Parallax (S. B. Rowbotham): Arbiter (Step 3)

Project: Zetetic Astronomy. Earth Not a Globe! (1865 edition, PDF of 229 pages) by "Parallax" (Samuel Birley Rowbotham [memory: high]), and Gleason's 1892 "New Standard Map of the World".

Inputs read in full: facts.json, claims.md, physicist.md, mathematician.md, contrarian.md, sites.md, the pendulum deep read, and the research notes as summarised in sites.md. I also went back to the book's text for the passages where the reviewers differ (PDF pp.46-47 Polaris, 56-57 southern circuit, 73-74 air-gun and tubes, 79 Sun distance, 112-114 tides).

Tags: [read: p.N] = the book, PDF page (book page = PDF page - 5). [calc] = my own calculation (numpy, venv; inputs stated). [web] = URL given. [memory] = recalled, with confidence. Where I rely on a reviewer's claim without re-checking it, I say so.

Source gap note

No source gap. The book is readable, but its text layer is OCR with number errors; only the pendulum section (PDF pp.138-159) had a deep read from page images, and the reviewers rendered a few more pages (pp.164-165, 18, 155). Figures in other sections are OCR-level unless a reviewer or I checked them. Conclusions that rest on [memory] alone are marked as such below (chiefly eclipse mechanics, star parallax and aberration, laser ranging, navigation practice). The 1849 pamphlet, the 1881 third edition, Hampden's and Carpenter's 1870 pamphlets, Blount 1904 and Wallace's own account were not read by anyone in this review; what is said about them is from Wikipedia, Schadewald and newspaper notes found by the Investigator, each with the stake of its source.

How the reviews relate

All three reviewers agree on the large shape of the verdicts. The plane model fails its own geometry, the book's curvature arithmetic is mostly correct, and the book's inference from it needs an unmeasured and very large refraction. They differ in a few places, and I settle each below. Three reviewer errors are corrected here; the reader should not carry them forward.

Disagreements settled by recomputation

1. Air-gun deflection (Claim 6). The physicist gives 3.8 cm east; the mathematician and contrarian give about 0.30 m west. The book says the ball was "on average 16 seconds in the atmosphere", 8 s up and 8 s down [read: PDF p.73]. Coriolis deflection of a ball that rises for t = 8 s is (4/3) x Omega x cos(latitude) x g x t^3, with Omega = 7.292e-5 rad/s. At 51.5 N that is 0.304 m. I also integrated the equations of motion numerically for a vertical shot with an 8 s ascent and got 0.304 m west [calc]. The physicist used t = 4 s (giving 3.8 cm) and the wrong sign: a rising body drifts west and a falling one east, and the net for up-and-down is west. The mathematician and contrarian are right. The physicist's 3.8 cm east is withdrawn. (The 16 s flight implies a vacuum apex of 314 m [calc]; with drag a pellet cannot do that, so the book's flight time is itself doubtful. That does not change the verdict on the book's premise.)
2. The book's surface speed. The book says the Earth's velocity is "700 feet per second" at London [read: p.74]. At 51.5 N the ground speed is 949 ft/s (about 647 mph) [calc]. The book's figure is about 26 percent low, and 700 is not the speed in mph either (the contrarian's remark that "700 is the right number for mph" is loose). By its own premise the displacement would be 7,600 ft in 8 s, not 5,600. The conclusion the book draws is wrong either way, because the ball keeps the ground's eastward speed.
3. Southampton "officer" data (Claim 4). The physicist calls them "internally impossible" ("on any shape two stations on one meridian differ in the Sun's altitude by their difference in latitude"). That holds only for a distant Sun and a globe. For a near Sun over a plane, which is the model being tested, no such rule applies. The mathematician and contrarian are closer. [calc] 800 miles of meridian is 11.6 degrees of latitude, so a globe with a distant Sun needs an altitude difference of about 11.6 degrees; the report says 7. With the Sun height from the London/Ackworth pair (H = 2,508 mi) a plane predicts a far-station altitude of 37.2 degrees, and the report says 38. So the datum contradicts the globe and agrees with the book's own plane triangulation. It stays in the record as that. It is a single printed report from an unnamed Royal Engineers officer, undated, with no stations, no simultaneity and no check that the stations share a meridian [read: p.79]. It does not rescue the plane, because the equinox test below fails on any single Sun height.
4. Polaris and "Captain Wilkins" (Claim 3 and 1). The physicist presumes the 23 deg 58 min is south latitude and refutes the report; the mathematician notes the hemisphere is not given. The page text says: Captain Wilkins "distinctly saw the Southern Cross and the polar star at midnight in 23 deg 58 of latitude, and longitude 35-46" (Times, 13 May 1862) [read: PDF p.46]. No hemisphere is stated. At 24 N both Polaris (altitude about 24 degrees) and the top of the Southern Cross (low on the southern horizon) can be seen on a globe [calc: Crux declination about -60 degrees, meridian altitude about 6 degrees at 24 N]. So the report is consistent with a globe if the latitude is north. If it is south, it is a real anomaly, since Polaris would be 24 degrees below the horizon and refraction cannot lift it. The physicist's "Refuted by calculation" is unsupported; I rate this Never properly tested (one newspaper line; the deciding record is the Times item itself and the ship's log).
5. Moon, tides, Neptune verdict labels. The reviewers agree on the facts and differ on labels. I settle the labels in the claim sections.
6. Refraction needed for the 1838/39 Bedford observation. The mathematician (flag top just visible at k = 0.73, waterline needs k above 0.95) and the contrarian (k about 0.7 for flag top, 0.9 for the boat at the water's edge) agree. [calc] Eye 8 in, 6 miles, R = 3,959 mi: the flag top (3 ft) just visible at k = 0.73; the waterline hidden by 0.5 ft at k = 0.9 and 0.08 ft at k = 0.95. No refraction: 16.7 ft (waterline), 13.7 ft (flag top). Standard k = 0.13: 14.1 ft and 11.1 ft. All three reviewers' numbers reproduce. Turning k into a temperature gradient with the formula k = 503 x (P/T^2) x (0.0343 + dT/dh) (P in millibars, T in kelvins) [web: https://en.wikipedia.org/wiki/Atmospheric_refraction, formula as returned by a page summary]: at P = 1013 mbar and T = 290 K, k = 0.73 needs air warming with height by about 0.09 K per metre and k = 1 about 0.13 K per metre [calc]. This matches the physicist's 0.13 and Wikipedia's "0.11 Celsius degrees per metre" for a flat-looking canal [web: https://en.wikipedia.org/wiki/Bedford_Level_experiment]. It is a strong, shallow temperature inversion over cold water; nobody measured one at Bedford.

Other numbers recomputed (all three reviewers agree; confirmed)

• Pole-centred disc, 45 S: circle of 58,570 miles and 162.7 miles per degree of longitude (the book says 69.44) [calc; physicist 58,600, mathematician 58,700, contrarian 163]. The 14,282-mile "globe circuit at 45 degrees" printed on PDF p.56 is wrong: at 45 degrees it is 17,608 miles; 14,282 is the circuit at 55 degrees [calc; mathematician's catch, confirmed].
• Equinox noon altitudes on the book's plane give a Sun height of 3,865, 3,588, 3,107 and 2,392 miles at latitudes 15, 30, 45 and 60 [calc]. No single height fits.
• Polaris on the plane needs a different height at every station: 976, 2,396, 3,113, 3,348 and 3,594 miles at 10, 30, 45, 51.5 and 60 N [calc].
• Sydney to Santiago on the pole-centred disc: about 15,930 miles. Real distance about 7,086 miles (11,401 km) [web: https://www.flightsfrom.com/SYD-SCL, via a search summary]; scheduled nonstop flights run about 12.5 to 13.5 hours [web, same search]. A 15,930-mile route at that speed would take over 28 hours [calc, at about 560 mph].
• London/Ackworth: Sun height 2,508 mi; the "800-mile" pair: 2,858 mi [calc].
• Jones pendulum (Manchester, 1851): predicted 0.20 deg/min; reported about 0.43; excess 0.23 deg/min. An elliptical-orbit (Airy) precession with a 6.3 mm minor semi-axis on a 1.455 m amplitude gives exactly that [calc, formula below].
• Eddystone at 14 miles from a 5 ft eye: hidden height 84.6 ft (k = 0), 71 ft (k = 0.13) [calc].
• Nab light-ship, 8 miles, eye 2 ft 8 in: hull base hidden 24.0 ft (k = 0), 19.9 ft (k = 0.13); the 10 ft bulwark top just visible needs k = 0.46, "the greater part of the hull" (base hidden by 5 ft or less) needs k = 0.65 [calc].

Web verification (budget 8, used 8)

Not rechecked and not load-bearing: Michelson-Gale-Pearson fringe shift (230 measured vs 237 predicted, the contrarian's [web: https://en.wikipedia.org/wiki/Michelson%E2%80%93Gale%E2%80%93Pearson_experiment]); Hall's 1902-03 drop series; Neptune position within 1 degree (physicist, mathematician and contrarian each cite Wikipedia).

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Corrected claim list

The central claims in claims.md stand, with these corrections.

1. The Earth is a stationary plane, north pole at the centre, the south a circumference of ice (book Sections 1-2, 4, 6; the Gleason map draws this layout). The plane model was never worked out in its own geometry; see Claim 1.
2. Level water proves it. The founding observation is the bather's eye 8 in above the Old Bedford, a 3 ft flag seen along 6 miles. The Southsea to Ryde sight is 4.5 miles, not 43 (the OCR "43" is an error: the diagram says 4 1/2, and the book's "40 inches" and "2 1/4 miles" fit only 4.5 [read: PDF pp.172-173; calc]). The Southsea Common eye height is 2 1/2 ft, not 24 ft [read: page images pp.164-165, reviewers]. The Nab Light-ship test was at an eye height of 2 ft 8 in and 8 miles [read: p.163]. The Grimsby "60 miles" figure is a newspaper sentence about the Queen's 1854 visit, not a measurement [read: p.179]. The facts.json and claims.md entries that say "43-mile" must be fixed.
3. Perspective, not curvature, explains ships sinking hull first. The "vanishing point at about 3,000 times an object's height" is the eye's one-arcminute resolution limit, which scales with an object's size; the book applies it to height above the water [read: pp.37-38]. Claim 3 also covers the Polaris point, circumnavigation and the lost day. The Polaris report names no hemisphere (see item 4 above).
4. The Sun, Moon and stars are small and near. The book never states a Sun height; it says "under 4,000 miles" [read: p.79]. From its own data the heights are 2,508 mi (London/Ackworth) and 2,858 mi (the Southampton pair) [calc]. The parallel-tube test is a prediction in the future tense, not a reported experiment [read: pp.74-75].
5. The Foucault pendulum does not prove the Earth rotates. The author reports no pendulum run of his own; the one measured case is Jones at Manchester (about 2.1 times the predicted rate in under 7 minutes). The ball-and-socket suspension is described only for Jones's apparatus.
6. Orthodox astronomy rests on assumed premises and has failed its tests. The air-gun premise (5,600 ft west) uses a surface speed that is 26 percent low; the book's tides mechanism is a floating Earth rocking "once only in about twelve hours" under atmospheric pressure [read: p.113]; the Neptune figures are right as figures but the prediction was right in position.
7. Scripture is literally true on the form of the Earth (Section 14). The author is an interested party with a stated religious motive.

QE revision additions to the list (details in "QE revision" below; the QE verdict on this review was MINOR):

8. Claim 4 includes an eclipse sub-claim: lunar eclipses are not caused by the Earth's shadow (Section 9, PDF pp.95-110). Its parts: horizontal eclipses; a visible, red Moon in totality; the Moon as self-luminous; no heat from moonlight; eclipse by an unnamed "semi-transparent body"; eclipse prediction "independent of every theory". Correction to the QE: the Hon. Mrs Ward's account is the partial eclipse of 7 February 1860 (more than eight-tenths covered), not 19 March 1848 [read: deep read, p.97]. Walkey (Phil. Mag. no. 220, Aug 1848) and Forster of Bruges are the 1848 witnesses.
9. Claim 6 includes the geodesy rebuttals (PDF pp.49-67): seconds-pendulum length put down to temperature and air density; meridian arcs said to show an "oblong" Earth; surveyors' levelling and the House of Lords No. 6 / Commons No. 44 standing orders; "spherical excess" put down to the lens of the theodolite.
10. Claim 4 also includes the New Zealand seasons and twilight argument (PDF pp.85-90). The book's premise "the latitude is about the same as in England" is false for Wellington (about 41 S against London 51.5 N).
11. Claim 2 also rests on long sightings and a lighthouse list: Great Orm's Head from Douglas, the Brighton line, balloon quotations (PDF pp.18-25), and 18 lights credited to Findlay's Lighthouses of the World (1862; PDF pp.172-178).
12. Claim 1 (southern circuit): the deep read of PDF pp.55-58 shows more slips than the arbiter listed. The book's printed 14,282-mile "circuit at 45 degrees" is 1,000 nautical miles below its own table (360 x 42.45 = 15,282 nautical miles, about 17,590 statute miles), so the original "circuit at 55 degrees" remark above is only a coincidence of numbers; the cause is a slip in print. The "69.44 miles per degree" is 25,000/360, whereas the book's own southern circuit of 26,433 statute miles would give 73.43; the nautical-to-statute factor used is 7/6 (1.1667) where the true factor is 1.1508.
13. Wilkins and the Polaris report: the sentence before it reads "as far even as the tropic of Capricorn" [read: PDF p.46], so the book frames it as a southern sighting. The report itself gives no hemisphere. The arbiter's statement above that it is "consistent with a globe if north" is tightened below.
14. Air-gun: the book says the ball fell "within a few inches" of the muzzle and twice "upon the very mouth of the barrel" [read: pp.73-74]. The physicist and facts.json wrote "feet".

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Verdicts by claim

Claim 1: Stationary plane, pole-centred, south a ring of ice

• Agree. All three: the plane fails its own geometry. The book's "69.44 miles per degree at 45 S" is the equator's value; on the disc it would be 162.7 miles, and the circuit 58,570 miles against the book's own 22,000-26,000 and the globe's 17,600 [calc]. The one measured figure the book offers fits the globe better than the plane.
• Differ. Physicist: the Gleason layout as a map is "Not testable as stated". Mathematician: the polar azimuthal map is "Established" as a projection. Contrarian: adds "No axial or orbital motion: Tested, not supported" (Reich, Hall, Michelson-Gale).
• Stronger argument. The mathematician's, on the map: the pole-centred equidistant map is a valid projection of a globe, and the Gleason patent itself calls the departure from a globe a distortion (an interested party's text, beside the printed slogan "As It Is") [web: https://patents.google.com/patent/US497917A/en, via Investigator]. "As it is" is the claim that fails: southern distances come out 2.2 to 2.3 times too long [calc, mathematician].
• Southern degree. The measurement the book itself demands ("proper geodetical operations", p.58) separates 49 miles (globe) from 163 miles (the book's own picture), not from 69.44.
• Final verdict, split.
• Plane Earth with the pole-centred layout: Refuted by calculation, and the southern-circuit argument is Internally inconsistent.
• The Gleason map as a projection: Established (valid distorting projection). "As it is": Refuted by calculation.
• A stationary Earth (no axial or orbital motion): Tested, not supported (Reich 1831 drop deviation of 28 mm east against 27.5 mm predicted, Michelson-Gale 1925; both via Wikipedia, secondary).
• What would settle it. A measured degree of longitude at 45 S (about 49 miles globe, 163 miles on the book's disc). Failing that, a single pair of timed southern flights, which already answer it on the numbers above.

Claim 2: Level water proves it

• Agree. The curvature arithmetic is right (8 in times miles squared; 6.0 ft mid-chord at 6 miles; 16 ft 8 in; the Nab and Southsea numbers once the 2 1/2 ft eye is used). The inference needs refraction that the book neither states nor measures: k about 0.73 for the flag and 0.9 to 1 for the boat to the water's edge, against standard 0.13. Wallace, Oldham and Stretton found curvature; Morrow's Illinois sights read concave, Blount/Clifton flat. No test in any camp measured refraction.
• Differ. Verdict labels only. Mathematician: "Tested, not supported" for "proves a plane". Physicist: the 1838 observation "Never properly tested". Contrarian: the anomalous reports "Never properly tested", the strong form "Tested, not supported".
• Stronger argument. The contrarian's split is the fairest, and it is supported by the others' arithmetic. Two different questions are being asked. (1) Is water flat at 6 miles at ordinary heights? Tested (Wallace at 13 ft, three signals, predicted 6.0 ft or 5.2 ft with k = 0.13, observed "more than 5 ft"; Oldham, Stretton) and not supported; the testers include interested parties (Walsh as umpire for The Field; Wallace the wagerer), and the losing party, Hampden, and his referee Carpenter, disputed it, were later (Hampden) convicted of libel; their pamphlets were not read here. (2) Did the 8-inch grazing sight see what is reported? Never repeated under that geometry with a temperature profile. It is possible, but needs about +0.09 to +0.13 K per metre of warming with height [calc, formula via web] over a cold canal in summer, and the book gives no date, weather or wave height. The founding observation also exists in at least two versions (the 1849 pamphlet: theodolite, boat on the New Bedford, "a fall of 24 feet", per Schadewald; the 1865 book: bather at 8 in, flag 3 ft, Old Bedford), which weakens it as a single clean experiment. The 24 ft figure equals 6 miles squared times 8 in with the full tangent drop and matches no one set of heights; whether these are two readings of one observation cannot be told without the pamphlet.
• Blount/Clifton 1904 (camera 2 ft, sheet 6 miles, a result the photographer "was surprised" to get) supports the book's visibility claim. It is by the movement's head's commission (an interested party), one photograph, unread primary, no temperature record; a 2 ft eye needs a sheet taller than 12 ft or k above 0.7 [calc by mathematician, reproduced approximately]. It stays in the record as an unresolved datum.
• Horizon at eye level (balloon, mirror). A real appearance. The dip at 110 ft is 11 arcminutes, and a mirror viewed from 10 in shifts the image 0.03 in; the committee could not have seen it, and the book's own "rose and fell with the eye" matches [calc, all reviewers]. Le Fevre (Balloon Society, 1882, first-hand: the surface looked concave) is one newspaper source and describes an appearance.
• Eddystone (Plymouth committee, Oct 1864, 14 miles, 5 ft eye). Does not discriminate: globe hides 85 ft (71 with k = 0.13), the lantern is 82-89 ft, so a globe predicts it is marginal; flat water predicts it visible; the committee saw nothing, which the author blames on waves [read: PDF pp.167-168; calc].
• Final verdict, split.
• The strong form (standing water is flat over miles, so the Earth is a plane): Tested, not supported.
• The 1838/39 Bedford observation as reported, Blount/Clifton 1904, the Nab "hull visible" days: Never properly tested (not dismissed without testing: the 1870 wager was a real test of the globe's prediction, but it did not repeat the grazing geometry and did not measure refraction).
• The curvature arithmetic: Established. Horizon dip and balloon "concavity": Established as appearances consistent with the sphere's dip.
• Eddystone, Southsea-Ryde, Grimsby: Not testable as stated (conditions unrecorded; Grimsby is press rhetoric).
• What would settle it. Repeat the Old Bedford sight at three eye heights (for example 8 in, 3 ft, 13 ft) on the same morning, with air temperature at two or three heights along the line and a long-focus camera; curvature plus the measured refraction should reproduce all three, or it will not.

Claim 3: Perspective, not curvature, makes ships sink hull first

• Agree. The resolution rule is a physical rule (1 arcminute, 3,438 times the size) but the book applies it to height, which misuses the quoted law; real hull-down distances depend on eye height (3.0 miles at 6 ft, 12.2 miles at 100 ft); a perspective effect would fade the whole ship and give no sharp waterline cut; a telescope shows rigging but not the hull behind the water ("the very ropes are easily distinguished, not the slightest portion of the hull", the book itself, PDF p.170). Lighthouse range figures and the Nab days fit variable refraction.
• Differ. Physicist: "Refuted by calculation". Mathematician: "Internally inconsistent" and "Refuted by calculation". Contrarian: "Tested, not supported".
• Stronger argument. The mathematician's: the rule as quoted is about size, and the author's step from "diameter" to "elevation" is not derived. That is an internal inconsistency, and the calculation then shows the observed sharp edge is what a horizon gives. The contrarian's concern is legitimate for a different sentence: the prediction "a telescope restores the hull on a plane" is a real, risky prediction that has not been run in a neutral controlled test with refraction measured. On the one day in the record when the hull was reported "distinctly visible" at 8 miles (Nab, May 1864), it needs k = 0.65. That is the same size of refraction as Bedford's, and the same pattern: a grazing sight over cold water. Rowbotham's waves explanation is untested.
• Polaris. The book's tangent argument assumes parallel lines cannot reach a star beyond the equator, which is true; its one example gives no hemisphere (see "Disagreements settled", item 4). Circumnavigation and the lost day: logic is correct for both shapes and favours neither.
• Final verdict, split.
• The vanishing-point law as used: Internally inconsistent (size and height confused); the resulting prediction (no sharp cut, no eye-height dependence) is Refuted by calculation.
• "A telescope restores the hull": Never properly tested under controlled conditions with refraction measured; the book's own sea results go both ways and the failures match the horizon.
• Polaris seen beyond the equator (the Times 1862 report): Never properly tested (one newspaper line; hemisphere not stated).
• Circumnavigation and the lost day: Not testable as stated as an argument for a plane (they do not discriminate).
• What would settle it. The Nab experiment repeated from 2 to 3 ft with a long telescope on a measured-refraction morning, hull height recorded; and the Times 13 May 1862 item and the ship's log for the Polaris report.

Claim 4: Sun, Moon and stars small and near

• Agree. The two-station plane formula is valid trigonometry but there is no single height. The equinox test uses only the book's own geometry (3,865 down to 2,392 miles). London/Ackworth fits the globe: 2.27 degrees observed against 2.19 degrees latitude difference. A Sun at 3,000 miles height would shrink about 6 times in angular size by 10 degrees altitude (slant distance 17,276 mi against 3,000) and the book's "perspective" rescue contradicts the observed constant size [calc, reviewers]; a 3,000 mile height Sun never goes below about 8.5 degrees from the far edge of a 20,000-mile disc, so on the book's numbers it would not set [mathematician's calc, plausible]. The tubes were never reported as run, and a delay is expected on any model (about 1 to 3 ms).
• Differ. Physicist: Moon self-luminous "Tested, not supported". Contrarian: "Refuted by calculation". Mathematician: "Tested, not supported" plus "Internally inconsistent". The Southampton datum: physicist "impossible"; contrarian "favours the plane"; mathematician "disagrees with a globe".
• Stronger argument. On the Moon, two separate claims: (a) "no thermometer rise from focused moonlight shows the Moon is self-luminous" is a non sequitur. Full moonlight is about 2.5e-6 of sunlight; even 3,000 to 6,000 times concentration gives 10 to 20 W/m^2, a few percent of full sun [calc], and no concentrator can exceed the Moon's surface brightness (about 12 percent of sunlight at best). The null result is what a reflecting Moon predicts, so (a) is Refuted by calculation. (b) "The Moon is self-luminous, not lit by the Sun" is contradicted by phases, eclipse behaviour and detected lunar heat (Piazzi Smyth 1856 [web]); eclipse mechanics are [memory: high] and were not re-checked: Tested, not supported. The physicist's and contrarian's labels are each right for one part. On Southampton, see "Disagreements settled", item 3.
• Final verdict, split.
• Near Sun and stars (under 4,000 and 6,000 miles): Refuted by calculation (no single height; angular size; the book's own London/Ackworth pair fits a distant Sun).
• "No heat from moonlight, so self-luminous": Refuted by calculation (the inference). "Moon self-luminous": Tested, not supported.
• Southampton officer data: Never properly tested (unsourced; it needs the Ordnance Survey record).
• Parallel-tube test: Not testable as stated at the sensitivity described; also never reported as run.
• What would settle it. A three-station simultaneous noon-altitude set on one meridian (public almanac or sextant data); the Ordnance Survey source for the Southampton figures.

Claim 5: The Foucault pendulum does not prove the Earth rotates

• Agree. The book's own figures follow 15 degrees per hour times sin(latitude) (Paris 11.29 deg/h, 31.9 h). The author reports no pendulum run of his own. The ball-and-socket joint is described only for Jones's apparatus. The Jones excess (0.43 against 0.20 deg/min) is explained by an Airy elliptical-orbit precession of (3/8)(ab/L^2) x omega0 with a 6.3 mm release error on a 1.455 m amplitude [calc; formula now web-confirmed, https://arxiv.org/html/2502.12230v1]; Jones himself named "some slight lateral bias at starting" beforehand [read: p.155]. Suspension errors (Onnes 1879) are a real source of scatter, but cannot give a steady turn with the sine-of-latitude dependence and the reversed sense in the south. The mathematician integrated the equations of motion (1.34 degrees in 7 minutes against 1.31 degrees) and showed that the book's "B. A. C." cancellation argument fails.
• Differ. Only in emphasis: the contrarian credits the book for a true statement of the 1851 popular argument's circularity; the mathematician calls the strong form Tested, not supported and "B. A. C." Refuted by calculation.
• Stronger argument. All three; they are compatible. What the book gets right: short, hand-released pendulums do scatter, and some 1851 popular explanations assumed what they set out to show. What it gets wrong: it concludes from scatter that the effect is not there.
• Magnetic-meridian reports (an unnamed writer; "a scientific gentleman in Dundee", Liverpool Journal, 17 May 1851): each a single newspaper-level report with no numbers. They remain in the record. A brass bob is non-magnetic, and the plane keeps turning past the meridian line.
• Final verdict, split.
• "The plane's turning is irregular, so it is no evidence": Tested, not supported. The weak form (careless short pendulums scatter): Established.
• "Earth under the pendulum or the pendulum over the Earth": Not testable as stated in kinematics; the sine-of-latitude law, the sign reversal and Coriolis effects elsewhere favour the rotating frame and give no support to a plane.
• Twisting ball-and-socket as the main cause: Tested, not supported (as the cause of the steady turn); as a source of scatter, Plausible, untested.
• Magnetic-meridian: Never properly tested (two newspaper reports, no data; not dismissed by testing).
• What would settle it. One 10 m or longer pendulum released by burning a thread, run for hours at two latitudes, with the Airy precession fitted.

Claim 6: Orthodox astronomy rests on assumed premises and has failed its tests

• Agree. Neptune: the book's figures are real (Le Verrier's period 217 yr, distance 36 AU against 165 yr and 30 AU; Kepler's third law reproduces both [calc]), but Galle found the planet within about 1 degree of the predicted position on 23 Sep 1846 [web: https://en.wikipedia.org/wiki/Discovery_of_Neptune, via physicist and contrarian]; the wrong elements came from an assumption (Bode's law). The book is right that this is an assumption; it is wrong to say the prediction failed. Air-gun and mast-drop: the premise (5,600 ft west) is wrong; the ball keeps the ground's eastward speed.
• Differ. Air-gun numbers (settled above). Tides: physicist and mathematician "Refuted by calculation"; contrarian "Not testable as stated".
• Stronger argument. On tides I read the book: the Earth, "once only in about twelve hours", rises and falls under atmospheric pressure, and the flood is the water moving as the Earth sinks [read: PDF pp.112-113]. It gives no amplitude. The mathematician's order-of-magnitude check stands: 1 hPa raises sea level by about 1 cm (hydrostatic, 100 Pa over rho g), storms of 20-30 hPa move it by tens of centimetres, and the semi-diurnal pressure oscillation is about 1 hPa [memory: medium], against tides of metres. The timing argument (12 h 25 min, high tide about 50 minutes later each day) is weaker, because the book says "about twelve hours" loosely. The contrarian's point that the book proposes no test is correct; the amplitude calculation is still decisive, so the label stands for the mechanism as stated.
• Air-gun and drop experiments. The reported result ("within a few inches", twice on the muzzle) is anonymous and undated, with no wind or drag record, against a predicted 0.30 m west for a vacuum 16 s flight. Not a clean test of the right prediction. Reich's mine shaft test (2.84 cm east against 2.75 cm predicted) is a clean test of the rotating-Earth prediction, and the unexplained 0.44 cm south residual [web] stays in the record.
• Final verdict, split.
• Neptune as a failure of Newtonian theory: Tested, not supported (position right; elements wrong from the Bode assumption). The book's facts on the elements are Established.
• Air-gun and mast-drop as proof of no motion: Refuted by calculation (the premise); the reported anonymous result: Never properly tested against the right prediction (0.3 m, not a mile).
• The floating-Earth tide mechanism: Refuted by calculation (order of magnitude).
• "Orthodox astronomy rests on assumed premises": Not testable as stated as a general charge. It has a true core (Bode's law, the circularity of popular Foucault accounts) and applies equally to the author's own assumed premises (the plane, the vanishing-point rule).
• What would settle it. The tide tables (period 12 h 25 min and ranges) are a self-check; for the air-gun, a vertical launch with a pellet and drag model, reading the drift against 0.3 m.

Claim 7: Scripture is literally true on the form of the Earth

Physics content falls under Claims 1-6. The theology is not an experimental question. Final verdict: Not testable as stated. The author is an interested party with a stated religious motive; the zetetic method ("facts first") sits in tension with a conclusion fixed in advance by text (contrarian), a point the physicist and mathematician do not dispute.

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Verdict table

What would settle it (collected)

1. Calculation, no apparatus. The equinox noon-altitude test (Sun heights 3,865 to 2,392 mi on the book's plane); the southern degree (162.7 miles on the disc against 49 on a globe); the Sydney-Santiago route (15,900 miles on the disc against 7,086 real). These already decide Claims 1 and 4.
2. Old Bedford sights at three eye heights on one morning, with a measured temperature profile along the line and a long-focus camera, repeated across seasons: the Rowbotham 1838, Wallace 1870 and Blount/Clifton 1904 designs under one refraction measurement. Decides what is left of Claim 2 and the Nab hull question.
3. Foucault pendulum, 10 m or longer, thread-burn release, hours, two latitudes, Airy fit (Claim 5).
4. Records, not obtained: the Times 13 May 1862 item and ship's log (Polaris); the Ordnance Survey source for the Southampton figures; the Manchester Examiner of 24 May 1851 and the Manchester Philosophical Society minutes (Jones); RAS minute book and MNRAS vol. 9 for 8 Dec 1848; the 1849 and 1851 pamphlets, the 1881 third edition, Hampden 1870 and Carpenter 1870 in full, Blount 1904 and Wallace's own account; the Western Daily Mercury report of the 25 Oct 1864 Plymouth trial.

Open questions

• Did the 1838/39 Bedford observation happen as reported, and under what temperature profile? Two versions exist; no independent witness is recorded.
• What did Captain Wilkins see in 1862, and where was he?
• What are the Southampton officer's figures, and were they simultaneous and on one meridian?
• Was the Blount/Clifton photograph an inversion image, a taller target or something else? The primary is not read.
• Why does the unexplained 0.44 cm southward deviation in Reich's drops remain (Reich, via web)? It is small and unrelated to a plane, but it is in the record.
• How did Wallace's differential test compare in sensitivity with Rowbotham's grazing sight? Both are line-of-sight; only temperature measurement separates them.
• Is The Anti-Newtonian (1819) the unacknowledged source of Rowbotham's layout (Schadewald, via the Investigator; not read)? It bears on priority, not truth.

Absence-of-evidence analysis

The overall record does not go dark. Rowbotham lectured through 1882, was president of the Zetetic Society in 1883 and died in 1884; the Universal Zetetic Society (1893), Blount, Carpenter, Hampden, Gleason and later Koreshan work continue it [web, via Investigator]. There is no vanished company or lost device to explain. There are, however, six places where the record is silent where it would be expected to continue; each is an anomaly to analyse, and none is a verdict.

1. The Jones pendulum run (Manchester, 1851). Only source: the Manchester Examiner, 24 May 1851, reprinted in the book [read: p.154-156]; the Investigator's search found nothing independent (negative). Explanations: (a) a local report of a casual demonstration that nobody followed up (consistent with Jones's own warning about "lateral bias"); (b) an inaccurate transcription; (c) the original contained more data than the author quoted. For (a): the Airy calculation explains the excess with a 6 mm release error, so no further publication is surprising. Against (b) and (c): nothing in the record. Deciding record: the Manchester Examiner of 24 May 1851 and Manchester Philosophical Society minutes.
2. The founding Bedford observation (1838/39). No independent witness; the author's two accounts differ (24 ft fall, theodolite, New Bedford in 1849 per Schadewald; bather, 8 in, 3 ft flag, Old Bedford in 1865). Explanations: (a) one observation retold with different arithmetic; (b) two separate trials; (c) an embellished report; (d) an unusual inversion that day (Wikipedia's temperature figure is for this case [web]). Evidence on each is thin. Deciding records: the 1849 pamphlet, local records for Manea Fen and Welney 1838-41 (Cambridgeshire Archives, not reached), Rowbotham's 1882 "many experiments" lecture notes.
3. The Royal Astronomical Society, 8 Dec 1848. The 1849 pamphlet says its argument was "a paper read before the Royal Astronomical Society"; De Morgan, the RAS Secretary, wrote that no account appears in the Notices and that he read some of it aloud "for your amusement" [web: Schadewald Ch.1, quoting A Budget of Paradoxes; via Investigator]. Documented in one printed source from an interested officer of the institution. Explanations: (a) the paper was never accepted for the Notices (institutional dismissal, in De Morgan's words); (b) an informal reading at the close of a meeting, not a formal paper; (c) the pamphlet overstated the credit. Deciding record: the RAS minute book and MNRAS vol. 9. This bears on how the work was received, not on the physics.
4. The Southampton officer (Ordnance Survey) data. One printed report in the book; no second source; no named officer or date. Explanations: an unverifiable hearsay report of two non-simultaneous altitude readings; a wrongly stated distance or meridian; or genuine OS figures that nobody published. Deciding record: Ordnance Survey correspondence of 1864-65.
5. The air-gun trials and the unnamed Plymouth, Nab, Southsea committees. The book names the Plymouth committee members for Oct 1864 (Parallax, "Theta", Osborne, Richards, Rickard, Mogg, Evers, Pearce) [read: p.167] but the Nab, Southsea and air-gun observers are unnamed. Proctor's critical account of Plymouth (Schadewald, via Investigator; not read) and the Western Daily Mercury original are the records that would show whether data were reported fairly. Competing explanations: casual friends' observations never written up; selective reporting; or loss of the notes.
6. Blount/Clifton 1904. The primary (The Earth vol.5 nos.49-50) was not reached (library.tfes.org was blocked by a TLS error, not bypassed). The Wikipedia summary says the photographer "was surprised". Explanations: a genuine strong-inversion image; an overstated report by an interested party; or a target larger than reported. Deciding record: the original article and photograph, and any temperature notes.

Note on how the record was resisted. The contrarian looked for omitted data, blocked funding or publication and found no evidence in this folder or the Investigator's finds; absence in this record is not proof of absence. The one documented institutional episode is De Morgan on the RAS (item 3). The only formal test of Rowbotham's claim by a neutral party on his own canal, the 1870 wager, was agreed beforehand, and its outcome was contested by the wagering party; its court record is Wikipedia-level here.

Notes on the reviewers

• Physicist. Reliable, with two errors corrected above: the 3.8 cm east air-gun figure, and "internally impossible on any shape" for the Southampton data. Also presumed the Polaris latitude was south. Its Jones/Airy estimate is now web-confirmed.
• Mathematician. Most careful on the arithmetic and on the 14,282 versus 17,600 mile error, and the one who caught the OCR errors at pp.164-165 and 18 together with the contrarian. Best on the B. A. C. argument and on the refraction thresholds.
• Contrarian. Right on the Southampton fit to the plane, on the Nab and Blount data, and on Neptune's two halves; correctly insists that nobody on record measured refraction. The claim "Moon self-luminous: Refuted by calculation" should be read as the thermometer inference only; and "700 is right for mph" is not.
• Retention. Every Investigator lead the reviewers weighed stays in this record: the founding-observation versions, the RAS episode, Le Fevre 1882, Blount/Clifton 1904, Hampden/Carpenter/The Field, Oldham, Stretton, Morrow's concave result, Proctor's Plymouth account, the Gleason patent and "As It Is" slogan, The Anti-Newtonian 1819, the inquests over Rowbotham's phosphorus remedies (medical record, not physics), Jones's single report, the magnetic-meridian reports, the Southampton data and the Nab hull days. Several of these favour the book; each is kept next to the verdict that judges it.

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QE revision

Why this section exists: the QE (qe.md, verdict MINOR) found that the arbiter, primer and reviews gave no verdict on the eclipse sub-claim, missed the geodesy, New Zealand and long-sighting arguments, and kept some known errors. Six new deep reads were done (all in deep/earth-not-globe-book-c293c9.md): eclipse and moonlight records (PDF pp.94-110); Orm's Head, the Brighton line and the balloon quotations (pp.18-25); geodesy (pp.49-67); the lighthouse list (pp.172-178); the Sun's circle, seasons and twilight (pp.80-90); southern navigation (pp.26-30, 55-58). I read all six, checked Wilkins at the page text (p.46), and recomputed the numbers below [calc, numpy in the project venv, script not kept]. Tags: [read: deep read] means the deep reader's transcription of the book, taken as given; [read: p.N] means I checked the page text; [calc] mine; [web] with URL; [memory] with confidence.

Result: no central verdict changes. The plane, the near Sun and the Foucault verdicts stand. The new material adds sub-verdicts, tightens two of my own statements (Wilkins, the moonlight null results), and corrects two QE statements.

Web verification for this revision (6 of 8 calls)

Not web-checked, and flagged where used: the Great Orme height (about 679 ft) and the Douglas-Great Orme distance (about 60 miles) [memory: medium]; the Greenwich sidereal time used for Wilkins [calc from memory: high]; Melloni's 1846 detection of lunar heat [memory: medium, not used for a verdict]; the cause of the Lancet cooling [memory: medium].

Changes to my earlier statements

1. Wilkins and the Polaris report (replaces item 4 under "Disagreements settled"). The QE is right that the book frames the report as a southern sighting: "as far even as the tropic of Capricorn", then the Times of 13 May 1862 "Captain Wilkins distinctly saw the Southern Cross and the polar star at midnight in 23 deg 58 of latitude, and longitude 35-46" [read: p.46]. No hemisphere or longitude direction is printed. [calc, local sidereal time at midnight on 13 May taken as about 15.4 h] At 24 S Polaris would be 24 degrees below the horizon and refraction (about 0.6 degree) cannot lift it; there the report is a real anomaly. At 24 N Polaris stands 24 degrees up, but at local midnight in mid-May the Southern Cross is then within about a degree of the horizon (Gacrux about +0.5, Mimosa about -0.5, Acrux about -4.5 degrees), and ship's time is unspecified. So my earlier "consistent with a globe if the latitude is north" was too generous: it is marginal, not comfortable. The report is one newspaper line; the deciding records are the Times item and the ship's log. Verdict unchanged: Never properly tested, and the book's own reading (south) is the one that would be anomalous.
2. Moonlight null results (Claim 4). I wrote that the null result "is what a reflecting Moon predicts". That is too strong. The book gives: De La Hire (35 in glass, x300, air-thermometer), Forbes (30 in lens, x6,000, about x3,000 net, thermo-pile, Moon 18 h past full) and an unnamed reflector with a thermometer good to 0.001 degree [read: deep read, pp.105-107]. [calc] Using my earlier irradiance (full Moon about 2.5e-6 of sunlight), x3,000 to x6,000 gives roughly 0.8 to 1.5 percent of full-sun irradiance on the receiver, before losses. A blackened bulb in full sun runs tens of kelvin above the air [memory: medium], so about 1 percent might give a few tenths of a kelvin: at or just inside the sensitivity of a good 1840s instrument, and easily lost to radiative cooling to the clear sky. So the nulls neither contradict nor confirm a reflecting Moon with any force. Later positive detections exist (Piazzi Smyth, Tenerife, 1856 [web, from the first pass]). What stays refuted is the inference "no heat, so self-luminous": a reflecting body also reflects the Sun's infrared and gives a faint, hard-to-measure signal; "a reflector gives off what it receives" is not what was shown. The label Refuted by calculation applies to that inference only; the nulls themselves are Never properly tested as a discriminating experiment (no sensitivity, no loss budget, no control).
3. Where the QE needs correction. (a) It lists Mrs Ward with Walkey as accounts of 19 March 1848. Ward's account is the partial eclipse of 7 February 1860 [read: deep read p.97]; the book's own text dates it. She cannot be a witness of "totality". (b) The QE puts Douglas to Great Orme at about 61 miles from coordinates recalled from memory; the book says 60. I use 60 to 61 [memory: medium], and the book's own 1,944 ft figure does not follow from its rule (below).

Eclipse sub-claim of Claim 4 (new verdicts)

The author's argument (Section 9, PDF p.95): a lunar eclipse by the Earth's shadow is "in every respect unsatisfactory", because "the Earth has been proved to have no motion" and is a plane beneath the Sun and Moon. All records below are second-hand quotations from popular books; no original was seen by the deep reader or by me [read: deep read §8].

• A. Horizontal eclipses. Records: Paris 19 July 1750 (Carey, Astronomy and Astronomical Instruments); 20 April 1837 and 20 September 1717 (McCulloch's Geography p.85); 17 July 1590, 3 Nov 1648, 16 June 1666, 26 May 1668 (Glaisher in the Illustrated London Almanack for 1864, "noticed as early as the time of Pliny") [read: deep read §2]. Glaisher's wording is "apparently above the horizon"; the book keeps that word in the quotation and drops it in its conclusion (p.102). [calc] Refraction at the horizon is about 34 arcminutes [memory: high]. The Sun is seen whole above the horizon if its true centre is at -0.83 degrees; the antisolar point is then at +0.83 degrees; the Moon's parallax (about 0.95 degrees) lowers it to about -0.12 degrees, and refraction then lifts its upper limb to about +0.7 degrees. So both can be above the horizon with the Moon in the Earth's shadow. The effect is named and accepted (selenelion) [web: https://en.wikipedia.org/wiki/Selenelion]. Verdict: the inference "so the Earth is not between Sun and Moon" is Refuted by calculation. The records themselves stay in the record as reported observations; they are not disputed.
• B. Visible, red Moon in totality. Avignon 22 Dec 1703 (OCR gives 1708; the image reads 1703); Forster of Bruges and others, 19 March 1848; Walkey near Collumpton, 19 March 1848 (Phil. Mag. no. 220, Aug 1848); Glaisher, total eclipse of 1 June 1863 ("seemed to be on fire", "a fire smouldering in its ashes, and almost going out"); Mrs Ward, partial eclipse of 7 Feb 1860 [read: deep read §3]. The Earth's shadow, as the mainstream describes it, is not black: sunlight bent through the Earth's atmosphere falls into the umbra. [calc] The umbra's angular radius at the Moon is about 0.68 degrees (Moon parallax 0.95 + Sun parallax 0.002 - Sun semi-diameter 0.27); light grazing the limb is bent by of order a degree [memory: high; not web-checked], which is enough to illuminate the Moon's face with a red cast. The witnesses' words ("reddish tinge", "red-hot copper", "iron grey", "almost going out") are what that predicts, and brightness varies from eclipse to eclipse [memory: high]. Walkey's "as perfect with light as if there had been no eclipse whatever" is much stronger than Ward's, Glaisher's or Forster's wording; the book's own quotation contains omissions (" * "), the experience is single-source (Phil. Mag. via the book), and the original was not read. Verdict: the inference "so no shadow" is Tested, not supported; Walkey's brightness statement alone is Never properly tested (original unread, no photometry).
• C and D (self-luminous Moon; no heat). See item 2 above; the verdicts in Claim 4 stand. Also kept in the record: Lardner's silver chloride (blackened by violet light, not by moonlight even through burning lenses; no numbers), the Lancet 14 March 1856 report that concentrated moonlight "reduced the temperature upon a thermometer more than 8 degrees" [read: p.107; page image], and Shelley's lines the author sets next to it. The Lancet item is the only report in the section of a measured effect. It is cited second-hand with no experimenters, instrument, scale or conditions; I did not read the Lancet. A cooling of a thermometer exposed to a clear night sky is the usual radiative-loss effect [memory: medium]. Verdict: Never properly tested (a cited measurement with no details; the original is the deciding record).
• E. Eclipse by "a body semi-transparent and well-defined". The authority cited is the RAS Council report of June 1850 ("we may well doubt whether that body which we call the Moon is the only satellite of the Earth") and an unnamed French director quoted from Lardner's Museum of Science p.112 [read: deep read §5]. As quoted, those passages concern a possible additional satellite and say nothing about eclipses; the step to eclipses is the author's. The book does not say why the Moon would be dimmed by such a body, nor why a lantern-like self-luminous Moon (his own picture) is darkened at all. The Earth's shadow as the cause is Established [memory: high; not re-checked here]. The unnamed body: Not testable as stated.
• F. Eclipse prediction needs no theory. Ptolemy's 600-year calculation, the Babylonian record "about 719 B.C." and the Saros of 6,585 1/3 days (18 years 11 1/3 days, which I checked: 18 y + 11.3 d) [read: deep read §6; calc]. True and not in dispute: a cycle fitted to observation predicts eclipses. It does not discriminate between a shadow and a body. Verdict: the weak form Established; as an argument against the shadow, Not testable as stated.
• Overall for the sub-claim "lunar eclipses are not caused by the Earth's shadow". Tested, not supported. Two of its three supports are answered by refraction, and the third (the Moon's visible face) is what the atmosphere-lit umbra gives. The eclipse section also rests on "the Earth has been proved to have no motion" from earlier sections, which Claim 1 judges separately.

New Zealand seasons and twilight (Claim 4)

The book (PDF pp.86-89) says New Zealand's "latitude is about the same as in England", quotes the Cook's Strait Almanack for 1848 (Wellington: 21 Dec day 14 h 58 m, 21 June 9 h 2 m; England 16 h 34 m and 7 h 45 m), adds Swainson, Thompson, an anonymous Nelson letter of 15 Sept 1857 and Basil Hall ("so low a latitude as 28 degrees") on short twilight, and concludes the difference is "altogether incompatible with the doctrine of the Earth's rotundity" [read: deep read §§5-7]. The book states no numeric latitude for any place in these pages except 28 degrees (Hall) and the hypothetical 50 S and 50 N [read: deep read §8]. - Day lengths [calc] (sunrise at the upper limb, refraction 0.83 degrees): Wellington (41.3 S) 21 Dec 15 h 10 m, 21 June 9 h 11 m; London (51.5 N) 21 June 16 h 38 m, 21 Dec 7 h 50 m. The almanack's Wellington figures are 12 to 18 minutes short and the England figures within 5 minutes. The "difference" the book finds is the difference between 41 and 51.5 degrees of latitude, which a globe predicts. A northern place at 41 N has the same day lengths as Wellington with the seasons swapped [calc: 15 h 10 m on 21 June]. The premise ("about the same latitude") is wrong by about 10 degrees. Refuted by calculation (the data fit the globe). - Twilight [calc]. Civil twilight: London 21 June about 48 minutes; Wellington 21 December about 34 minutes (the deep reader found 31). On a globe twilight is shorter at lower latitude, so the residents' reports agree with the globe: their statements are of short twilight in a lower latitude, and no northern place at a similar latitude is cited for comparison. The Swainson and Thompson texts are colonial promoters or officials writing about a colony, a stake the reader should weigh; the Nelson letter is one private letter published only here. They stay in the record as witness accounts. - The plane's own numbers [calc; my construction, since the book gives no radii, Sun height or light radius]. On a pole-centred equidistant plane (69.1 miles per degree of colatitude) England is at 2,660 miles from the pole and Wellington at 9,070. Put the Sun on circles through the tropics (4,600 miles in June, 7,840 in December) and fit the radius of the lit disc to England's day lengths: it comes out 6,480 miles (June) and 6,820 (December), a consistent figure. With that radius the plane gives Wellington a day of about 6 hours on 21 December and 6 hours on 21 June, against the almanack's 15 h and 9 h. Wellington on 21 December needs a lit radius of 14,060 miles, twice England's. So the plane explanation fails against the same table the book quotes. The book's velocity argument ("velocity is the space passed over multiplied by the time") also states the definition backwards [read: deep read §7]; the conclusion it draws (larger radius, higher speed) is what the model implies, and gives a twilight ratio of about 3.4 (radius ratio) against the globe's about 1.4 (my civil figures, 48 against 34 minutes); no twilight was measured in the book. The plane's day-length and twilight predictions: Refuted by calculation, under my stated assumptions (the book's own picture, with free parameters fitted to its favourable data). - Glaisher's 1848 altitude table (PDF p.82). Two entries disagree with London geometry: 21 Dec "12" (geometry about 15; its neighbours say 15 and 15 1/2) and 21 March "42 1/2" (geometry 38.5) [read: deep read §3; calc]. Both look like misprints in the source or book; the remaining entries I rechecked agree to about a degree. It stays as a note; it carries no verdict.

Geodesy rebuttals (Claim 6; PDF pp.49-67)

• Seconds-pendulum length put down to temperature (pp.51-54). The book prints (Phillips, Million of Facts p.475) 39.027 in at the equator, 39.139 in at London and 39.197 in at the pole, and mean temperatures from 84.2 F to 0 F; Noad: a change of 30 F alters the length by 1/5000; and Derham: arcs of vibration longer in vacuo, "two seconds in an hour" [read: deep read §3]. [calc] The temperature change from equator to pole in the book's table is 84.2 F, giving 84.2/30 x 1/5000 = 5.6e-4 of the length. The tabulated lengths differ by 0.170/39.027 = 4.36e-3, 7.8 times larger. Derham's 2 s/hour is 5.6e-4, also small. Both together give about 1.1e-3, about a quarter of the observed difference, and the quoted standard length is already stated "in vacuo ... at the temperature of 62 deg" [read: deep read §3], so the lengths are already corrected for both. The tabulated numbers are the length a pendulum must have to beat seconds at each place, so they are the effect to explain. The measured gravity ratio pole to equator is 1.0053 against a length ratio of 1.0044 here [calc from WGS84 constants, memory: high], in line with the effect being gravity. Verdict: "temperature and air explain the pendulum variation without a spheroid": Refuted by calculation, from the book's own figures. The book also argues the premise "the Earth is a globe with a centre of attraction has not been proved"; that is the same circularity charge as Claim 5's, and is not decided by the pendulum alone.
• Meridian arcs and the "oblong" Earth (pp.49-51). The book prints an eight-row Arbury Hill-Clifton series: 60,766 fathoms at 52 deg 50' N to 60,890 at 51 deg 13' N (degree lengthening southward, i.e. against oblateness), Peru 56,653 toises, Lapland 57,422, and the Swedish correction of 196 toises, and concludes "no two sets of experiments agree" [read: deep read §2]. [calc] Over that 1.8 degree span an oblate Earth predicts a change of about -3e-4 (shorter toward the south); the table shows +1.9e-3, six times larger and opposite. An error of about 11 arcseconds in the astronomical latitude difference over a 1.5 degree arc produces 0.2 percent [calc], the size of the spread; local plumb-line deflection of that order is known [memory: medium] and the book's own quoted source says the disagreement was "impossible to explain in a satisfactory way". Small arcs near one latitude cannot measure the flattening. For the two long arcs, the book does not subtract its own correction: 57,422 - 196 = 57,226, still 573 toises (1.0 percent) above Peru. Modern degree lengths are 56,733 toises at the equator and 57,214 at 66.3 degrees (481 toises, 0.85 percent) [calc, WGS84, memory: high]; the Swedish remeasurement of 57,196 toises [web, above] sits within 20 toises of the modern figure. So the sign and size of oblateness survive the book's own correction. Verdict: "meridian arcs show an oblong Earth, or no two agree": Tested, not supported. The book's quotation that the Beachy Head-Dunnose perpendicular degree differed from the meridional degrees is kept as the source's admission (an unexplained disagreement, read from an encyclopedia, not by the author), unresolved here.
• Surveyors' levelling and the standing orders (pp.59-61). The book says engineers abandoned allowing for curvature and adopted back-and-fore sights, and that House of Lords order No. 6 and Commons order No. 44 made "the abandonment of all ideas of rotundity compulsory" [read: deep read §5]. The curvature drop is 8 inches in one mile (2/3 ft per mile squared) [calc], and with equal sight lengths it cancels between the two readings by design, so the method says nothing about whether curvature exists. The quoted order requires a section on a horizontal scale with a "datum HORIZONTAL LINE"; the quoted words say nothing about the shape of the Earth. Verdicts: back-and-fore levelling as evidence of no curvature: Refuted by calculation (cancellation). The book's reading of the orders: Internally inconsistent (the claim contradicts the text the book itself quotes; the orders' full text, session and year are not given and were not read).
• Spherical excess put down to the lens (pp.63-67). The book (quoting Castle) states the rule "divide the area of the triangle by the radius of the Earth in seconds" and replies that the excess comes from the lens's "dilating" of objects out of the axis (Fig. 21) [read: deep read §6]. Spherical excess is area/R^2 [web: https://en.wikipedia.org/wiki/Spherical_trigonometry]. [calc] A 100-chain (6,600 ft) triangle has an excess of 0.009 arcsecond; a 64-mile equilateral triangle (the Beachy Head-Dunnose scale) 23 arcseconds. The excess is a property of angles measured between stations, which a fixed crosshair offset cannot change. The dip of the sea horizon below a levelled instrument grows with the observer's height: 3.4 arcminutes at 10 ft, 5.8 at 30 ft, 10.6 at 100 ft, 18.4 at 300 ft [calc, no refraction]; a fixed lens offset has no height dependence. The book gives no measurement, focal length or comparison. Verdict: Refuted by calculation. The book's concession, "the conclusion ... would completely satisfy the minds of scientific men ... if a perfect explanation could not be given" [read: deep read §6], stays in the record.
• Fluid forms (p.62) (drops spherical by cohesion, not gravitation): the author asserts this and defers the proof of no motion to "a subsequent part". Not decided here; kept in the record.

Long sightings and the lighthouse list (Claim 2)

• Great Orm's Head from Douglas, Isle of Man, from 100 ft (pp.18-19). The book: 60 miles; globe hides 1,944 ft at the arc's centre; from 100 ft the horizon is "nearly 13 miles", the remaining 47 miles squared times 8 in is 1,472 ft, the Head is "600 feet high" so its summit is "872 feet below the horizon". No observer, date or source is given for "it is well known"; "many similar experiments" across St George's Channel are unnamed [read: deep read, Orm's Head §1]. [calc] 47 squared x 8 in = 1,472.7 ft (the book is right); 1,944 ft does not follow from the book's own rule (60 squared x 8 in = 2,400 ft; 54 miles gives 1,944). The deep reader's 1,944 observation stands as an internal inconsistency in the arithmetic. Using 100 ft eye height, 60 miles [memory: medium] and a summit of 600 ft (the book) or 679 ft [memory: medium], the summit is just visible only with a refraction coefficient k of about 0.50 or 0.46 (standard k is about 0.13, which gives a range of about 45 miles for 600 ft) [calc]. Verdict: the sighting Not testable as stated (no conditions recorded); the 1,944 ft figure Internally inconsistent with the book's rule.
• Brighton line (pp.20-21). Poles 6 yards apart, a line parallel to the horizon, a vessel followed 20 miles each side for "several hours", the line cutting the rigging; the globe would put the vessel 266 ft below the line at each end (20^2 x 8 in = 266.7 ft, correct arithmetic) [read: deep read §2; calc]. No date, observer height, line height, vessel distance or speed is given. The 266 ft treats the line as tangent at the centre of a track; whether the ship's distance from the observer is the same at the ends and the centre is not stated, and a straight track at constant distance is not what the figure assumes. Not testable as stated. It stays in the record as an anonymous report ("tried in various parts of the country").
• Balloon quotations (pp.22-24). Wise, Mayhew, Elliott, London Journal 18 July 1857, and Glaisher and Coxwell ("the horizon always appeared on a level with the car") [read: deep read §4]. Details the book's use leaves out: Wise himself calls the concave look "an optical illusion"; Elliott writes "Philosophy imposes the truth upon us", accepting rotundity while describing the appearance; none gives a measured dip. This adds to, and does not change, the existing verdict: Established as an appearance (the dip at 110 ft is 11 arcminutes, from my first pass).
• Lighthouse list (pp.172-178; 17 lights credited to Findlay, Lighthouses of the World, 1862, plus Ballycotton from the Illustrated London News, 20 Oct 1849). The book's method: remove 4 miles for a 10 ft observer, square the rest, multiply by 8 inches, subtract the light's height; the remainder is "the amount which the light ought to be below the horizon" [read: deep read, lighthouse §1]. Two facts from Findlay that the book quotes on p.166 and does not use on pp.174-178: his tabulated ranges already add 10 ft for the observer's deck and are, he says, "the minimum range of the light", and "the effect of refraction will also sometimes increase their range" [read: deep read, lighthouse §1]. [calc, observer 10 ft, statute miles] For all 18 lights the stated range is longer than the geometric range with k = 0.13; the k needed ranges from about 0.17 (Calf of Man) to 0.80 (Spurn Point, a coal fire "seen 30 miles off") with a median about 0.40, and Bonavista (0.71) and Ballycotton (0.70) at the top. Ryde Pier (12 nautical = 14 statute miles from a 21 ft light): geometric range 9.5 miles, k needed 0.54. Findlay's own statement is that the tabulated figures contain no refraction, yet they exceed his stated geometry, so the two statements in the book cannot both describe the same quantity; the nature of the "range" (luminous, nominal, observed) cannot be settled without Findlay, which is not in the folder. The author's own arithmetic has slips: Farn Island prints 67 ft below the horizon without subtracting the 45 ft height (22 ft by his method); Calf of Man, Cromer and Whitby differ from his method by up to 14 ft; Ballycotton adds the island and tower heights above sea level against Findlay's above-high-water convention [read: deep read, lighthouse notes A, B, E]. Verdict: Not testable as stated (catalogue ranges with undefined conditions; the refraction each would need is above). The data stay in the record as catalogue entries that the book reads as observed ranges.

Southern navigation (Claims 1 and 6; PDF pp.26-30, 55-58)

• "Navigators failed to sail round the south" and the Wilkes letter (p.27). "I hope you intend to circumnavigate the antarctic circle. I made 70 degrees of it", from a letter Wilkes is said to have written to Ross; no date, archive or source [read: deep read §B]. It is a single-source report in the book's own words, quoted here; no second source was found in this review and its wording is unchecked. Silence elsewhere is not contradiction, and Ross's own text was not read. That sea ice blocks circumnavigation is not a point of dispute; the globe also predicts a ring of ice-bound sea, so it discriminates little. Verdict: Not testable as stated as a discriminator. The arbiter's earlier remark that the Antarctic coast on a plane would be about 78,000 miles against a coast of about 11,000 to 22,000 [web, first pass] stands as the quantitative test.
• Ross's reckoning errors (p.27). "Every day from 12 to 16 miles by observation in advance of our reckoning" and "58 miles to the eastward of our reckoning in two days" (Ross's voyages, p.96) [read: deep read §C]. Dead-reckoning error is normal at sea from currents and log error; no drift correction is given. Not testable as stated.
• Ross's barometer (Ross p.483, "a gradual diminution of atmospheric pressure ... as we proceed southwards from the tropic of Capricorn", cause "remains to be determined") [read: deep read §D]. An observation by a named expedition commander, not by the author. Southern low pressure around Antarctica is a real feature [memory: medium]. The author's step from lower pressure to a higher southern sea is his own; Ross says nothing about the sea's height or the Earth's shape. [calc, from the first pass] 1 hPa lifts sea level by about 1 cm in equilibrium, so a pressure deficit of tens of hPa moves it by tens of centimetres, not the many miles a plane's "higher southern circumference" would need. Verdicts: the observation Established [memory: medium; Ross not read]; the link to a higher sea Not testable as stated (no amplitude given), and Refuted by calculation as a mechanism for anything large.
• The Challenger frigate, 1845 (p.58). Quoted from Milner, Tour through Creation (popular): navigators to India "fancied themselves east of the Cape when still west", driven ashore "on the African coast", "a fine frigate, the 'Challenger', in 1845" [read: deep read §E]. [web] An HMS Challenger (28 guns) was wrecked off Chile, 19 May 1835, a different year and coast; I found no 1845 African wreck of that name. The deep reader flagged this as [memory: low]; it is now partly checked (the match fails), but the book's wreck is not shown to be a mistake. Single secondary source; the cause (errors from the Earth's shape) is asserted. Not testable as stated. The deciding record is the Admiralty list of losses.
• The longitude table and the Cape Horn to Port Philip quotation (pp.55-58). The table of degrees of longitude is 60 cos(latitude) to within 0.02 nautical miles except 85 degrees (5.53 against 5.23, probably a misprint) [read: deep read §F; calc]. The sums: 22,000 miles round the south at an "average longitude 45 deg" is compared with 14,282 (should be 15,282 from the table: 360 x 42.45), so the "error of 7,718" is 6,718; Ross's 9,000 miles for 143 degrees gives 22,657 (correct), but "8357 more" is 8,375 by the book's own figures (7,375 from the table-consistent 15,282); 22,657 x 7/6 = 26,433 statute miles (the true nautical-to-statute factor, 1.1508, gives about 26,070) [read: deep read §F; calc]. The three sailing legs span about 133, 142 and 85 degrees of longitude [memory: medium], giving 60 to 71 nautical miles per degree: an uneven set the book does not discuss. Ross's 9,000 miles is a route distance, and Cape Horn to Port Phillip is nearer 148 degrees than 143 [memory: medium], which would give about 21,890 miles [calc]; the book treats the figure as the length along a parallel without saying so. These slips do not come from observations; they are arithmetic and typesetting errors in the book. They add to the "internally inconsistent" part of Claim 1 (the book's proposed test of 69.44 against 49.52 miles per degree has the 69.44 equal to 25,000/360, not the 73.43 its own circuit implies); they do not change the verdict.

Missed material the QE listed, now recorded (no verdict beyond the above)

• Kane's "open polar sea" tide argument (pp.114-115), spirit-level bubbles that never settle as evidence of a floating Earth (p.115), Herschel's 1,900,000-year light-time and the 6,000-year chronology (pp.200-202), the Saros (p.109, now checked), the RAS 1850 and French Academy notes on further non-luminous bodies (p.108; see item E). These sit in the record. The floating-Earth tide verdict (Claim 6) already covers the rocking Earth; the bubble argument is a further appeal to the same mechanism and is covered by the same amplitude test.
• Schadewald's accounts of how Rowbotham handled tests (Investigator, from Schadewald's The Flat-Earth Bible, a critic's book; the primary newspapers were not read): at Burnley on 5 and 7 December 1849 he did not appear for the second lecture after a question about ship hulls (Blackburn Standard, per the Investigator's notes); and he reportedly walked out of an agreed repeat of the marker test on the Teign because the committee had placed the markers without him [read: research/2026-10-06-cantab-planetruth.md items 4 and 5]. The 1849 Trowbridge lectures were given as "S. Goulden" (Wiltshire Independent, favourable and hostile correspondents) and he was using "Parallax" by the end of 1849. Schadewald's stake: he is a critic writing against the flat-Earth movement. These count against the inventor on how he handled testing, and they must stay beside the contrarian's "how claims were rejected" finding: the one documented institutional episode remains De Morgan on the RAS (item 3 of the absence-of-evidence analysis). The deciding records: Blackburn Standard, Dec 1849; Wiltshire Independent, Jan 1849; the Teign committee's own report.

Changes to the numbers

• Southampton datum, Moon, Neptune, tide and Jones verdicts: unchanged.
• The 14,282-mile statement: see item 12 above.
• Absence-of-evidence list: add (7) the Lancet 1856 cooling report, whose original is unread (explanations: a poorly controlled thermometer exposed to the clear sky; an overstated citation by the book; a genuine measurement of a different quantity). Deciding record: Lancet, 14 March 1856. And (8) the Wilkes letter: a single quotation in the book; explanations: an accurate letter, a paraphrase, or a misattribution. Deciding record: the Wilkes and Ross papers.

What the revision does not settle

• Whether the Wilkins report was north or south; the Times item and the ship's log decide.
• The exact refraction at which the long sightings (Orm's Head, Bedford, Nab, the lighthouses) were made; the same single study as before (three eye heights, measured temperature profile) decides them.
• The origin of Findlay's "range" figures; Findlay's text decides.
• The size and sign of the Beachy Head-Dunnose perpendicular-degree disagreement the book quotes; the Ordnance Survey's account decides.