Charles F. Brush: a kinetic (push) theory of gravitation — primer

Charles Francis Brush (1849-1929) was the Cleveland engineer whose arc-lighting dynamos made him rich in the 1880s [read: biography and 1910 magazine profile]. From 1910 until his death he used his private laboratory to argue that gravity is a push from waves in the aether, and he ran careful pendulum, drop and calorimeter experiments to prove it.

Source tags used here: [read] = from Brush's own documents in the project folder (often read from page images); [web] = checked online, URL given; [memory] = recalled, with confidence; [calc] = arithmetic done for this review (most of it is in example.py). "Arbiter" means the Step 3 report arbiter.md, whose verdicts are final here.

Source gap. Most of Brush's PDFs have no text layer and were read by OCR (optical character recognition) of page images, with page images checked by eye where the OCR was garbled. The key papers were read complete: the 1922 pendulum paper (journal pp.167-183 of a 349-page volume; the rest of the volume is other authors' work, apart from the Gregorio-Brush priority exchange in the Minutes, PDF pp.328-335, also read in full), the 1917 steel paper, the 1928 Franklin Institute address, and the handwritten 1914 abstract (manuscript pp.17-29, read after the quality check). Not obtained: his 1921, 1923, 1924, 1926, 1927 and 1928 Proc. APS papers (so the raw drop-test tables and every calorimeter power figure are missing), the 1915 steel paper, and any Bureau of Standards report. No direct repetition of Brush's own zinc-bismuth pendulum or his drop experiment is known from the sources, but other pendulum tests of the same general question were made in 1910 and 1923 (section 3.3). Conclusions resting on [memory] alone are flagged where they occur (mainly: steel quench metallurgy, rock-heat chemistry, and the added-mass coefficient of a short cylinder).

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1. The idea in one paragraph

Brush started from a puzzle he found unsatisfying: when you lift a stone and let it fall, it gains speed, yet the cold, still stone shows no sign of having "stored" any energy. He proposed that the energy comes from outside: space is filled with an aether carrying an enormous amount of energy in the form of extremely penetrating waves arriving equally from all directions. Every atom absorbs a tiny fraction of these waves and so casts a faint "energy shadow". Two bodies each sit in the other's shadow, so the waves push them together harder from the outside than from the inside, and that unbalanced push is what we call gravity. If this were true, gravity might depend slightly on what a body is made of, since different atoms might absorb the waves differently. Brush set out to measure that difference. He swung zinc and bismuth pendulums of equal mass side by side and dropped containers of different powders side by side, and he reported small but repeatable differences. He also reported that certain silicates give off a slow, steady trickle of heat, and that these same materials seemed to fall slightly slower. He read this as the aether's wave energy turning into heat.

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2. What you need to know first

Energy and potential energy. Near Earth, lifting a mass m (kg) through height h (m) takes work m g h, where g is about 9.8 m/s² (the acceleration of free fall). In general the gravitational potential energy of a mass m at distance r from a mass M is U = −G M m / r, where G = 6.674×10⁻¹¹ N m²/kg² is Newton's constant. The point you need: U belongs to the pair (or to the field between them), not to the stone alone. That is why nothing about the stone looks different after you lift it. Read: Kleppner & Kleppner-Kolenkow, An Introduction to Mechanics, chapters on work and energy; or Taylor, Classical Mechanics, ch. 4 [memory high on content; chapter number medium].

Force versus potential. Force is minus the slope (gradient) of potential energy: F = −dU/dr. Zero force means the potential is flat at that point. It does not mean the potential is zero. Brush's central paradox turns on mixing up these two (section 4).

The pendulum. A simple pendulum (a point mass on a massless string of length L) swinging through small angles has period T = 2π√(L/g). A real "compound" pendulum (a rigid body) has T = 2π√(I / (m g d)). Here I is the moment of inertia about the pivot (kg m²), m the total mass, and d the distance from the pivot to the centre of mass. Because the mass m appears both in the inertia (top) and in the weight (bottom), it cancels for a point bob. This is exactly why a pendulum tests whether "weight is proportional to mass": if gravity pulled harder per kilogram on bismuth than on zinc, the bismuth pendulum would swing faster. Read: Taylor, Classical Mechanics, ch. 5 (oscillations) [memory medium on the chapter number].

Buoyancy and "added mass". Archimedes: a body of volume V in air of density ρ_a (about 1.2 kg/m³) is pushed up with force ρ_a V g. Less familiar, but just as real: a body that accelerates through a fluid must also accelerate some of the fluid around it. So it behaves as though its mass were increased by m_a = k ρ_a V. Here k is the "added-mass coefficient", a pure number set by the body's shape (k = 0.5 for a sphere; about 1 for a long cylinder moving sideways). Bessel introduced this correction in 1828 for pendulums in particular [web https://en.wikipedia.org/wiki/Added_mass, via arbiter]. Stokes (1851) extended it to include air viscosity, which makes the effective k somewhat larger for a slowly swinging bob [memory high]. Read: any fluid mechanics text on potential flow, e.g. Batchelor, An Introduction to Fluid Dynamics, or Lamb, Hydrodynamics.

The equivalence principle. The weak equivalence principle (WEP) says that all bodies fall with the same acceleration in the same gravitational field, whatever they are made of. Put another way, gravitational mass (what weight responds to) equals inertial mass (what resists acceleration). Experiments measure the Eötvös parameter η, the fractional difference in acceleration between two materials. The lower the limit on η, the stronger the test. Read: Clifford Will, "The Confrontation between General Relativity and Experiment", Living Reviews in Relativity (free online), section on the equivalence principle.

Le Sage's push gravity. In 1748-1784 Georges-Louis Le Sage proposed that gravity is caused by tiny particles streaming through space from all directions and being partly absorbed by matter, so each body shadows the other [memory high]. Brush's theory is the wave version of this (Oliver Lodge said exactly this in Nature in 1911 [read]). Brush was not the only one with a push theory. The Marquis Antonio de Gregorio of Palermo wrote to the American Philosophical Society (APS) on 20 July 1922 to claim priority. His letter was read at the Society's meeting of 3 November 1922. Brush's reply, dated November 1922, was read at the next meeting, on 1 December 1922 [read: Proc. APS 61, Minutes, PDF pp.328-335]. The exchange went like this: - Gregorio's claim. He says he presented the theory to the Palermo Academy in 1892 and printed it in 1893, and that he discussed it again in 1914. In his picture the aether is a pressure ("tension") medium that passes through matter. Matter absorbs part of its energy, so the pressure between two bodies is lower than the pressure outside them, and the bodies are pushed together. He calls Brush's work "valuable and commendable" and does not accuse him of copying [read: p.331-332]. - Brush's reply. Brush worked from a translation of Gregorio's 1895 papers in the Palermo Academy's proceedings (Atti), made for him by Prof. Borgerhoff of Western Reserve University. He does not dispute that Gregorio wrote first. He disputes that it is the same theory. His own "second postulate" is that the aether's energy travels as waves, equally in every direction, with intensity falling off as 1/r². He calls that postulate "original with me" and "essential", and says it is nowhere in Gregorio. He also makes two objections to Gregorio. First, nothing explains how the pressure deficit around a body is kept up once absorption stops. Second, nothing says where a falling body gets its energy [read: p.333-334].

The Minutes never mention Le Sage, "shadows" or "screening". Calling both men's theories "Le Sage-type" is this review's interpretation [memory high on Le Sage's theory]. Of the two, Brush's isotropic wave flux is the closer to Le Sage's pattern. Notice one thing in Gregorio's letter: matter "absorbs some part of its energy". That is exactly what produces the heating objection below, though the Minutes do not discuss heating. Neither side's priority dates have been checked against the 1893 and 1895 originals, which are not in the folder, and no experiment by Gregorio is reported. The standard objections to all such theories are screening, drag and heating (section 3). Read: Feynman, Lectures on Physics Vol. I, ch. 7 ("The Theory of Gravitation"), the section "What is gravity?" [memory high]; and the Wikipedia article "Le Sage's theory of gravitation" as a historical survey.

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3. The textbook view

3.1 Energy of a falling body

For two masses M and m separated by distance r, the system has potential energy

U(r) = −G M m / r.

Here U is in joules, G is Newton's constant, M and m are in kg, and r is in metres. When a body falls from r₁ to r₂ < r₁, U drops by G M m (1/r₂ − 1/r₁) and the kinetic energy ½ m v² rises by the same amount. Nothing comes from outside. In field language, the energy is stored in the gravitational field that the pair creates together. General relativity (GR) refines this but does not overturn it for everyday situations.

3.2 Push (shadow) gravity and its three problems

Suppose space carries an isotropic flux (the same in all directions) of something moving at speed c, and each body absorbs a small fraction of it. The geometry really does give an inverse-square law. A small absorber of cross-section σ₁ removes a fraction σ₁/(4π r²) of the flux seen at distance r. A second absorber σ₂ then feels a net push proportional to σ₁ σ₂ / r². If σ is proportional to the number of nucleons, the push is proportional to the product of the masses: Newton's law in form [calc, arbiter]. That part of Brush's picture is sound.

The problems are these:

1. Screening. The flux must pass almost unabsorbed through the whole Earth. Otherwise the Earth's far side would be shielded by its near side, and gravity would not add up mass by mass. Yet each atom must absorb enough to push. Lodge raised this in 1911 [read].
2. Drag. A body moving at speed v through the flux meets slightly more of it head-on than from behind. The resulting drag force is of order (v/c) × (the gravitational force itself). For the Earth orbiting the Sun: v = 29.8 km/s, v/c ≈ 1.0×10⁻⁴, solar pull per kg ≈ 5.9×10⁻³ m/s². The drag is then about 5.9×10⁻⁷ m/s², which removes about 18.6 m/s of orbital speed per year [calc, checked here]. Over geological time the Earth would spiral into the Sun. It has not, in about 4.5 billion years.
3. Heating. Absorbing momentum from a wave or particle stream also absorbs energy, at least (wave speed) × (momentum absorbed). For a flux strong enough to make gravity, this would heat every body enormously (Poincaré's classic analysis) [memory high].

3.3 Universality of free fall (the measurements)

Brush claimed effects of about 4×10⁻⁵ to 2×10⁻⁴ in acceleration. (His pendulum figure, 1 in 32,000, is a difference in period; since T ∝ g^(−1/2), the implied difference in g is twice that, about 6×10⁻⁵ or 1 in 16,000.) That is three to four orders of magnitude above what Eötvös had already excluded in his day, and ten or eleven orders above today's limits.

Notice the two pendulum rows. Pendulums are Brush's own kind of apparatus, and Southerns (1910, a decade before Brush's pendulum work) and Potter (1923, one year after Brush's pendulum paper) both reached limits 10 to 20 times smaller than Brush's effect. So a better pendulum was built in Brush's lifetime, and it saw nothing at his level. Two cautions [web check failed, per arbiter]: which materials Potter used (in particular, whether bismuth was among them) and whether he cited Brush are unverified; and Southerns compared a radioactive substance with ordinary matter, not zinc with bismuth. Which materials Eötvös used is not on the cited page either, so it is not known whether bismuth, zinc or Brush's silicates were ever tested directly.

3.4 Speed of gravity

Laplace argued that if gravity were a static central pull that travelled at finite speed, the resulting aberration would make the Moon's orbit drift measurably. He concluded that gravity must travel at least about 7×10⁶ times faster than light [web https://en.wikipedia.org/wiki/Speed_of_gravity, via arbiter]. GR escapes this argument: in GR the field of a uniformly moving source points to where the source is now (to first order), so gravity can travel at c with no aberration problem [web, same URL]. A push from a wave flux has no such built-in cancellation.

3.5 Mercury

Mercury's perihelion (the point of its orbit closest to the Sun) slowly rotates by 574.10 ± 0.65 arcsec per century. Planetary perturbations explain all but about 43 arcsec of this; GR supplies 42.98 arcsec with no adjustable parameter [web https://en.wikipedia.org/wiki/Tests_of_general_relativity, via physicist]. In 1914, when Brush wrote, that 43 arcsec was a genuine open puzzle.

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4. Where Brush departs

The neutral-point paradox, and why it fails. Brush imagined lifting a pound of iron to the point between Earth and Moon where their pulls cancel. There it "remains stationary", so (he argued) its "potential energy of position has disappeared entirely", even though work was done to lift it [read: Nature 1911]. The numbers say otherwise [calc, checked here]:

• The neutral point lies 3.46×10⁸ m from Earth's centre, where G M_E/x² = G M_M/(D − x)², with D = 3.844×10⁸ m the Earth-Moon distance.
• The potential there (energy per kg) is φ = −1.28×10⁶ J/kg; at Earth's surface it is −6.26×10⁷ J/kg.
• Lifting one pound (0.4536 kg) therefore stores 2.78×10⁷ J. Released, that is enough to give it 11 km/s.

The force is zero but the potential is not. The neutral point is a saddle of the potential (a maximum along the Earth-Moon line), so the iron sits in unstable equilibrium, and a nudge sends it back down with all that energy. Lodge gave the same reply in words in 1911 [read].

Speed of gravity, in numbers. Brush computed that, if gravity moves at c, Earth's centre shifts 52 ft in the light-travel time to the Moon. That gives a sideways force 1/24,000,000 of gravity [read: OCR 1914]. His arithmetic is right: light time 1.282 s × Earth's wobble speed 12.4 m/s = 15.9 m = 52 ft; 12.4/c = 4.15×10⁻⁸ ≈ 1/24,100,000 [calc, checked here]. The error came next. He said the effect on the Moon was "a very few seconds of arc in a century". In fact a steady tangential push of 1.1×10⁻¹⁰ m/s² drifts the Moon's position by about 4.4 radians (about 9×10⁵ arcsec) per century [calc, arbiter; spot-checked here]. That is ten thousand to a hundred thousand times what is observed. The handwritten 1914 abstract repeats the "very few seconds of arc" claim and gives no calculation behind it [read: manuscript p.28].

The x term, and why it cannot be checked. Brush hoped x, "alternately plus and minus" as a planet falls toward the Sun and climbs away, would explain Mercury's 43 arcsec per century and the outstanding lunar irregularities [read: manuscript pp.24-26]. He never gave x a value or a formula, so no orbit can be computed from it. Two things can still be said. First, a force that depends on velocity of fall rather than on position alone is non-conservative: it has no potential energy function U(r), so the whole energy bookkeeping of section 3.1 no longer applies. Second, if x is odd in the radial velocity (as "alternately plus and minus" suggests), averaging over one orbit gives no perihelion advance at all, only a slow change in eccentricity [calc, arbiter, conditional on that form].

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5. Worked example: Brush's zinc-bismuth pendulum, and what air alone predicts

This is the strongest experiment Brush ran, and the one where fairness matters most. He was careful and candid. The question is whether his ~1 in 32,000 effect needs new physics.

All inputs below were read from the page images of Brush's 1922 paper (Proc. APS 61, pp.167-183) unless tagged otherwise. example.py reproduces every number.

Step 1. What Brush did [read pp.169-172]

• Two pendulums hang side by side from a common rigid plate on knife edges. Each has a steel rod and a cylindrical bob of about 1.384 kg: zinc 72 mm in diameter, bismuth 61 mm, both 48 mm high.
• He adjusts the rod lengths until the two swing in step (synchronism). Then he exchanges the bobs. If bismuth really swings faster, the bismuth pendulum now has the shorter rod as well, so the difference shows up twice.
• He times how long the bismuth pendulum takes to gain one full swing ("one beat") on the zinc. The long pendulums make about 2,388 single swings per hour.

Step 2. Reproduce his headline numbers [calc]

If one pendulum gains one swing in N swings, its period is shorter by a fraction 1/N. Because of the exchange, the real zinc-bismuth difference is half of that.

• Table I (zinc bob 7 g light): 7.3 h × 2,388 = 17,432 swings. Then 1/(2 × 17,432) = 2.87×10⁻⁵ = 1 in 34,900. Brush (1921): "one part in 35,000". ✓ Note that this 1921 figure was uncorrected and came from the mismatched bobs; in 1922 Brush restated the same run, after his geometric correction, as 1 in 51,000 [read: deep read, p.198].
• Table II (masses equalised): 311 min = 5.183 h; 5.183 × 2,388 = 12,378 swings. Then 1/(2 × 12,378) = 4.04×10⁻⁵. Brush's table: 40.3×10⁻⁶. ✓

Note that removing a 7 g (0.5%) mass mismatch moved the result by 40%. (The bobs were then matched on a 2 kg Becker balance sensitive to 0.1 mg, to within 0.19 g of 1,383.8 g [read: p.193-194]. Nothing in the paper says the weighing was done in vacuum, so it was done in air, which matters in Step 4.) Brush himself called unequal bob weight "the largest and most dangerous source of error" [read p.174].

Step 3. Check his geometric correction [calc]

The zinc cylinder is fatter, so it has more moment of inertia about its own centre. That slows the zinc pendulum for a reason that has nothing to do with gravity. A cylinder of radius R and height h, rotating about a horizontal axis through its centre, has

I_cm = m (R²/4 + h²/12).

The bob sits at distance d from the pivot, so I = m d² + I_cm. With equal m and h, only the R²/4 term differs. Since T ∝ √I,

ΔT/T ≈ ½ × (R_zn² − R_bi²)/4 / d².

From the swing rate, the full period is T = 2 × 60/39.834 = 3.0125 s. The equivalent length is d = g T²/(4π²) = 2.253 m. With R_zn = 0.036 m and R_bi = 0.0305 m:

ΔT/T = 0.5 × (0.001296 − 0.000930)/4 / 2.253² = 9.0×10⁻⁶.

Brush's table gives 9.0×10⁻⁶ (and 25.2×10⁻⁶ for the short pendulums; this method gives 25.3×10⁻⁶). His correction is right. Subtracting it: 40.3 − 9.0 = 31.3×10⁻⁶ = 1 in 32,000, his headline result. Brush's arithmetic and geometry are sound.

Sanity check: a zinc cylinder (density 7,140 kg/m³) of these dimensions has mass 1.395 kg, and a bismuth one (9,780 kg/m³) 1.372 kg. Both are within 1% of the 1.384 kg Brush weighed [calc; densities memory high]. The dimensions are consistent.

Step 4. The term Brush left out: the air [calc]

Equal mass with different density means different volume: the zinc bob is about 37% bigger. A bob swinging in air feels two air effects:

• buoyancy reduces the restoring weight: (m − ρ_a V) g instead of m g;
• added mass increases the inertia: m + k ρ_a V instead of m.

So the small-angle equation of motion, with θ the swing angle and L the length, is

(m + k ρ_a V) L θ″ = −(m − ρ_a V) g θ,

which gives

T = 2π √( L/g × (m + k ρ_a V)/(m − ρ_a V) ).

Put V = m/ρ, where ρ is the bob's density, and expand to first order in the tiny ratio ρ_a/ρ (SymPy does this in example.py):

ΔT/T = (1 + k)/2 × ρ_a/ρ.

The less dense bob (zinc) swings slower, so bismuth gains, the same sign Brush saw. For the difference between the two bobs:

ρ_a (1/ρ_zn − 1/ρ_bi) = 1.2 × (1/7140 − 1/9780) = 4.54×10⁻⁵.

Brush's corrected result: 3.13×10⁻⁵ (1 in 32,000). One refinement: every run had small compensating paper vanes on the bismuth, and Brush says that "wholly uncompensated" bobs would show an effect "about 10 per cent" larger [read: p.199]. So the bare-bob prediction in the table should be compared with about 1.1 × 3.13×10⁻⁵ = 3.4×10⁻⁵, which is exactly the k = 0.5 row [calc]. The value of k for a squat 48 × 72 mm cylinder is [memory medium], somewhere around 0.5-1. Ordinary air therefore predicts an effect of the right sign and the right size, within 10-45%. The ordering (zinc, then iron, then bismuth) is the ordering of density (7.14, 7.87, 9.78 g/cm³) [read; densities memory high]. And bismuth against bismuth (same density, different grain) gave only 2.5% of the zinc-bismuth effect [read p.175], which is what a density effect predicts.

Could weighing on a balance in air, rather than in vacuum, have left a mass error? The buoyancy difference on the balance is ρ_a × (V_zn − V_bi) = 0.063 g. Brush's own test showed that 7 g moves the result by 40%, so 0.063 g moves it by roughly 0.4%: negligible [calc].

Step 5. A cross-check from Brush's own data [read pp.179-180; calc]

Brush tested drag by turning cardboard vanes (48 mm high) face-on to the swing. Short pendulums, double bobs, 51.752 swings per minute, baseline 186 min per beat:

• Vane face-on on the zinc (50 mm wide): 137 min. The rate changes by +3.7×10⁻⁵.
• Vane face-on on the bismuth (83 mm wide): 274 min. The rate changes by −3.3×10⁻⁵.

Brush treated these as drag tests. But damping hardly changes a pendulum's period (the correction is second order in the damping). What a face-on plate does do is carry air with it. Using the long-strip added-mass formula, m_a ≈ ρ_a π (w/2)² h for a plate of width w and height h, gives +2.0×10⁻⁵ (zinc vane) and −5.6×10⁻⁵ (bismuth vane). That is the same sign and order of magnitude as observed. This is rough: the vanes sit next to the bob, the plates are nearly square, and the clock drive interacts with amplitude. One point does not fit: the strip formula scales with width squared, so it predicts the 83 mm bismuth vane should act about 2.8 times as strongly as the 50 mm zinc vane, yet the observed responses are nearly equal [calc, deep read]. So the vane data support air inertia qualitatively, not as a precise number. Brush himself wrote, "The effect of the air vanes on the bismuth is to slightly lengthen its period" [read: p.199]: a first-order period change from a light card, which damping alone cannot produce. Air inertia at the 10⁻⁵ level is visibly present in this apparatus, in Brush's own measurements.

Step 6. What this does and does not show

• It does not prove Brush's effect was air. The arbiter's estimate ignores the steel rod's share of the inertia and the exact k. The short-pendulum corrected values (19.4 and 25.9×10⁻⁶, against 31-32×10⁻⁶ for the long ones) fit neither a constant air effect nor a constant gravity effect well, and Brush himself distrusted them [read p.177]. Note the logic, though: a genuine difference in weight per kilogram would give the same fractional period difference at every pendulum length, so a corrected effect that changes by 20-40% with length is itself a warning sign. The north/south exchange values also differ by up to 4-7% between repeats, and bismuth against bismuth gave a few-percent residual, which sets a floor on how well any single number is known [read: deep read, pp.194-198].
• It does show that a conventional effect of the right sign, size and material ordering was never excluded. Asked whether a vacuum test might "obliterate" the effect, Brush answered "To this I can confidently answer no" [read p.178]. He reasoned that vacuum would only remove unequal drag, which his vanes already compensated. Buoyancy and added mass are not drag, and they do not show up as unequal damping, so his vanes could not have caught them.
• The drop test is a different case. In 1922 Brush also dropped zinc and bismuth side by side, each inside identical aluminium containers of equal outer size and weight, through about 120 cm. Bismuth arrived first, by a time "of the order of a hundred thousandth part of a second" [read: p.203-204]. With fall time t = √(2h/g) ≈ 0.495 s, Δt/t ≈ 2×10⁻⁵, which means Δg/g ≈ 4×10⁻⁵, the same order as the pendulum [calc]. Here the outside air sees identical shapes, so the air added-mass explanation does not carry over. Brush gave no table, no number of trials and no error analysis, and the cause (release timing, load position, something else) is open. He also mentions a "persistent collateral phenomenon" of the drop apparatus, "of great interest", reserved for a later paper; the 1922 text does not say what it was [read: p.204]. (It is tempting to guess it led to his later heat work, but nothing in the readable documents supports that.)
• The settling experiment (arbiter): swing the zinc/bismuth pair in vacuum, or use bobs of equal volume and different mass, and repeat the drop in a vacuum tube. Air predicts the pendulum effect vanishes. Brush's hypothesis predicts it persists at about 3×10⁻⁵. Eötvös-type experiments in vacuum have already found no composition effect above 10⁻⁸ to 10⁻¹⁵ [web, section 3.3].

Run: .venv/bin/python review/Brush-Charles/example.py

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6. Evidence table

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7. What a learner should take away

Solid. - Brush's geometry is correct: shadowing from small absorbers does give 1/r² and mass-proportionality. That is why Le Sage-type ideas keep returning. - His experimental arithmetic is right throughout: 1 in 35,000, 40.3×10⁻⁶, the 9.0×10⁻⁶ gyration correction, 52 ft, 1/24,000,000, the drop ratio. - His quenched-steel calorimetry looks like good, ordinary physics with sensible controls. - He published his error sources openly, which is exactly what lets us diagnose the results a century later.

Wrong, and why it is instructive. - Force is not potential. The neutral-point paradox is a classic confusion, worth getting straight once and for all. - Push gravity dies on drag. Any isotropic-flux mechanism makes moving bodies feel a headwind of order (v/c) × gravity. This one-line estimate kills a whole family of theories. Brush answered the heating objection by retuning the wave frequency, and the retuning drifted: very low frequency in 1910-11, "a wide range of frequencies as do the well-known X-rays" in 1928 [read: 1928 address p.5], above cosmic rays in 1929. He never gave a drag estimate. (His 1914 abstract says the atoms suffer "no collisions because neighboring particles follow very nearly parallel paths" [read: manuscript p.19], but that concerns atoms hitting each other, not the headwind from the flux.) His 1922 reply to Gregorio is a good piece of physics criticism. He asked how Gregorio's pressure deficit is kept up and where a falling body's energy comes from [read: Minutes p.334]. Ask the same two questions of Brush's own wave flux and you get the heating and drag objections. - Finite speed needs a field theory. Brush's own 52 ft computation is the start of Laplace's argument. Carry it through and a static push at c wrecks the Moon's orbit. GR survives because its field equations cancel the aberration. - Someone did build a better pendulum. Southerns (1910) and Potter (1923) made pendulum tests 10-20 times more sensitive than Brush's effect and saw nothing at his level [web]. Brush's result was not ignored for want of testing the general idea; it was contradicted by the same kind of instrument, run more carefully. (A targeted repeat of his exact zinc-bismuth pairing is still not documented.) - A 10⁻⁵ effect needs a 10⁻⁶ error budget. In air, buoyancy and added mass are 10⁻⁴-level effects on each bob. Their difference between zinc and bismuth is the size of the signal. The lesson: list every physical effect at the level of your signal before claiming new physics, and run the control that would kill your result (here, vacuum).

Genuinely open (historically, not physically). - Did anyone repeat Brush's exact zinc-bismuth pendulum or his drop experiment? Not known from the sources. Which materials Potter (1923) used, and whether he was answering Brush, is unverified. - What caused the 1922 drop result (bismuth ahead by ~10⁻⁵ s inside identical containers), and what was the "persistent collateral phenomenon"? The 1923-24 papers that would say are not in the folder. - What exactly did the Bureau of Standards measure for Sandusky clay? In 1928 the check was still in progress; no report has been found. - Who wrote first, Gregorio or Brush? Gregorio's 1892-93 and 1895 papers are not in the folder, so neither man's priority statement has been checked. On the Minutes' evidence the two are different push mechanisms, and Brush did not deny that Gregorio came first [read: Minutes pp.331-334]. - A full reduction of Brush's pendulum to vacuum (rod inertia, exact k, Stokes viscous correction) would turn "same size" into a precise number. It is a good project for a learner. - Whether Brush's specific silicate samples have ever been in an equivalence-principle test: unknown. Physically, though, modern tests over many materials leave no room for a 10⁻⁴ effect.

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8. Check yourself

1. At the Earth-Moon neutral point the net gravitational force on a body is zero. Is its gravitational potential energy (relative to Earth's surface) zero, positive or negative? Why does the body "remain stationary"?
2. A Le Sage flux pushes on the Earth with the full solar gravitational force, 5.9×10⁻³ m/s² per kg. Estimate the drag deceleration and the speed lost per year (v = 30 km/s, c = 3×10⁸ m/s).
3. Two equal-mass bobs, one aluminium (ρ = 2,700 kg/m³) and one lead (ρ = 11,340 kg/m³), swing in air. Take k = 0.5. Which swings slower, and by roughly what fraction?
4. Why can't Brush's air vanes, which equalise damping, remove a buoyancy and added-mass difference?
5. Brush's falling containers showed a raw lag of 0.099 mm in 1,100 mm. What fractional effect is that, and what extra assumption turns it into "1 part in 4,450"?

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9. Further reading

Mainstream - C. M. Will, "The Confrontation between General Relativity and Experiment", Living Reviews in Relativity (open access): equivalence-principle tests, Mercury, speed of gravity. - R. P. Feynman, R. B. Leighton, M. Sands, The Feynman Lectures on Physics, Vol. I, ch. 7 (gravitation; includes the push-gravity drag argument) [memory high]. - J. R. Taylor, Classical Mechanics: energy, oscillations, compound pendulum. - D. J. Griffiths, Introduction to Electrodynamics: energy stored in fields (the electrostatic analogue of "where is the potential energy?"). - G. G. Stokes, "On the effect of the internal friction of fluids on the motion of pendulums", Trans. Camb. Phil. Soc. 9 (1851): the classic treatment of air's effect on pendulum periods [memory high on the paper; volume medium]. - C. W. Southerns, "A Determination of the Ratio of Mass to Weight for a Radioactive Substance", Proc. Roy. Soc. (1910), and H. H. Potter, "Some Experiments on the Proportionality of Mass and Weight", Proc. Roy. Soc. (1923): the contemporary pendulum tests [web: titles from https://en.wikipedia.org/wiki/Equivalence_principle; not read; author initials memory medium]. - Wikipedia: "Equivalence principle" (table of tests), "Eötvös experiment", "Added mass", "Le Sage's theory of gravitation", "Speed of gravity" (URLs in the text). - M. R. Edwards (ed.), Pushing Gravity: New Perspectives on Le Sage's Theory of Gravitation (Apeiron, 2002): sympathetic modern collection, useful for the history [memory medium].

Brush's own key works (in the project folder unless noted) - "A Kinetic Theory of Gravitation", Nature 86, 130-132 (1911), with Lodge's reply (30 March 1911): brush-rexresearch.pdf. - "Discussion of a Kinetic Theory of Gravitation", Proc. Amer. Philos. Soc. 53 (1914): discussion-kinetic-theory-gravity-spcbru01027.pdf. - "Spontaneous Generation of Heat in Recently Hardened Steel II", Phys. Rev. 9, 228-236 (1917): Spontaneous-gen-of-heat-in-hardened-steel-Physical_review.pdf. - "Discussion of a Kinetic Theory of Gravitation II; and Some New Experiments in Gravitation", Proc. Amer. Philos. Soc. 61, 167-183 (1922), the pendulum paper used in section 5: Proceedings_of_the_American_Philosophica.pdf (PDF pp.184-203). The same PDF holds Gregorio's priority letter (read 3 Nov 1922) and Brush's reply (read 1 Dec 1922), in the Minutes, PDF pp.328-335. - "Some Experimental Evidence Supporting the Kinetic Theory of Gravitation", J. Franklin Inst. 206, 143-150 (1928): Evidence for Kinetic Theory of Gravitation (1).pdf. - "Gravitation", Proc. Amer. Philos. Soc. 68, 55-68 (1929): brush-rexresearch.pdf. - Not in folder (worth obtaining): Proc. APS papers of 1921, 1923, 1924, 1926, 1927, 1928 (drop tests, calorimetry; the 1923 and 1924 papers, "Some New Experiments in Gravitation", Proc. APS 62 and 63, describe the drop apparatus [read: cited in the 1928 address]), and Hadfield, Main & Brush, Proc. Roy. Soc. (1917) on steel.

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Answers

1. Positive. (The absolute potential, −1.28×10⁶ J/kg, is still negative, but it is far above the surface value of −6.26×10⁷ J/kg.) Relative to the surface, the body has gained about 6.1×10⁷ J/kg (2.78×10⁷ J for a pound). Only the slope of the potential is zero there. The point is a saddle (a maximum along the Earth-Moon line), so the body balances in unstable equilibrium, and a small push sends it back toward Earth, releasing that energy.
2. Deceleration ≈ (v/c) × 5.9×10⁻³ = 1.0×10⁻⁴ × 5.9×10⁻³ ≈ 5.9×10⁻⁷ m/s². Times 3.16×10⁷ s per year gives ≈ 19 m/s per year. A million years would cost 19,000 m/s, most of Earth's orbital speed.
3. Aluminium (less dense) swings slower. ΔT/T = (1 + 0.5)/2 × 1.2 × (1/2700 − 1/11340) = 0.75 × 1.2 × 2.82×10⁻⁴ ≈ 2.5×10⁻⁴, about 1 in 4,000. That is eight times Brush's zinc-bismuth signal, an easy classroom-scale demonstration that air matters.
4. Vanes change the damping (energy loss per swing), which affects the period only at second order. Buoyancy and added mass change the restoring force and the inertia directly, so they shift the period at first order without any visible difference in damping. Matching the amplitude decay of the two pendulums says nothing about them. Only removing the air, or making the bob volumes equal, controls for them.
5. 0.099/1100 = 9.0×10⁻⁵, about 1 in 11,100, for the whole container. Brush divided by 0.403, the fraction of the container's mass that was the test powder. That assumes the whole lag comes from the powder and none from the container, its drag, or the packing. The result is 2.2×10⁻⁴ ≈ 1 in 4,480 (he quotes 4,450).