Crookes and "radiant matter": a primer

Project folder: Researchers/Willams-Crookes. It holds one document: Sir William Crookes, "On Radiant Matter", a lecture given to the British Association for the Advancement of Science at Sheffield on Friday 22 August 1879, reprinted in two parts in The Popular Science Monthly, vol. XVI (23 PDF pages) [read: p.13 footnote].

Source note (repeated from claims.md and arbiter.md). There is no source gap for the lecture itself: all 23 pages were read in full from the text layer, and the page images were checked where the OCR (optical character recognition) failed. Three printed numbers differ from the text layer, and the page-image values are used throughout: the ruby line is "about 6,895" (not 6,595), the highest vacuum is 1/20,000,000 of an atmosphere (not 1/6,754,000), and the bulb holds 10^24 molecules (not 10^15) [read: page images p.7, p.21, p.22, via the deep read]. But the folder holds only this popular lecture. It is a set of live demonstrations: it gives no pump, no pressure gauge, no coil voltage or current, no magnet strength, no beam speed and no temperatures, and no tables of data [read]. Crookes's technical papers of 1878-79, the Royal Society referee reports on them, his laboratory notebooks and the later papers that tested his explanation (Starke 1900, Thomson 1897 and 1903, Perrin 1895) were not read by any role; they are known from catalogue entries, a museum demonstration page, Wikipedia and one review article. Where a statement below rests on them, it says so.

QE revision (2026-10-06). After a quality review (qe.md, verdict MINOR) four passages of the lecture were re-read from page images (Fig. 18 on pp.18-19; the Morgan footnote and potash tube on pp.7-8; the hot-ring apparatus on pp.14-15; bulb A on p.9), and the arbiter added a "QE revision" section. This primer follows that revision: the Fig. 18 "repulsion" is now an open question (section 3.4), the hot-ring thermionic idea is ruled out by a calculation (section 5, side checks), and a seventh claim, that the highest vacuum does not conduct, is added (sections 3.5, 4 and 6). The new numbers are printed by example.py Part 5.

Source tags: [read] = from the lecture or the project's own review files; [web] = Internet source, URL given; [memory] = recalled, with confidence; [computed] = calculated for this primer (see example.py, which prints every number in section 5).

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1. The idea in one paragraph

In the 1870s William Crookes, a London chemist and physicist, pumped glass tubes down to about a millionth of normal air pressure, among the emptiest vessels of his time, and ran a high-voltage spark through them. Something invisible shot out of the negative metal plate. Where it hit the glass, the glass glowed green; where it hit a diamond or a ruby, these glowed brightly. It travelled in straight lines, cast sharp shadows, could be focused by a curved plate until it melted metal, pushed a little paddle wheel along a glass track, and was bent sideways by a magnet. Crookes's explanation was that the gas left in the tube was now so thin that its molecules almost never hit one another, so they behaved as individual flying bullets rather than as a gas. He called this a "fourth state of matter" (after solid, liquid and gas), borrowing Michael Faraday's old name "radiant matter", and he thought the bullets were gas molecules that had picked up a negative electric charge from the negative plate. Almost every demonstration he showed is real and can be repeated today. What changed is the identity of the bullets. In 1897 J. J. Thomson showed that they are far lighter than any atom: they are electrons, which come out of the metal, not from the gas. This primer explains the real physics Crookes started from (the kinetic theory of gases and the mean free path), and then uses a single calculation, the bending of the beam in a magnet, to show where his inference holds and where it fails.

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2. What you need to know first

The kinetic theory of gases. A gas is a crowd of molecules flying in all directions and bouncing off each other and the walls. The pressure p is the push of those impacts on a wall. For an ideal gas, p = n k T, where n is the number density (molecules per cubic metre), T is the absolute temperature in kelvin, and k (Boltzmann's constant) = 1.38 x 10^-23 joule per kelvin. So at a fixed temperature, halving the pressure halves the number of molecules in each cubic centimetre. At 0 C and 1 atmosphere, n is 2.69 x 10^19 molecules per cubic centimetre (Loschmidt's number) [web: https://en.wikipedia.org/wiki/Johann_Josef_Loschmidt, via arbiter.md]. Read: any introductory physics text, the chapter on the kinetic theory of gases (e.g. Halliday, Resnick and Walker, Fundamentals of Physics); for more depth, Schroeder, An Introduction to Thermal Physics.

The mean free path. The mean free path, written with the Greek letter lambda (λ), is the average distance a molecule travels between collisions with other molecules. Picture each molecule as a sphere of diameter d. It hits any other molecule whose centre comes within d of its own path, so as it moves a distance x it sweeps out a cylinder of cross-section π d^2 and volume π d^2 x. It meets one molecule on average when that cylinder holds one molecule: π d^2 λ n = 1. Allowing for the fact that the other molecules are moving too adds a factor of the square root of 2:

λ = 1 / (√2 π d^2 n) = k T / (√2 π d^2 p).

The key fact for Crookes: λ is inversely proportional to the pressure. Pump out 999,999 of every million molecules and the free path becomes a million times longer. Crookes stated exactly this rule: "the length of the mean free path being inversely proportional to the number of molecules present" [read: p.2]. Read: the same chapters as above; vacuum engineers use it daily (O'Hanlon, A User's Guide to Vacuum Technology).

Charged particles in a magnetic field (the Lorentz force). A particle of charge q moving with velocity v through a magnetic field B feels a force F = q v x B (the cross product, so the force is at right angles to both the velocity and the field). Because the force is always at right angles to the motion it does no work: it changes the direction of the particle, not its speed. When v is at right angles to a uniform B, the path is a circle (derived in section 3). Read: Griffiths, Introduction to Electrodynamics, Ch. 5 (magnetostatics; the Lorentz force law and cyclotron motion).

Energy from a voltage. A charge q that falls through a voltage difference V gains kinetic energy K = qV. For an electron (charge e = 1.60 x 10^-19 coulomb) falling through 10,000 volts, K = 1.60 x 10^-15 joule, also written 10 keV (kilo-electron-volts). Kinetic energy and momentum are related by K = p^2 / (2m) at speeds well below light (p here is momentum, not pressure; the context makes clear which). Read: Griffiths Ch. 2 (electric potential); any modern-physics text for the electron-volt.

Forces between currents and between charges. Two parallel wires carrying currents in the same direction attract (this is how the ampere used to be defined). Two like charges repel (Coulomb's law). Crookes used the difference between these two cases as a test (claim 4). Read: Griffiths Ch. 2 and Ch. 5.

What "a state of matter" means. Solid, liquid and gas are separated by phase transitions: at a definite temperature and pressure the substance changes abruptly (it melts, or boils), with latent heat and a jump in density. A plasma, often called the fourth state of matter today, is a gas in which a large share of the atoms have lost electrons, so that it contains free charges and responds collectively to electric and magnetic fields. The word "plasma" in this sense dates from Irving Langmuir in 1928 [web: https://en.wikipedia.org/wiki/Plasma_(physics), via sites.md]. Read: F. F. Chen, Introduction to Plasma Physics and Controlled Fusion, opening chapter.

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3. The textbook view

3.1 A gas at very low pressure

Using the formula above for air at 20 C, with an effective molecular diameter d = 3.7 x 10^-10 m (a textbook value [memory, high]), the free path at the pressures Crookes names is [computed, example.py Part 1]:

When λ becomes as large as the container, gas molecules fly from wall to wall and hardly ever meet one another. Engineers call this free-molecular flow (the Knudsen regime, after Martin Knudsen, who studied it around 1909 [memory, medium]). Its measure is the Knudsen number Kn = λ / L, where L is the size of the container; when Kn is near or above 1, ordinary gas dynamics (which assumes constant collisions) fails, and each molecule must be followed separately. This is the regime Crookes described: "we have no longer to deal with a continuous portion of matter ... but we must here contemplate the molecules individually" [read: p.4]. It is still a gas, though: it obeys p = nkT, and nothing abrupt happens as the pressure falls; λ simply grows smoothly.

3.2 What actually happens in a discharge tube

The modern account, built from about 1890 to 1910 (Thomson, Townsend and others) [memory, high]:

1. Where the beam comes from. A few stray ions in the residual gas are pulled to the negative plate (the cathode) by the strong electric field and knock electrons out of the metal. A strongly heated metal also releases electrons by itself (thermionic emission). The positive plate is the anode.
2. The beam. The electrons are accelerated away from the cathode, at right angles to its surface because that is the direction of the electric field just outside a conductor. Once the gas is thin enough that they rarely collide, they fly in straight lines across the tube. This beam is what the 19th century called cathode rays (Goldstein's name, 1876 [web: Busch 2023, https://pmc.ncbi.nlm.nih.gov/articles/PMC10311274/]).
3. The dark space. Next to the cathode there is a region with a very strong electric field where the electrons are still gaining speed and have not yet got enough energy to make the gas glow. It looks dark. It is now called the cathode dark space or Crookes dark space. Its thickness grows as the pressure falls (roughly as 1/p, the same scaling as λ), but it is set by how far an electron must travel in the field to gain enough energy to ionise a molecule, so it also depends on the voltage and the gas [memory, medium-high; e.g. Raizer, Gas Discharge Physics].
4. The glow. When the beam strikes glass, a diamond or a ruby, the electrons' energy is turned partly into light. This is cathodoluminescence. In ruby the red light comes from chromium ions in the aluminium oxide crystal, at two sharp wavelengths, 694.3 and 692.9 nanometres (the "R lines") [web: https://fluomin.org/uk/fiche.php?id=870 and https://duffy.princeton.edu/laboratory/ruby-fluorescence-measurement, via arbiter.md].
5. Heating. The beam carries energy. A beam of 1 milliampere at 10,000 volts carries power P = VI = 10 watts [computed, Part 4c]. Focused onto a few square millimetres, that is enough to make metal white-hot; electron-beam melting and welding are industrial processes today [memory, high].

3.3 Bending in a magnet

For a charge q moving at speed v at right angles to a uniform field B, the force has size qvB and points to the centre of a circle. Newton's second law for circular motion (force = mass x centripetal acceleration, v^2/r) gives

m v^2 / r = q v B, so r = m v / (q B) = p / (q B),

where r is the radius of the circle, m the mass and p = mv the momentum. Written with the kinetic energy K = ½ m v^2 (so v = √(2K/m)):

r = √(2 m K) / (q B).

Two particles with the same charge and the same energy in the same field therefore bend on circles whose radii are in the ratio of the square roots of their masses:

r₂ / r₁ = √(m₂ / m₁).

This one line is the heart of the worked example. A heavy particle with the same charge and energy is much stiffer: it bends far less. Slowing a particle down (smaller p) makes it bend more sharply. Thomson's 1897 experiment combined this magnetic bending with an electric deflection to measure the charge-to-mass ratio q/m of the cathode-ray particles; he found the mass about 1/2000 of a hydrogen atom for the same charge, and the same value whatever the gas or the cathode metal [web: Busch 2023 (Thomson, Phil. Mag. 44, 293-316, 1897); https://en.wikipedia.org/wiki/Cathode_ray].

3.4 Two parallel beams

Two parallel streams of like charges moving at speed v push each other apart electrically and pull each other together magnetically (each moving stream is a current). The magnetic pull is a fraction (v/c)^2 of the electric push, where c is the speed of light, so the net force is repulsive unless the particles move near light speed. For 10 keV electrons, (v/c)^2 = 0.038, so the net force is 96% of the electric push and repulsive [computed, Part 4d]. Wires behave differently because a wire is electrically neutral: its moving electrons are balanced by fixed positive ions, so only the magnetic attraction is left.

But how big is the push? The direction is right; the size has to be checked. A beam of current I moving at speed v carries a charge per metre λ_q = I/v (λ_q, "line charge", is not the mean free path). By Gauss's law its electric field at distance r is E = λ_q / (2π ε₀ r), where ε₀ = 8.85 x 10^-12 F/m is the permittivity of free space. Take two beams 1 cm apart, 10 kV, 1 mA, and a 30 cm run (all assumed; Crookes gives none of these). Then λ_q = 1.7 x 10^-11 C/m, E = 31 V/m, and an electron in the second beam drifts sideways by only about 0.07 mm over the run (0.67 mm at 10 mA) [computed, Part 5a]. Positive ions from the residual gas would partly neutralise the beam and make it smaller still. That is far too small for the visible "jump" Crookes showed in Fig. 18. The drift grows as I / V^(3/2), though: at 1 kV it is about 2 mm at 1 mA and about 21 mm at 10 mA [computed, Part 5a], which would be visible. Crookes gave no voltage, current, pressure or spacing, so the calculation weakens his explanation without ruling it out. A second explanation is that the strong electric field around the second negative terminal (the cathode fall, hundreds to thousands of volts across its dark space) pushes the first beam near its source. That is physically reasonable but also unproven: the QE recalled a report by Goldstein (about 1880) of cathode rays deflected by a neighbouring cathode, and the arbiter's web check for it failed [memory, medium; unverified]. The arbiter rates both explanations Plausible, untested [read: arbiter.md, QE revision].

3.5 When the gas is too thin to conduct

A discharge needs a supply of charge carriers. In the textbook account an electron accelerated by the field hits a gas molecule and knocks out another electron (ionisation), and the avalanche keeps the current going. The voltage needed to start a discharge across a gap depends on the product of pressure and gap length, p x d, and plotting it gives the Paschen curve: a U shape with a minimum. On the high-pressure side, electrons collide too often to gain enough energy. On the low-pressure side, there are too few molecules for an electron to hit any on its way across, so the needed voltage rises steeply [memory, high for the textbook statement; web partly confirmed, https://w3.pppl.gov/~ikaganov/pdf_files/Three_Regimes.pdf, via arbiter.md, which notes that fast ions and neutrals also matter at low pressure and high voltage]. So a good enough vacuum stops conducting. Read: Raizer, Gas Discharge Physics, the chapter on breakdown.

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4. Where Crookes departs

Crookes starts from sound physics: the kinetic theory of gases, the inverse law of the mean free path, Faraday's speculation, and careful observation. His demonstrations are excellent. The departures are in the inferences.

The exact point of departure. Crookes had two true facts: (1) at high vacuum the gas molecules almost never collide, and (2) something flies from the negative pole in straight lines, carries negative charge and momentum-like effects, and is bent by a magnet. He joined them by assuming that the "something" is the gas molecules, now free to fly. That assumption is natural: in 1879 nobody knew of any particle lighter than a hydrogen atom, and fact (1) seemed to explain fact (2). It is also the one step a calculation can test, because the amount of bending in a magnet depends on the mass of what is bending. That is the worked example.

Two things to keep in view, to be fair to him:

• Priority. Crookes did not discover most of these effects. Hittorf (1869) reported straight-line travel, glass fluorescence and shadows; Goldstein (1876) named "cathode rays" and found emission at right angles to the cathode; Plücker and Hittorf had earlier reported magnetic deflection [web: Busch 2023]. Cromwell Varley (1871) had argued that the rays were particles [web: Notes Rec. R. Soc. 2006 snippet and Wikipedia, via sites.md]. Crookes's contributions were much better vacua (with C. H. Gimingham's multiple-tube Sprengel mercury pump, 1876 [web: https://ietarchivesblog.org/2017/05/10/charles-and-edward-gimingham-light-bulb-pioneers/]), ingenious apparatus shown in the lecture (the focusing cup, the hinged cross, the paddle wheel railway, the magnetic water wheel; the lecture credits Gimingham with building the last three, Figs. 9, 11 and 17, and does not credit him with the focusing cup [read: pp.10-13, 17, 19]), and a public demonstration that made the subject famous.
• He was right against his main rival school. Goldstein, Hertz and E. Wiedemann held that cathode rays were waves in the ether, not particles [web: Busch 2023; Wikipedia "Crookes tube"]. Crookes's particle view (charged, negatively, flying in straight lines, carrying momentum and energy) was the side that won. On the particle-versus-wave question, he was wrong only about which particles (his other errors, on the dark space, the paddle-wheel mechanism and the "fourth state", are listed in section 7). He later wrote, as quoted in his obituary: "What I then called 'Radiant Matter' now passes as 'Electrons,' a term coined by Dr. Johnstone Stoney" [web: B. Dyer, Obituary notices, J. Chem. Soc. 1920, https://pubs.rsc.org, via the Investigator]. This is documented in one published obituary; the original place and date of the statement have not been found yet (his presidential addresses of 1891 and 1898 are the likely places [memory, low]).

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5. Worked example: what bends in the magnet?

Question. Crookes showed a thin glowing line along a long, highly exhausted tube, bent "like a flexible wand" by a horseshoe magnet held underneath (Fig. 14) [read: p.15-16]. If the line were made of gas molecules carrying a negative charge, how much would it bend? How much would it bend if it were made of electrons?

Assumptions. The lecture gives no voltage and no magnetic field [read]. I use the reviewers' typical values: an accelerating voltage V = 10,000 volts (an induction coil of the period could give that or more [memory, medium]) and a field B = 0.01 tesla (100 gauss, reasonable a few centimetres from a horseshoe magnet). The molecule is nitrogen, N₂ (mass 28.0 atomic mass units, 4.65 x 10^-26 kg), the main gas in air, carrying one electron's worth of charge, e = 1.60 x 10^-19 C. Both particles fall through the same voltage, so both get the same energy. The final comparison does not depend on V or B, only on the masses (section 3.3).

Step 0: is the beam really collisionless? First, check Crookes's own starting point, because the whole argument needs a beam that flies freely. From the table in section 3.1, at a millionth of an atmosphere λ = 6.6 cm, about half the 13.5 cm bulb, and at his best vacuum λ = 1.3 m [computed, Part 1]. So Crookes's picture is right: the residual gas is close to collisionless, and anything flying from the pole can cross the tube without being stopped. (Electrons go even further between collisions than gas molecules do, because they are so small.)

Step 1: the energy. Each particle gains

K = eV = (1.60 x 10^-19 C)(1.0 x 10^4 V) = 1.60 x 10^-15 J.

Step 2: the electron. Speed: v = √(2K/m) = √(2 x 1.60 x 10^-15 / 9.11 x 10^-31) = 5.93 x 10^7 m/s, about 0.20 times the speed of light. At that speed relativity changes the answer by only about 1% (the exact value is 5.85 x 10^7 m/s), so the simple formula is good enough. Radius:

r_e = m v / (e B) = (9.11 x 10^-31)(5.93 x 10^7) / ((1.60 x 10^-19)(0.01)) = 0.0337 m = 3.4 cm [computed, Part 2; 3.39 cm with relativity].

A beam that curls on a circle 6.8 cm across bends right round within a few centimetres of entering the field: a strong, obvious "wand-waving" bend.

Step 3: the nitrogen molecule. Same charge, same energy, mass 4.65 x 10^-26 kg, which is 51,000 times the electron's mass. Speed: v = √(2 x 1.60 x 10^-15 / 4.65 x 10^-26) = 2.6 x 10^5 m/s. Radius:

r_N₂ = √(2 m K) / (e B) = √(2 x 4.65 x 10^-26 x 1.60 x 10^-15) / ((1.60 x 10^-19)(0.01)) = 7.6 m [computed, Part 2].

Step 4: the ratio. r_N₂ / r_e = √(m_N₂ / m_e) = √51,100 ≈ 226. This number holds for any voltage and any field, as long as the two particles have the same charge and the same energy.

Step 5: what you would see. Over a 30 cm run through the field, a beam on a 7.6 m circle drifts sideways by about L^2 / (2r) = (0.30)^2 / (2 x 7.6) = 5.9 mm [computed, Part 2]. A nitrogen beam would therefore move by a few millimetres along a whole tube, hardly a "flexible wand". To make the molecule beam bend as much as Crookes saw, the magnet would have to be about 226 times stronger (about 2 tesla, a large laboratory electromagnet, not a hand-held horseshoe [memory, high]).

Step 6: the gas-independence check. If the beam were the gas, changing the gas would change the bending. Hydrogen (H₂, 2 mass units) and carbonic acid (CO₂, 44 mass units) would give radii of 2.0 m and 9.6 m, a factor of √(44/2) = 4.7 apart [computed, Part 3]. Crookes reported the shadows, glow and magnetic deflection "identical" in hydrogen, carbonic acid and air [read: p.21]. He gave no measured deflections, so this is a qualitative observation, but it points the same way: the bending particle is the same whatever gas fills the tube.

What the calculation shows, and what it does not.

• It supports Crookes on the starting points: the gas is near collisionless (Step 0), the beam is made of charged particles (it bends in a magnet), and the bending grows when the particles are slowed (r is proportional to v), which is exactly what he saw when he let in a trace of gas and "my molecular bullets fall to the bottom before they have got more than half way" [read: p.17].
• It shows that the bending he saw needs a charge-to-mass ratio of the electron's order, hundreds of times larger than any gas molecule could have with the same charge and energy. The carriers are not gas molecules.
• It rests on assumed values (V, B) and on the premise "same charge, same energy". The ratio of 226 does not depend on V or B, but the premise is the reviewers', not Crookes's: he gave no charge, energy or deflection [read]. That is why the arbiter rates the "molecules" interpretation Historically superseded but instructive, with this calculation as supporting evidence, rather than "Refuted by calculation". The deciding evidence was an experiment: Thomson's 1897 measurement of q/m [web: Busch 2023].
• Crookes himself said that it would be "of great interest" to find the law of the magnetic deflection [read: p.17]. That law is r = mv/(qB). Had he measured r with a known field and voltage, he could have weighed his own "molecules".

Side checks on his other numbers (example.py Parts 4 and 5):

• His best vacuum. He says 1/20,000,000 of an atmosphere "corresponds to about the hundredth of an inch in a barometric column three miles high" [read: p.21]. Check: 0.01 inch / 3 miles = 0.000254 m / 4,828 m = 5.26 x 10^-8 = 1/19.0 million [computed]. His figure is internally consistent (the column must be air of uniform density, not mercury; that is the reviewers' reading).
• The molecule count. Bulb volume = (π/6)(13.5 cm)^3 = 1,288.25 cm^3 (his 13.5^3 x 0.5236 gives the same). With his 10^21 molecules per cm^3: 1.288 x 10^24 at 1 atm, 1.288 x 10^18 at a millionth; filling at 10^8 a second takes 1.288 x 10^16 s = 408.50 million years of 365 days, exactly his printed "408,501731" (digits grouped in sixes) [read: page image p.22; computed]. His arithmetic is perfect. His input is not: with n = p/kT the true density at 0 C is 2.69 x 10^19 per cm^3, 37 times smaller (40 times at 20 C). The bulb really holds about 3.5 x 10^16 molecules at a millionth of an atmosphere, and the filling time is about 11 million years [computed]. His point survives: a "vacuum" of a millionth of an atmosphere still holds about 3.5 x 10^16 molecules (tens of thousands of trillions in today's short scale).
• Number words. Crookes writes "1,000000,000000,000000,000000 (a quadrillion)" and "a trillion" [read: page image p.22]. In the British long scale of 1879, a million is 10^6, a billion a million millions (10^12), a trillion 10^18 and a quadrillion 10^24 [memory, high for the usage]. Read in today's short scale (trillion = 10^12, quadrillion = 10^15), the lecture's numbers come out a million or more times too small; the project's own digest made exactly that misreading.
• The paddle wheel. A 10 kV, 1 mA electron beam (current assumed) carries momentum at a rate F = (I/e) p = 3.4 x 10^-7 N, about the weight of 0.03 milligrams [computed, Part 4c]. The same beam carries 10 W of power. A force that small would hardly push a mica wheel along a glass rail, while 10 W of heating is a lot. That is why the heating (radiometer) explanation is the accepted one.
• "Three hundred trillions a second." Crookes says that if a pinhole let in 300 trillions of molecules a second, the bulb would fill "before you leave this room" [read: pp.22-23]. In the long scale that is 3 x 10^20 per second. Then 1.288 x 10^24 / 3 x 10^20 = 4,300 s, about 72 minutes [computed, Part 5c]: self-consistent with his own count. With the modern count (3.5 x 10^22 at 1 atm) it would take about 2 minutes.
• The hot ring (Fig. 13). With the induction coil "disconnected altogether", a platinum ring heated red-hot by a small battery spun the mica vanes "as fast as they did when the induction-coil was at work" [read: p.15]. Could the hot ring be boiling electrons off (thermionic emission) and pushing the vanes with them? Richardson's law gives the current density from a hot metal: J = A T^2 exp(-W / kT), where A ≈ 1.2 x 10^6 A m^-2 K^-2 is a constant, T the temperature in kelvin and W the work function (the energy to free one electron; about 5.6 eV for platinum) [memory, high]. At red heat, 900 to 1100 K, J is 4 x 10^-20 to 3 x 10^-14 A/m^2. For a fine wire of about 10^-5 m^2 surface that is under 10^-18 A, and even an unrealistically low W = 4.5 eV gives only about 3.5 x 10^-14 A at 1100 K [computed, Part 5b]. Nothing pulled charge off the ring either: it had no voltage on it. So a thermionic push is ruled out by calculation for red heat. What remains is a hot body next to a radiometer-type fly (mica vanes at 45 degrees) in a near vacuum: the light-mill effect, whose thermal explanation is the accepted one. The lecture gives no pressure, distance, rotation direction or control, so this is the accepted physics applied to an unmeasured demonstration [read: arbiter.md, QE revision]. (Edison first noticed the effect named after him on 13 February 1880, a few months after the lecture, and in 1883 measured a current across the vacuum of a lamp with a glowing filament [web: https://wikipedia.com/wiki/Thermion, via arbiter.md]; Richardson's law is from 1901.)

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6. Evidence table

Verdicts are the arbiter's [read: arbiter.md]. "Tested by" names who tested a claim; most of the later tests are known from secondary sources only (see the source note).

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7. What a learner should take away

What is solid.

• Crookes's demonstrations. Straight-line beams, sharp shadows, focusing by a curved cathode, magnetic bending, the jump of one beam when a second cathode is switched on, coloured glow of minerals, heating to white heat at a focus, "tired" glass that glows less after long bombardment [read: p.11-12], and the failure of conduction at the highest vacuum [read: pp.7-8]. All of these are real and can be seen today in a school cathode-ray tube or a museum Crookes tube.
• His use of the kinetic theory. He correctly saw that at a millionth of an atmosphere the free path becomes as large as the vessel, and that this opens a new regime. Section 5, Step 0 confirms it with numbers.
• His particle picture against the ether-wave school. On the question that divided physicists in 1879 (particles or waves?), he was on the side that turned out right.
• His figures were careful. The vacuum comparison, the bulb volume and the 408-million-year sum all check to the last digit. Only the borrowed molecular density was off, and that was the best estimate of 1868.

What is wrong, and why the mistake is instructive.

• Identifying the carrier. He combined two true facts (collisionless gas; a charged beam) by assuming they were the same thing. A single quantitative measurement (the bending radius with a known field and voltage) would have shown the carriers to be hundreds of times lighter than any molecule. The lesson: a qualitative match ("it bends like a projectile") cannot identify a particle; the amount of bending can. Thomson won the argument because he measured.
• Same scaling is not identity. The dark space and the free path both grow as 1/p. That shows they are related, not that they are the same length. Many things scale as 1/p in a gas.
• The paddle wheel. A visible push is not proof of momentum transfer. In a near-vacuum, heating one side of a vane gives a force (the same effect that drives the light radiometer Crookes himself invented in 1873-76 [memory, high]). His own hot-ring demonstration, in which a heated wire with no coil spins the vanes "as fast" [read: p.15], fits the thermal explanation. A thermionic push from the ring is ruled out at red heat by Richardson's law (section 5, side checks: under 10^-18 A). Crookes's own reading, that "a hot wire will set [radiant matter] in motion" [read: p.15], stays in the record as his interpretation.
• Checking the direction but not the size. Every reviewer accepted the Fig. 18 jump as beam-on-beam repulsion because like charges repel. Nobody estimated the force until the QE did: at 10 kV it moves the beam by a fraction of a millimetre (section 3.4). The lesson: a force that points the right way can still be far too weak. Here the size depends on a voltage Crookes never gave, so the question stays open.
• A "state" needs a boundary. Calling a regime a state of matter is a claim that something changes abruptly. In a thinning gas nothing does.

What is genuinely open (in the record, not in the physics).

• What G. G. Stokes, refereeing Crookes's 1879 paper for the Royal Society, found unclear, and what "further clarifying experiment" he suggested (Royal Society RR/8/152; page images online, not read by any role; three fetch attempts failed) [web: https://makingscience.royalsociety.org/items/rr_8_152].
• The working numbers behind the lecture (pump, gauge readings, coil, fields): they are in Crookes's laboratory notebooks (Science Museum MS/0410, 1875-1883, including notes for the Sheffield lecture), which are "currently unavailable" because "the volumes register slight radiation" [web: https://collection.sciencemuseumgroup.org.uk/documents/aa110067393/laboratory-notebooks-of-william-crookes]. The museum's stated reason (contamination from his later radium and uranium work) is ordinary and on record; nothing suggests concealment, but the record is out of reach. C. H. Gimingham's ledger for 1878-81 (IET archive SC MSS 285) is an independent record of the apparatus work.
• How large the thermal and momentum shares of the paddle-wheel force are in a well-characterised tube (Starke 1900, Annalen der Physik 3, 101-107, has data; not read).
• The hot ring: whether any part of the spin is thermionic is answered by calculation for red heat (no; section 5). It stays open only for a ring far hotter than red heat. The direct test, a ring run unbiased and then biased at a known pressure, with a cold ring and a shield as controls, is still not in the record.
• What made the first ray jump in Fig. 18: beam-on-beam repulsion (needs a low voltage or a high current to be visible) or the field of the second cathode. The deciding test is the two-cathode tube with the second terminal present but shielded or held at a different potential, with voltage and current measured; Crookes's 1879 Phil. Trans. paper may give his numbers (not downloaded).
• At what pressure the spark failed in Crookes's tubes, and how he measured 1/20,000,000 atm: probably in "On Electrical Insulation in High Vacua" (1878), not read.
• Where Crookes's "radiant matter now passes as electrons" first appeared, and whether he meant it as a concession or as a claim that the electron was his radiant matter all along.
• Two unresolved attributions: Busch (2023) quotes a remark about "foggy" shadows on photographic plates as from the 1879 lecture, but it is not in this copy (possibly a different printing or paper); and Wikipedia credits the hinged-cross tube to Plücker in 1869, while the lecture credits Gimingham's workmanship and Plücker died in 1868 [memory, high].

Kept in the record (later reception). Modern plasma-physics sources credit Crookes's 1879 "fourth state" as the first identification of plasma [web: plasmas.org, plasma-universe.com, Wikipedia, via sites.md]. That is a retrospective reading: his own definition was a collisionless neutral gas, though his tubes did contain partly ionised gas. Johann Puluj, a rival experimenter with his own theory (charged particles torn from the electrodes, "radiant electrode matter", closer to the modern answer than Crookes's), called the fourth state "transcendental" with an inclination towards spiritualism; that is Puluj's characterisation, as Busch reports it [web: Busch 2023]. H. P. Blavatsky and the Theosophists took radiant matter as evidence of "more refined states of matter" [web: Theosophy Wiki snippet, via sites.md], a reading the lecture's closing words about "the border-land where matter and force seem to merge into one another" [read: p.23] invited. Neither reading has measurable content.

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8. Check yourself

1. Air at one millionth of an atmosphere has a mean free path of about 6.6 cm. What is it at one ten-millionth of an atmosphere (same temperature), and would the gas in a 13.5 cm bulb then be collisionless?
2. A proton and an electron both fall through 10,000 V and enter the same 0.01 T field at right angles. The proton is 1,836 times heavier. What is the ratio of their bending radii, and what is the proton's radius?
3. Crookes saw his magnetically bent beam curve more when he let a little gas into the tube. Use r = mv/(qB) to explain why, and say whether this observation can tell an electron from a molecule.
4. Two neutral wires carrying parallel currents attract; Crookes thought his two parallel beams repelled. (a) Why the difference, and why is the net force between two free beams repulsive at 10 keV? (b) A 10 kV, 1 mA beam (speed 5.85 x 10^7 m/s) runs 1 cm from a parallel one. Compute its line charge λ_q = I/v and its field E = λ_q / (2π ε₀ r). Then estimate how far an electron in the other beam drifts sideways over 30 cm (use a = eE/m_e, t = L/v, y = ½ a t^2, ignoring the small magnetic and relativistic corrections). Could the audience have seen it?
5. Crookes's molecule count was 1.29 x 10^18 at a millionth of an atmosphere; the modern number is about 3.5 x 10^16. Was his arithmetic wrong? What single number caused the difference, and does his conclusion survive?

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9. Further reading

Mainstream physics

• D. J. Griffiths, Introduction to Electrodynamics: Ch. 5 for the Lorentz force and circular motion in a magnetic field; Ch. 2 for potential and Coulomb's law.
• D. V. Schroeder, An Introduction to Thermal Physics: kinetic theory and the mean free path.
• J. F. O'Hanlon, A User's Guide to Vacuum Technology: pressure units, mean free path and free-molecular flow in practice.
• Yu. P. Raizer, Gas Discharge Physics (Springer, 1991): the glow discharge, the cathode fall and the dark space.
• F. F. Chen, Introduction to Plasma Physics and Controlled Fusion: what a plasma is (opening chapter).
• J. J. Thomson, "Cathode Rays", Philosophical Magazine 44 (1897) 293-316: the q/m measurement [web: cited in Busch 2023].
• J. J. Thomson, Conduction of Electricity Through Gases (Cambridge, 1903), p.501 on the paddle wheel [web: Harvard page].
• U. Busch, "Claims of priority: the scientific path to the discovery of X-rays", Z. Med. Phys. 33 (2023) 230-242, open access: https://pmc.ncbi.nlm.nih.gov/articles/PMC10311274/ (Hittorf, Goldstein, Crookes, Puluj, Thomson).
• Harvard Natural Sciences Lecture Demonstrations, "CRT (cathode-ray tube) Paddle Wheel": https://sciencedemonstrations.fas.harvard.edu/presentations/crt-paddle-wheel

Crookes's own works (archive.org identifiers from sites.md; not read in this review)

• "On Radiant Matter", Sheffield lecture, 22 August 1879 (the project's document; also in Nature 20 (1879) 419-423, 436-440 [web: Arabatzis, via sites.md]).
• Bakerian Lecture, "On the Illumination of Lines of Molecular Pressure, and the Trajectory of Molecules", Phil. Trans. R. Soc. 170 (1879) 135-164, DOI 10.1098/rstl.1879.0065 (archive.org philtrans06253890).
• "Contributions to Molecular Physics in High Vacua. Magnetic Deflection of Molecular Trajectory. Laws of Magnetic Rotation in High and Low Vacua. Phosphorogenic Properties of Molecular Discharge", Phil. Trans. 1879 Part II (archive.org philtrans07220971). The "laws of magnetic rotation" the lecture lacks should be here.
• "On Electrical Insulation in High Vacua" (1878); "On Discontinuous Phosphorescent Spectra in High Vacua" (1881); "On Radiant Matter Spectroscopy" (Bakerian Lecture 1883) and sequels to 1887, where the glow became a tool for analysing rare earths.

Contemporary rivals and history

• J. Puluj, Strahlende Elektrodenmaterie und der sogenannte vierte Aggregatzustand (Vienna, 1883); an English version is on archive.org as puluj-4th-state-of-matter.
• H. Starke, "Notiz über die mechanische Wirkung der Kathodenstrahlen", Annalen der Physik 3 (1900) 101-107.
• A. E. Woodruff, "William Crookes and the Radiometer", Isis (1966); R. K. DeKosky, "William Crookes and the quest for absolute vacuum in the 1870s" (1983); H. Gay, "Invisible resource: William Crookes and his circle of support, 1871-81", British Journal for the History of Science 29 (1996) 311-336.
• Stokes's referee reports RR/8/151 and RR/8/152, Royal Society "Science in the Making": https://makingscience.royalsociety.org/items/rr_8_151

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Answers

1. λ is inversely proportional to pressure, so ten times lower pressure gives ten times the free path: about 66 cm. That is about five times the bulb diameter, so molecules cross the bulb with almost no collisions with each other.
2. With the same charge and energy, r is proportional to √m, so r_p / r_e = √1836 ≈ 43. With r_e = 3.4 cm, r_p ≈ 1.4 m [r = √(2 m_p K)/(eB) = √(2 x 1.67 x 10^-27 x 1.60 x 10^-15)/(1.60 x 10^-21) ≈ 1.44 m]. Even the lightest atom (hydrogen, as a proton) bends 43 times less than the electron.
3. Collisions with the extra gas slow the particles, which lowers v and so lowers r = mv/(qB): the path curves more sharply. (Crookes's reason, "the magnetism has longer time on which to act" [read: p.17], is part of the story, but the radius itself shrinks.) This is true for any charged particle, electron or molecule, so it cannot tell them apart. Only the size of r for a known field and energy can.
4. (a) A wire is neutral overall: its moving electrons are balanced by fixed positive ions, so the electric forces between two wires cancel and only the magnetic attraction remains. A free beam has no balancing positive charge, so the electric repulsion acts in full; the magnetic attraction is only (v/c)^2 of it, 0.038 at 10 keV, so the net force is repulsive. (b) λ_q = 10^-3 / 5.85 x 10^7 = 1.7 x 10^-11 C/m; E = 1.7 x 10^-11 / (2π x 8.85 x 10^-12 x 0.01) ≈ 31 V/m; a = (1.60 x 10^-19 x 31) / 9.11 x 10^-31 ≈ 5.4 x 10^12 m/s^2; t = 0.30 / 5.85 x 10^7 = 5.1 x 10^-9 s; y = ½ a t^2 ≈ 7 x 10^-5 m, about 0.07 mm (example.py Part 5a gives 0.067 mm with the corrections). No audience could see that, and positive ions in the residual gas would shrink it further. So at 10 kV beam-on-beam repulsion cannot explain the jump; it would need about 1 kV and several milliamperes (the drift grows as I / V^(3/2)), or another cause such as the second cathode's field. The arbiter rates both causes Plausible, untested.
5. No, his arithmetic was exact (1,288.25 cm^3 x 10^21 x 10^-6 = 1.288 x 10^18; 408.50 million years with 365-day years). The difference comes from one input: Johnstone Stoney's 1868 estimate of 10^21 molecules per cubic centimetre, about 37 times the modern 2.69 x 10^19 at 0 C. His conclusion, that even a millionth of an atmosphere leaves an enormous number of molecules (about 3.5 x 10^16 in the bulb), survives.