The sun (5800 K) does better, at about 10⁻⁶¹ to 10⁻¹³² in the Boltzmann factor [calc, arbiter], but its EUV never reaches the ground because the atmosphere absorbs it [memory, high].

Step 5: could they cross 1.5 cm of aluminium? Use the measured CXRO data for aluminium [web] https://henke.lbl.gov/optical_constants/sf/al.nff, with N_a = 2.70 g/cm³ × 6.022 × 10²³ / 26.98 g/mol = 6.03 × 10²² atoms/cm³.

At 152.1 eV (λ = 8.15 nm): f₂ ≈ 9.63, and λ = 8.15 × 10⁻⁷ cm. L = 1 / (2 × 2.818 × 10⁻¹³ × 8.15 × 10⁻⁷ × 6.03 × 10²² × 9.63) = 1 / (2.67 × 10⁵ cm⁻¹) = 3.75 × 10⁻⁶ cm = 37.5 nm. Then x/L = 1.5 / 3.75 × 10⁻⁶ ≈ 400,000, and T = e^(−400,000) = 10^(−173,689).

At 70.4 eV (λ = 17.6 nm): this is just below aluminium's L absorption edge at 72.7 eV, the most transparent point in his whole band, so it is his best case. Here f₂ ≈ 0.252 and L = 662 nm. Then x/L ≈ 22,700 and T = 10^(−9,840).

So the best case is a transmission written as a decimal point followed by nearly ten thousand zeros. This explains why real EUV filters made of aluminium are films about 100 nm thick [memory, medium; consistent with L above]. The result barely depends on the details. Even if L were 1000 times larger, the plate would still block the rays completely.

Step 6: compare his indices with aluminium's real ones. From the same table, n = 1 − r_e λ² N_a f₁ / 2π:

Blondlot's n − 1 ranges from 0.04 to 0.85. The real n − 1 stays between about −0.01 and +0.04. At 17.6 nm his prism would bend the ray by about 60 times as much as a real aluminium prism could (0.85 / 0.014) [calc]. A caution for fairness: the reviewers said "n must be below 1", which is too strong. Just under the absorption edge aluminium really does have n slightly above 1 [calc, arbiter]. But it is 1.04 at most, never 1.85.

What the example shows. Blondlot's geometry is right. His numbers, read the only way his own method allows, describe radiation that his lamps cannot emit, that his screens would block, and that his prism could not bend by the amount he reports. Something other than a radiation produced the readings. The obvious candidate is the observer.

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6. Evidence table

Verdicts are the arbiter's (arbiter.md). Test history rests on [web] https://en.wikipedia.org/wiki/N_ray unless marked.

"No independent replication" does not mean "no one else reported it". Blondlot's book names colleagues, nearly all at Nancy, who reported related observations [read: deep read of PDF pp.54-111]: - Bichat: ethyl ether under tension emits N₁ rays (PDF p.104); lead blocks N rays only because of its oxide coating (C.R. t.138 p.548, 1904; note 5). - Charpentier: physiological N-ray work (C.R. t.137 p.1049, 24 Dec 1903); wet cardboard passes the rays from a knife blade (notes 11-12). - Gutton: a magnetic field or electromotive force changes the glow of a dim luminous surface (PDF p.106). - Macé de Lépinay: sound brightens a phosphorescent screen (PDF p.106). Blondlot calls the Gutton and Macé de Lépinay effects analogous to N rays, not N rays themselves. - Sagnac: a rival long-wavelength reading from multiple images in a quartz lens (PDF p.85).

None of them gives numbers that independently repeat a Blondlot measurement. The one name from outside Nancy is Rubens: "M. H. Rubens made the same observation, as he was kind enough to write me" (PDF p.55). The sentence follows both Blondlot's null thermopile reading and his phosphor-brightening test, so it is unclear which one Rubens confirmed. It is a private, undated report, and Rubens later failed to find N rays [web] https://en.wikipedia.org/wiki/N_ray. Do not count it as confirmation. These reports are the "believed at first in Nancy" half of the story. The other half is the failures elsewhere.

Not suppressed: the Academy awarded Blondlot the Leconte prize in 1904 for his work as a whole [web] https://en.wikipedia.org/wiki/Ren%C3%A9_Blondlot. The claim fell because nobody outside Nancy could reproduce it.

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7. What a learner should take away

Solid. - Blondlot's optics arithmetic. The grating angles, prism deviations and lens thresholds all check out. Self-consistent geometry shows the observer applied the formulas correctly to positions he judged. It does not show the thing he measured exists. - The general background: sparks are sensitive to ionizing radiation and to their surroundings, and X rays are polarizable. - His honesty in reporting. He printed his null thermal tests (a thermopile and a resistance bridge showed nothing) and his one photographic failure [read pp.29-32, 67, per reviewers]. Nothing suggests fraud.

Wrong, and why it is instructive. - A detector that knows the answer. Every number came from an eye that expected a result, on a signal at the edge of visibility, under rules that blamed failures on the observer ("some never succeed"). Wood's prism removal is the cleanest demonstration: the "spectrum" stayed when its cause was gone. - Numbers that don't hang together across physics. Each measurement looked fine alone. Combine wavelength (grating) with source (Planck) and penetration (Beer-Lambert), and the set is impossible by hundreds to hundreds of thousands of orders of magnitude. Checking claims against each other with standard laws is a powerful, cheap test. You did it in Section 5 in a few lines. - Patching after the fact. Rock salt, lead, salt water, and quartz going from 2.9 to aluminium 1.04: each surprise was handled with a new exception. He even added a second, "inverse" species, N₁ rays, which dim a phosphor, with indices 1.004-1.041 and wavelengths of about 0.003-0.0081 μm [read: PDF pp.97-104]. Those points continue the same rising n-versus-λ curve, so they make the dispersion anomaly worse, not better. A theory that can absorb any result predicts nothing.

Genuinely open (minor). - Was there a real but mundane effect behind the spark photographs, such as humidity, draughts or sound acting on a delicate spark? Nobody tested that separately (arbiter, open question 1). - How large is the expectation effect on brightness judgments under exactly Blondlot's viewing rules? The primary studies were not found (arbiter, open question 2). - Did anyone record N-ray data with something other than the eye? Nothing in the folder shows it (arbiter, open question 4).

Resolved since the first draft. The quartz-lens index 2.93 is not a misreading of the page. The OCR text confirms the printed distances, and the one printed pair gives about 1.72 (Section 4). The 2.93 is a mean of pairs the book does not print, so it cannot be checked.

None of these reopens the case for N rays as a radiation.

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8. Check yourself

1. A grating has 100 lines per mm. Blondlot's entry for n = 1.04 is 0.00795. What is the angle of the 10th-order fringe if the unit is micrometres? Why can't the unit be millimetres?
2. Using E[eV] = 1239.84/λ[nm], what is the photon energy for Blondlot's n = 1.68 line? Roughly how many times a yellow photon (2.1 eV) is it?
3. Suppose N rays had an attenuation length of 1 mm in aluminium, which is about 1500 times more generous than the measured best case. What fraction would cross his 1.5 cm plate? Would a careful observer notice "no notable weakening"?
4. In normal dispersion, does n rise or fall with wavelength? Which way do Blondlot's aluminium indices go? Name one physical situation where n can rise above 1 for EUV in aluminium, and say how large it gets.
5. Design a test of the claim that hardened steel emits N rays which Blondlot himself would have accepted as fair, and which could not be passed by expectation alone.

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9. Further reading

Mainstream physics - D. J. Griffiths, Introduction to Electrodynamics, Chapter 9: electromagnetic waves, absorption and dispersion, the Lorentz oscillator model. - E. Hecht, Optics: diffraction gratings, Newton's rings, dispersion. - D. V. Schroeder, An Introduction to Thermal Physics, Chapter 7: blackbody radiation and the Planck spectrum. - D. Attwood, Soft X-Rays and Extreme Ultraviolet Radiation (Cambridge University Press, 1999): the optical constants of section 3(c), and why EUV optics need vacuum and mirrors [memory, high]. - CXRO X-ray interactions with matter (Henke tables): https://henke.lbl.gov/optical_constants/ [web]. Try the aluminium transmission calculator yourself.

History and the psychology of measurement - R. W. Wood, "The n-Rays", Nature 70, 530-531 (29 September 1904): the prism-removal visit [memory, medium for page numbers; the date is from the N_ray page, web]. - I. Klotz, "The N-Ray Affair", Scientific American 242(5), May 1980 [memory, medium]. - M. J. Nye, "N-rays: an episode in the history and psychology of science", Historical Studies in the Physical Sciences 11 (1980) [memory, medium]. Covers the French context and why the claim lasted longer there. - I. Langmuir, "Pathological Science" (1953 lecture, transcribed in Physics Today, October 1989) [memory, high]. N rays are one of his case studies. - Wikipedia, "N ray": https://en.wikipedia.org/wiki/N_ray [web].

Blondlot's own work - R. Blondlot, "N" Rays: A Collection of Papers Communicated to the Academy of Sciences, trans. J. Garcin (Longmans, Green, 1905). This is the folder's PDF. Read the Preliminary Notice (p.viii, the velocity reassignment), the quartz-lens passage (pp.14-15), the thermopile test and the Rubens sentence (p.30), the wavelength table (p.58), the Newton's-ring check (p.59), the error statement (p.60), the strained-steel and aluminium-plate passage (p.50), and the observing instructions (pp.80-83). - The original notes are in Comptes Rendus de l'Académie des Sciences, vols. 136-138 (1903-1904) [memory, medium]. They are not in the folder.

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Answers

1. d = 1 mm / 100 = 10 μm. sin θ₁₀ = 10 × 0.00795 / 10 = 0.00795, so θ₁₀ = 0.456°. In millimetres, λ = 7.95 μm. Then first order alone needs sin θ = 0.795 (possible), but the 10th order needs sin θ = 7.95, which is impossible. So he could not have measured 10th-order fringes. With the 200 lines/mm grating even first order fails. Together with the Newton's-ring check (69 rings per yellow ring), only micrometres fit.
2. λ = 14.6 nm, so E = 1239.84 / 14.6 = 84.9 eV, about 40 times a yellow photon.
3. T = e^(−15/1) = e^(−15) ≈ 3 × 10⁻⁷. The rays would be cut to three ten-millionths of their strength. That is not "without any notable weakening". The claim fails even with a hugely generous L.
4. In normal dispersion, n falls as wavelength rises. Blondlot's indices rise with wavelength (1.04 at 8.15 nm, 1.85 at 17.6 nm), and he admits this runs against ordinary light. Just below aluminium's L absorption edge (about 72.7 eV, 17 nm), f₁ turns negative and n rises above 1. The CXRO data give at most about 1.04, far below 1.85.
5. One example: have a third party prepare a set of identical-looking chisels, half hardened and half annealed, coded so nobody in the room knows which is which. Present them in random order to Blondlot's own phosphor screen, with Blondlot, or any observer he picks in advance, reporting "brighter" or "not". Agree the scoring rule beforehand (for example, at least 18 of 20 correct). Add a photometer, or a photographic plate read by a densitometer, viewing the same screen. Chance gives about 10 of 20. The aim is that only a real effect, not expectation, can pass. This is essentially what Wood did informally with the file and the piece of wood.