Parallax: Science Contrarian review (Step 2)

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

Page convention: every [read: p.N] is a PDF page (book page = PDF page - 5), as in facts.json. Where I recomputed a figure I mark it [calc]. Calculations use R = 3959 statute miles, so the "8 inches per mile squared" rule is d^2/(2R) [calc]. Refraction is written k (standard value k = 0.13: the ray's curvature is 13% of the Earth's) [memory: high].

Source note: no source gap. The book is readable. Its text layer is OCR and has number errors; I rendered PDF pp.164 and 165 and found two (see Corrections). Claims 2-4 and 6 rest on my own reading of the OCR text of the key passages (PDF pp.16-22, 42-44, 60-66, 72-81, 160-175) plus page images where noted. The pendulum section rests on the Step 1 deep read, which I re-checked against its own quotations.

How I read the job: judge by experiment, not by reputation. Separate "tested and failed", "never properly tested" and "dismissed without testing". Build the strongest honest case. Apply the same rigour to Rowbotham as to his critics.

0. What the evidence base is

• Rowbotham's own text is a set of reported observations (Bedford Level, Nab Light-ship, Eddystone, Camera house, air-gun, pendulum) collected from newspapers and unnamed observers, plus arithmetic on them. He performs few measurements himself in the 1865 text: the Bedford Level (his own, 1838/39), possibly the Plymouth committee of 1864 (he was a member [read: p.167]) and the unnamed air-gun trials.
• The Investigator's material adds: the repeat tests of the canal (Wallace 1870, Oldham 1901, Blount/Clifton 1904, Stretton 1905, Morrow 1896), the contradictory versions of the founding experiment, De Morgan's account of the RAS episode, the Gleason patent text, and the 1882 Balloon Society lecture. All of this is secondary or newspaper-level except where marked; I keep it in the review below whatever my verdict.
• Not yet obtained (named by the Investigator as deciding records): RAS minute book and MNRAS vol. 9 for 8 Dec 1848; the 1849 and 1851 pamphlets; Hampden 1870 and Carpenter's tract in full; Blount 1904 primary; Wallace's own account (S202); the 1881 third edition.

Corrections to Step 1

1. "43-mile Southsea to Ryde sight" is wrong; the distance is 4.5 miles. facts.json, claims.md and sites.md all carry "43". The OCR reads "43 statute miles" on PDF p.173, but the diagram label on p.172 reads "DISTANCE ACROSS 4½ MILES", and the book's own arithmetic fits only 4.5: (4.5/2)^2 x 8 in = 40.5 in, matching its "40 inches" and "2¼ miles to the centre" [read: pp.172-173; calc]. A 43-mile line of sight would be a very different claim. The claim in facts.json should read "a telescope fixed at Southsea pier cuts the same part of a steamer's funnel across 4.5 miles to Ryde, May 1864, no name or numbers given".
2. Southsea eye height is 2½ ft, not 24 ft (PDF p.164, rendered; the OCR "24" is "2½"). Likewise p.165 (Cowes) reads "2½ feet" in the image. With a 24 ft eye the argument would fail by the book's own rule; with 2½ ft the book's 16 ft figure is right (5^2 x 8 in = 16.7 ft) [calc]. This correction goes in the book's favour.
3. The "Nab Light-ship" test was at 2 ft 8 in, distance 8 miles [read: pp.163-164]. The Investigator's lead says "the book's Nab Light-ship" without these numbers; fine, but note the book's 24 ft "should be below the horizon" is computed with no refraction. With k = 0.13 the hull base would be about 20 ft down and a 10 ft bulwark still entirely hidden [calc]; to see "the greater part of the hull" (base hidden by about 5 ft or less) needs k near 0.65 [calc]. See claim 3.
4. Claims.md claim 2 says the flag was "seen along 6 miles" and the "43-mile" sight; the Bedford Level geometry check in sites.md is right. I re-derived it: eye 8 in, 6 miles, the flag top would sit about 13.7 ft below the line of sight with no refraction and about 11.1 ft with k = 0.13 [calc]. The book's own figure (16 ft 8 in below the tangent at 5 miles beyond the tangent point; flag top "13 feet below") is internally correct [read: p.17; calc]. The Wikipedia figure "about 11 ft" matches the refracted case. Step 1 and the Investigator are right on this.
5. The parallel-tubes "experiment" (pp.74-76) was never reported as performed. facts.json says "the digest does not give a result". The text itself gives none: it says "let the following experiment be tried" and then states what "will" happen [read: p.74-75]. The claim "a delay between signals" is a prediction in the future tense, not a result. Step 1 should record: no performer, no date, no data.
6. The air-gun speed contains a unit slip. The book says the surface speed at London is "more than 700 feet per second" and, from that, a 5,600 ft displacement in 8 s [read: pp.72-74]. But its own figure of a 16,000-mile circumference at London gives 978 ft/s (about 667 mph); the true rate at 51.5 N is 946 ft/s = 645 mph [calc]. "700" is the right number for miles per hour, not feet per second (700 ft/s is 477 mph). The book's displacement therefore should read about 7,600 ft by its own premise; the conclusion is unchanged but the quoted number is wrong. This is for the Mathematician as well.
7. The claim "Foucault's suspension was ball-and-socket" (claim 5): the deep read already noted that the globular joint is described only for Jones's apparatus. I confirm that from the quoted passages. Step 1 did flag it; I add the Airy/ellipticity point below, which Step 1 gives only as context.
8. The Neptune item is two-sided. facts.json lists it as "the Neptune prediction does not support Newtonian theory". The record I checked says Le Verrier's predicted position was within 1 degree of where Galle found Neptune on 23 Sep 1846 [web: https://en.wikipedia.org/wiki/Neptune], while the planet's real semi-major axis is 30.07 AU (period 164.8 years) against the 217 year orbit the book cites [web: same page; book digest pp.131-138]. The book's fact is right; its inference (that the prediction failed) leaves out the successful position. See claim 6.

Verdicts at a glance

Claim 1: The Earth is a stationary plane, north pole at centre, south a circumference of ice

a. Is the mathematics internally consistent? The geometry of the book is simple Euclidean trigonometry, and where I recomputed it the arithmetic of curvature is right (8 in per mile squared; 6 ft at 6 miles' mid-chord) [calc]. But the plane model fails its own tests. - The southern degree of longitude. The book argues (pp.55-58) that sailing distances give 22,657 nautical miles round at about 45 S, so on a plane "a degree of longitude on the parallel of Port Jackson will be 69.44 statute miles", against 49.52 on a globe [read: pp.56-58]. But the plane the book and the Gleason map draw (north pole at the centre, equator at about 6,250 miles radius, south at the rim) puts 45 S at 135 degrees of colatitude. One degree of longitude there is 135 x 69.09 x pi/180 = 163 miles, not 69.44 [calc]. The book's own proposed test (measure a degree in Australia) therefore distinguishes the globe (about 49 miles) not from a "69 mile" plane but from a 163-mile one, and the book's prediction does not follow from its picture [calc]. On the same plane the rim (the ice at 90 S) would be a circle of about 78,000 miles; known Antarctic coast is of the order of 11,000-18,000 miles [memory: medium]. - The Sun distance (claim 4) gives different heights from different stations. - Gleason's map is the same geometry and carries the same problem. The patent text itself describes the map as the geography of "first class geographical globe maps" with its departure from a globe called a distortion (the Investigator's lead, [web: https://patents.google.com/patent/US497917A/en]). The patent holder's own characterization is that the layout is a projection of a globe, while the printed slogan "As It Is" says the opposite. Both are statements by the patent holder, who has a commercial stake; neither is neutral.

b. Consistent with established experiments? No, in several independent ways. A planar north-centred layout predicts large distances between southern places. I computed the plane distance between Sydney and Santiago (both about 34 S, 138 degrees of longitude apart) as about 16,000 miles, against about 7,050 miles on the globe [calc; coordinates from memory: high]. Scheduled flights cover the pair in a time consistent with the globe distance [memory: medium; not web-checked, so treat as a lead]. Perth to Johannesburg: about 11,400 plane vs 5,200 globe [calc]. Stationary Earth: the falling-body deviation experiments (Reich, 158.5 m mine, mean eastward deviation 2.8 cm, 106 drops; Guglielmini and Benzenberg earlier) and Hall's 948 drops in 1902-03 are direct tests of Earth's rotation [web: search result, e.g. https://arxiv.org/pdf/1112.5408 and https://periodicos.ufmg.br/index.php/transversal/article/view/34845]. The Michelson-Gale-Pearson experiment of 1925 measured a fringe shift of 230 parts in 1,000 (accuracy 5) against 237 predicted, from Earth's rotation with a 1.9 km ring interferometer [web: https://en.wikipedia.org/wiki/Michelson%E2%80%93Gale%E2%80%93Pearson_experiment]. Wikipedia is a secondary source for these; the primary papers were not read.

c. Tested? The strongest form ("the Earth is a plane") was tested by the inventor only through the sightings under claim 2 and claim 3. His own proposal for a decisive geodetic test in the southern hemisphere (p.58: "the scientific world will demand that the question be decided by proper geodetical operations") was never carried out by him. It was in effect answered by later navigation, but I have no cited source in the folder for a specific southern geodetic degree measurement, so I mark that [memory: medium]. It was not "dismissed without testing" in the sense of refusing to look: the 1870 canal wager shows that mainstream parties did test on his own canal (claim 2).

d. If true, what would have to change? Everything that depends on celestial mechanics and global navigation: gravity as universal, satellite orbits, time zones and sun-angle navigation, Antarctic geography, and the physical meaning of the Michelson-Gale result.

Verdict: Plane geometry: Refuted by calculation (distances, the Sun-height inconsistency in claim 4, and the 163-mile figure), with the southern-degree argument Internally inconsistent as written. "No axial or orbital motion": Tested, not supported (falling-body and ring-interferometer experiments, above).

Strongest honest case for the claim. Rowbotham's method was right in form: he asked for measurements of things that could be measured, and several of his proposals (southern degree, canal sightings, mirror horizon) were real tests. The model is also a coherent and quantitative picture, not a vague one, which is why it can be refuted. The "Anti-Newtonian" of 1819 is a likely earlier source of the disc and ice wall (Schadewald, as relayed by the Investigator [web: https://www.cantab.net/users/michael.behrend/ebooks/PlaneTruth/pages/Chapter_01.html]); that bears on origin, not on truth.

Claim 2: Level water proves it (the surface of standing water does not curve)

a. Mathematics. The book's curvature arithmetic is right: 5^2 x 8 in = 16 ft 8 in; the Orm's Head figure (47^2 x 8 in = 1,472 ft) is right; the Brighton 20-mile figure (266 ft) is right [read: pp.17-21; calc]. The book's approach to the "horizon" fall is also sound for the Nab, Southsea and Cowes cases once the 2½ ft eye heights are used (Corrections 2-3). What is missing is refraction as a quantity. The book mentions refraction only as a "1/12th" correction to lighthouse figures [read: p.179 text] and treats it as small. It is not small in the cases that matter.

Refraction needed [calc, eye 8 in, 6 miles]:

So the book's report (flag and "the boat down to the water's edge clearly visible", p.16) needs k of about 0.9, many times standard, i.e. the ray bending almost as strongly as the water curves. That is not impossible over a calm canal in summer: strong temperature inversions over water can give very large k [memory: medium; Wikipedia's Bedford Level page, via the Investigator, cites an inversion of about 0.11 C per metre as sufficient to make the canal look flat; that is the encyclopedia's characterization, not checked against a paper]. But it has to be measured, and Rowbotham measured neither temperature nor refraction.

b. Consistent with established results? It conflicts with the standard geometry unless refraction is extreme. The book's own results are not consistent with a flat-water law either: the same author reports the Eddystone, at 14 miles and 5 ft eye height, "entirely out of sight" for a committee that included himself [read: p.167], when a flat surface predicts visibility at every distance. Globe geometry with k = 0.13 predicts the lantern's base about 71 ft below the sight line, i.e. the 89 ft lantern marginally visible [calc], and the committee saw less than that, so neither model fits without weather. The Nab Light-ship and the Cowes pier case are consistent with the globe plus moderately strong refraction (Nab needs k about 0.65). One piece of evidence the book prints against itself: "the lower parts of such objects are sooner lost sight of when the sea is rough than when it is calm" [read: p.168]. That is variability of ray path and wave obscuration, which a flat law does not explain and which the book attributes to waves "magnified by the telescope" with no test.

c. Tested? By whom? Replicated? This claim has the best testing history, and the Investigator's findings are pertinent: - The founding observation (1838/39). It exists in at least two versions: the 1849 pamphlet (theodolite, a boat sent 6 miles on the "New Bedford", "a fall of 24 feet") and the 1865 book (bather's eye 8 in above the Old Bedford, a flag 3 ft high) [web: Schadewald Ch.1 as relayed in research/2026-10-06-cantab-planetruth.md; read: pp.16-18]. Schadewald calls the versions contradictory and dates the observation to summer 1839, Wikipedia to 1838. These are the critic's characterization; I have not seen the 1849 pamphlet. The 24 ft figure is (6)^2 x 8 in, i.e. the bare rule with no eye height, so it is not the same arithmetic as the 1865 version. No contemporary independent witness to either version appears in the record the Investigator found. - Wallace, 5 March 1870, on the same canal under a written wager (stake £500): three signals each 13 ft 4 in high, 3 miles apart; the central signal was predicted and observed about 5 ft above the line of the end ones; the umpire, J. H. Walsh, editor of The Field, found for curvature [web: Cambrian 15 Apr 1870, https://newspapers.library.wales/view/3330809/3330814/29/; Nature 1, 581 (1870)]. My bulge check: 6.0 ft with no refraction, 5.2 ft with k = 0.13 [calc]; the umpire's "more than 5 ft" matches. The method is a differential test; it removes the eye-height problem but is still sensitive to refraction if refraction varies along the line. Hampden (the losing party and a party with a stake) published Is Water Level or Convex After All? The Bedford Canal Swindle Detected & Exposed (1870) denouncing it; Carpenter, his referee, published his own account [web: Wallace Online S179aa]. I have read only the first pages of Hampden; the full text of both sides is still to obtain. The Field itself (an interested party, as umpire) reported that Carpenter had previously held a "Parallax" treatise describing a similar canal test "with a result exactly the reverse" and called him an improper referee [web: Cambrian, same URL]. Hampden was later convicted of libel on Wallace (Times, 8 Mar 1875, 12 months, per Wikipedia via the Investigator), and a court later held the wager void [web: https://en.wikipedia.org/wiki/Bedford_Level_experiment]. This is not a case of "dismissed without testing". It is a test that the movement agreed in advance and then disowned. - Later canal tests: Oldham 1901 (middle pole about 6 ft; BA Report 1901 pp.725-6) and Stretton, Ashby Canal, 20 Jan 1905 (about 8 in dip at 1 mile; English Mechanic 80:546), both reported curvature; Morrow and the Koreshan Unity 1896 (Illinois Drainage Canal) reported a concave result, i.e. in the opposite direction from the globe and not in support of a plane either [web: Wikipedia via the Investigator]. Lady Blount and Edgar Clifton, 11 May 1904: a telephoto photograph of a white sheet 6 miles away with the camera 2 ft above the water at Welney; the photographer was reported "surprised" to obtain the image (The Earth vol.5 nos.49-50, via Wikipedia). That is the one on-the-record replication of Rowbotham's visibility claim by a non-trivial observer, and it is the Investigator's best lead for the strongest case. Per my table, a 6-mile sheet at 2 ft needs k of about 0.7 or above [calc, approximate: eye 2 ft raises the visible fraction a little]; it is a result that I cannot dismiss, and refraction measurement is exactly what it lacked. The primary has not been read by anyone in this review. - Plymouth 1864: Proctor (a critic) reports weaker-than-usual refraction on the Eddystone day [web: Schadewald Ch.1]; the book's Plymouth committee found the Eddystone out of sight at 5 ft; the mirror test at 110 ft found the horizon at eye level [read: p.171]. The Investigator's calculation stands: the horizon's dip at 10 in viewing distance is 0.031 in for a 100 ft height, too small to see [calc; web: Proctor via Schadewald]. The mirror test therefore cannot distinguish the models, and the book says so inadvertently: the committee notes that the horizon "rose and fell with the eye", which is just the definition of eye-level horizon. - Balloon concavity: Wise's Aeronautics and another aeronaut [read: p.22 and following], and in 1882 W. H. Le Fevre, C.E., president of the Balloon Society, said he had often seen the surface appear concave, more so with height [web: Denbighshire Free Press, 4 Feb 1882, https://newspapers.library.wales/view/3609549/3609555/55/]. A first-hand aeronaut's statement printed in a newspaper, one source. It describes an appearance. The actual dip angle at 1.5 miles is about 1.4 degrees [calc], small against a field of view; "concave" is a perceptual statement that a flat Earth also needs to explain (a flat plane seen from height would not look concave either). It is consistent with both, so it does not discriminate. - The Southsea-Ryde funnel sight (4.5 miles; Corrections) is a clean, specific, testable claim: the telescope line should cut the funnel 40 in lower at mid-channel on a globe. It is single-source and unnamed; no figures or witnesses are recorded. It deserves a modern repeat with a refraction record.

d. If it were true? If water is level over 6+ miles at sea level under normal refraction, then geodesy (the whole geoid and every survey that corrects for curvature), the GPS system's coordinate model and the sea-level definition would have to change. The book's claim that surveyors ignore curvature [read: pp.60-61] is mistaken as a general statement: his own quotation from Castle's Treatise on Levelling gives the spherical-excess correction as standard practice [read: p.64], and the House of Lords standing order he quotes concerns drawing sections to a horizontal datum, not denying curvature [read: p.60].

Verdict: Strong form (water is flat, so the Earth is a plane): Tested, not supported. The specific anomalous reports (Bedford 1838/39, Blount-Clifton 1904, the Nab hull) are Never properly tested: the one step that would settle them, a measured temperature or refraction profile along the line during the sighting, was never done by anyone I can find in the record. Not "dismissed without testing": Wallace's test was a sound differential design agreed by both sides and ended with the loser's side alleging a swindle and being found against in court.

Strongest honest case. (1) Over standing water, refraction in calm summer conditions can approach the curvature of the Earth. If it does, then the canal observation is a real measurement of refraction, not an error, and nobody has disproved that it happened as reported. (2) Blount-Clifton (1904) is a photograph, not a memory. (3) The mainstream gloss that "the Earth's curvature is established, therefore the sighting must be refraction" is circular unless the refraction is measured. (4) Rowbotham's observations were reproducible in principle; the movement's loss was in the Wallace design, which tested the thing the globe predicts by a method that refraction affects less. Against that: the book's flat inference does not follow even if the sighting is exact; a plane with the Eddystone invisible at 5 ft cannot be right either; and the founding story exists in contradictory versions.

Claim 3: Perspective, not curvature, explains hulls sinking first

a. Mathematics. The "vanishing point at about 3,000 times an object's height" is, to the precision it is stated, the resolution limit of the eye: 1 arcminute = 1/3,438 rad, so a 6 ft figure is lost at about 3.9 miles [calc]. So the number is physical; the law is "objects below the eye's resolution vanish", not "bottoms vanish before tops". A telescope with magnification M moves the limit out by M. The book's own passage says so: a powerful telescope should restore the hull on a smooth horizontal surface [read: pp.162-163]. On a globe it cannot, because the hull is behind the curved surface. This is a genuine differential prediction.

b. Consistent with experiment? The book reports both outcomes. In May 1864, from 2 ft 8 in above the water, "the greater part of the hull of the Nab Light-ship was ... distinctly visible" through a telescope on calm days at 8 miles; on other days "no portion of it could be seen from the same elevation, notwithstanding that the most powerful telescopes were employed" [read: p.163]. The second outcome is the globe's prediction; the first needs k near 0.65 [calc]. The author's own explanation (waves obscure the line of sight, "magnified by the very instrument") is a hypothesis with no test, and it is the opposite of the claim that perspective acts the same on a plane at all times. He also says: "while a powerful telescope will render the sails and rigging ... so distinct that the very ropes are easily distinguished, not the slightest portion of the hull can be seen" [read: p.170]. That is the standard hull-down appearance of a ship past the horizon, with the lower part hidden by a barrier that stays put as magnification increases; it is what the horizon predicts and what "perspective" does not.

The lighthouse list (pp.173-175) is the weakest data in the book. The author takes catalogue ranges ("visible 23 nautical miles") and applies the 8-in rule to find lights "124 ft below the horizon", etc. [read: p.175]. The catalogue's own stated rule is that the range is computed from flame height plus 10 ft for the deck, with refraction sometimes adding more [read: p.166, quoting Lighthouses of the World (1862)]. A geometric range for Bidston (228 ft light, 10 ft eye) is 1.06 x (sqrt 228 + sqrt 10) = about 19.5 nautical miles, against the catalogue's 23 [calc], so the catalogue figure is about 18% longer than no-refraction geometry; refraction at k = 0.13 gives about 21, and k near 0.35 gives 23 [calc]. That is a stretch from the standard value but of ordinary scale, not "hundreds of feet". The Grimsby tower "seen 60 miles out at sea" is a sentence from the Times account of the Queen's visit, 16 Oct 1854 [read: p.179]; the geometric range of a 300 ft tower from a 10 ft eye is about 22 nautical miles [calc]. The book treats a newspaper's figure as a measured distance and builds a 2,600 ft discrepancy on it. No measurement is behind it. I note this plainly as bad data from the inventor's side, as the brief requires.

c. Tested? The book's own committee tests (Plymouth 1864, Nab 1864) are real and went both ways; the discriminating telescope test was done once on a good day and failed on others. No neutral, controlled test of "does a long-focus telescope restore a hull below the horizon, with k measured" is on record in the folder. Rowbotham and the Plymouth committee are named [read: p.167]; the Nab and Southsea observers are unnamed.

d. If true? Optics would need an "ideal flat surface" ray law different from the one used in every surveying and marine telescope; and ships and satellite horizons would have to be explained without a horizon.

Verdict: the vanishing-point law as stated: Tested, not supported (the author's own days with no hull visible; hull-down appearance). The telescope-restores-hull prediction under neutral conditions with refraction measured: Never properly tested. Circumnavigation and the lost day: the book's argument (pp.42-44) is correct logic: the lost day and circumnavigation do not by themselves distinguish a plane from a globe; I agree with him on that narrow point [read: pp.42-44]. They are not evidence for a plane either, and the southern-distance problem (claim 1) is what discriminates.

Strongest honest case. The vanishing point is a real optical phenomenon. The restore-by-telescope prediction is risky and was reported to succeed at least once on calm water. Mainstream accounts treat horizon dip as a one-line fact, but they also rely on refraction numbers that vary with weather by a factor of several; nobody on record repeated the Nab telescope test with k measured. That leaves a gap where a modern repeat could settle it.

Claim 4: Sun, Moon and stars are small and near and move over the fixed Earth

a. Mathematics. The two-station method is valid trigonometry for a plane and a nearby Sun. Applying it to the book's data [calc]: - London 55 deg 18' and Ackworth 53 deg 2', 151 miles apart [read: p.79]: Sun height H about 2,510 miles, and the height does not match the "under 4,000" in a way that is falsifiable. For a distant Sun and a globe, the altitude difference should equal the latitude difference: 151 miles is 2.19 degrees; the reported difference is 2.27 degrees [calc]. The globe fits this to about 0.08 degrees (about 4%). - Southampton officer, 45 deg and 38 deg, 800 miles apart [read: p.79]: H about 2,860 miles by itself. On a globe with a distant Sun, 800 miles on a meridian is 11.6 degrees of latitude, so the altitude difference should be about 11.6 degrees; the report gives 7. On the plane with H = 2,508 from the first set, the far altitude would be 37.2 degrees against 38 reported [calc]. So this one datum, if real, favours the plane. I do not suppress it: it is documented in one printed source, attributed to an unnamed Royal Engineers officer at Southampton, undated ("recently made"), with no record of the stations, the date or whether the readings were simultaneous or on the same meridian. No second source found. Mainstream practice would predict the globe figure for a true meridian pair; the discrepancy of 4.6 degrees is far more than an instrument error, so either the stations were not on a meridian, the readings were not simultaneous, or the report is wrong. It needs the Ordnance Survey records to resolve. - The consistency test the plane cannot pass. If the plane model is right and the Sun is at one height H, then H derived from any pair of noon altitudes must agree. Using the plane's own distances (69.09 miles per degree of latitude) and the equinox noon altitude 90 - latitude (the book prints the almanack altitude table, [read: p.81]), H comes out 3,868 miles from latitude 15, 3,590 from 30, 3,109 from 45 and 2,393 from 60 [calc]. A single Sun height cannot be right. The globe gives a single formula, altitude = 90 - |latitude - declination|, that sextant navigators have used worldwide for centuries [memory: high]. This is the decisive calculation and it uses only the book's own geometry. - Apparent size. On the plane with H = 3,000 miles, the Sun's slant distance at altitude 10 degrees is 17,276 miles against 3,000 overhead, so its angular diameter should be about 6 times smaller at 10 degrees altitude [calc]. The Sun's apparent diameter is within a few percent the same from noon to sunset [memory: high]. The book answers sunsets by "perspective" (p.80+), but the perspective law acts through angular size, so that answer leads to the predicted shrinking. - Stars within 6,000 miles. The star "distance" rests on the same triangulation with the same defect. Stellar parallax was measured in 1838 (Bessel, 61 Cygni) before the book was printed [memory: high; not web-checked]. The tubes "experiment" (Correction 5) was never reported as performed, and its logic (a one-yard baseline) does not bear on the stars' distance.

b. Experiments. Lunar eclipses with the Sun above the horizon (Paris, 19 July 1750; [read: pp.94-103, via digest]) are real observations, but they are what refraction gives at the horizon (about 35 arcminutes lifts both bodies above the geometric horizon) [memory: high]. They are not evidence that the shadow is not the cause. The thermometer argument is a calculation problem: the full Moon's light is about 2.5 x 10^-6 of the Sun's [calc from 3.4 mW/m^2 against 1361 W/m^2, memory: medium], so even De La Hire's 300x or Forbes' 3,000-6,000x burning-glass concentration gives an irradiance of at most a few per cent of ordinary sunlight, too small to read on a thermometer of 1850s sensitivity. The null result is what a reflecting Moon predicts, so it does not show the Moon is self-luminous. Lancet 1856 thermometer tests [read: digest pp.103-107] are described in the digest; I did not read them in detail.

c. Tested? Parallax and aberration were measured by astronomers; the book's tests were never done in a controlled way. The altitude data in the book are cited secondhand from the Ordnance Survey and an unnamed officer.

d. If true? Stellar parallax, aberration and the entire distance scale would have to be rebuilt; the Sun's constant angular size would need a new optics.

Verdict: Sun and stars at those distances: Refuted by calculation (the single-H consistency test, the angular-size test, using the book's own geometry). Moon self-luminous: Refuted by calculation (the null thermometer result is expected). The one unusual datum (Southampton, 800 miles) remains Never properly tested as a record: it needs the Ordnance Survey source.

Strongest honest case. Plane trigonometry applied to two nearby stations does give a finite Sun height, as any pair of stations will; the method is not nonsense, it is an incomplete test, and the book's "demonstration" is only that two stations fit one height. A proper test needs three stations, which the book half-supplies (set 2 fits H from set 1 to within 0.8 degrees). The honest result is that the globe fits set 1 more closely, the plane set 2, and nobody on record resolved the discrepancy. A modern repeat would settle it in an afternoon.

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

I rely on the deep read (deep/earth-not-globe-book-c293c9.md) and re-checked its quoted numbers against its own table.

a. Mathematics. The book's figures agree with the standard sin(latitude) rule within minutes of arc (Paris 11.29 deg/h, period 31.9 h; Edinburgh 12.43 deg/h; Cairo 48.0 h) [read: pp.147-150; calc in deep read]. Jones's prediction of 1 degree per 5 minutes at Manchester is correct [calc]. The book's three-point objection is a logic argument and an engineering argument: - Point 2 ("what forces the conclusion that the Earth moves under the pendulum rather than the pendulum over the Earth?") is a fair question about interpretation. The answer is that the plane stays fixed relative to the stars in an inertial frame, which is the mainstream view; in a rotating frame it is the Coriolis term. But the rate (sin latitude), its sign reversing between hemispheres, and its vanishing at the equator are specific predictions that any alternative cause (a twisting joint) must also reproduce. A random twist in a suspension does not give a rate proportional to sin(latitude) at five places. The book never shows its twist cause reproducing that rule [read: pp.158-159]. - Point 3 (ball-and-socket) applies to Jones's apparatus [read: p.155], not Foucault's [read: p.145]; no measurement of any twist is offered. - Point 1 ("variable, therefore not evidence"): it is right that short pendulums show irregular behaviour, and the mainstream has a quantitative account of why. The elliptical-orbit (Airy) precession is Omega = 3ab/(8L^2) x omega, where a, b are the semi-axes of the ellipse, L the length and omega the swing frequency, and it can swamp the Foucault rate [web: search result summarising the formula, e.g. https://arxiv.org/html/2502.12230v1]. The Dutch physicist Kamerlingh Onnes's thesis showed that suspension elasticity and imperfection produce beats between the horizontal modes [web: https://en.wikipedia.org/wiki/Foucault_pendulum]. Applying the formula to Jones [calc, approximate because the swing is large]: L = 7.62 m, a about 1.4 m: a start with a minor axis of only about 6.5 mm (under 0.5% of the amplitude) adds the 0.23 degrees per minute by which Jones's reported 0.43 degrees per minute exceeds the Foucault 0.2. Jones himself named "some slight lateral bias at starting" before the run [read: p.155]. So the excess is the ordinary size of a launch error, and the single 7-minute interval reported cannot tell. This is more than a 'dismissal'; it is a quantified explanation, and it also shows that Rowbotham's point 1 identifies a real artefact whose size is measured, not a refutation.

b. Experiments. Foucault's Pantheon pendulum (67 m, 28 kg bob) turned once in about 31.8 hours at Paris [web: https://en.wikipedia.org/wiki/Foucault_pendulum], and the long-pendulum case removes most of the launch problem. The 1925 ring interferometer measurement of Earth's rotation by a different physical principle agrees with the predicted rate to 3% [web: Michelson-Gale page, above]. The Foucault rate also changes sign in the southern hemisphere [memory: high], which a magnetic-meridian or suspension-twist account does not predict.

c. Tested? The book reports one experiment (Jones) and cites two reports of a magnetic-meridian preference: an unnamed writer, and a "scientific gentleman in Dundee" in the Liverpool Journal, 17 May 1851 [read: p.153]. Neither gives a method or numbers; one newspaper source each; no replication found. I do not discard them: they are an observational claim by two unnamed experimenters. Foucault's and Jones's bobs were brass [read: pp.144, 154], which is not magnetic, so a magnetic mechanism has nothing to act on in those two cases; no test of a magnetised bob is recorded. The Investigator's search for the Jones event found nothing independent (negative), so Jones's result is one newspaper report (Manchester Examiner, 24 May 1851) reprinted in the book. How it was received: the book quotes objections (B. A. C., T. T.) that were theoretical and conceded the facts; the experimental objections were the Dundee and Jones items. I found no record of Foucault's result being blocked or reanalysed; it was repeated by Arago at the Observatory (said to be fully confirmed, [read: p.141]).

d. If true? If the pendulum plane followed a local magnetic or suspension cause, the sin(latitude) rule and the sign reversal would be coincidences across places and the mainstream account of Coriolis forces in a rotating frame would need a rival.

Verdict: "The turning is inconstant, so it is not evidence": Tested, not supported (the quantified Airy and suspension effects, the Pantheon 67 m result and the independent 1925 measurement). "Twisting ball-and-socket causes it": Never properly tested by Rowbotham (no measurement; the description is of Jones's apparatus). The magnetic-meridian reports: Never properly tested (two newspaper-level reports, no data). Interpretation point 2: Not testable as stated as a philosophical complaint, answered by the rate law.

Strongest honest case. The book's picture of the 1851 reports is accurate: the early demonstrations were short, launched by hand, and some did show wrong rates (Jones at 2.1x), and the mainstream publicly said so (Airy 1851). The book's logical point 2 is a fair question, and a sceptic could ask for the rate law at more than five places on the same day, which was later done. The author reports no experiment of his own in this section [read: pp.140-159], which should be recorded.

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

• Neptune. Fact: Le Verrier's orbit differed from the real one (period 217 against 164.8 years) [read: digest pp.131-138; web: https://en.wikipedia.org/wiki/Neptune]. But the same source gives the position as within about 1 degree of the predicted place when Galle found it on 23 September 1846. Reducing this to "the prediction failed" suppresses the half that succeeded. The book is correct that the orbital elements disagreed, and it is fair to say a successful search with partly wrong elements is not a clean validation of the theory. Verdict: Not supported as stated (a failed test of Newtonian theory); the mismatch is real and documented.
• Air-gun and mast drop. The premise that a vertically fired ball should land 5,600 ft west is wrong. Under the mainstream account the ball keeps the Earth's horizontal speed while in flight, so the predicted westward displacement is the Coriolis term only. For an 8-second ascent at 51.5 N it is 4/3 x Omega x g x cos(lat) x t^3 = about 0.30 m (a foot) [calc; formula standard, memory: medium]. The book reports "within a few inches", twice "the mouth of the barrel" [read: p.73] against a predicted foot, with no measurement of drift, wind or drag, and a 16-second flight for a hand air-gun, which would need a 78 m/s launch in a vacuum and a rise of about 314 m [calc] that I cannot verify for the guns of the 1860s. The premise is Refuted by calculation; the reported result is Never properly tested against the right prediction (a foot, not a mile). The unit slip in the book's own speed (Correction 6) is the author's error; I record it.
• Tides. The book offers the floating Earth rocking twice a day under air pressure [read: digest pp.111-115]. No test is proposed; it does not predict the lunar timing (about 24 h 50 min) that the mainstream account explains [memory: high]. Verdict: Not testable as stated.

How it was rejected: the book's claim that astronomy was "assumed" has partial truth (the book's complaint about the Foucault "proof" circularity, p.156, is a fair point about how the experiment was presented to the public in 1851), but the experiments cited against the mainstream fail on quantities the book did not compute. No negative experiments of the mainstream side were blocked or reanalysed in what I read.

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

The physical content of the claim (a flat, fixed Earth with a firmament) falls under claims 1-4. The theological content is not an experimental question. Verdict: Not testable as stated. I keep it in the record: the book (Section 14, pp.178-229) frames the plane as the answer to atheism and to the "plurality of worlds"; it is an interested motive, stated openly by the author. Zetetic method ("inquiry before conclusion") is then in tension with a conclusion that is fixed in advance by text. I note that tension as a methodological criticism of the inventor.

Weighing the Investigator's findings

Pertinent findings kept, whatever my verdict: the three diverging accounts of the founding experiment (own work); Le Fevre's balloon statement; the Blount-Clifton photograph; Wallace 1870 and the Hampden-Carpenter-Field dispute; Oldham 1901; Stretton 1905; Morrow's concave result; Proctor's Plymouth account; De Morgan's account of the RAS 1848 episode (the 1849 pamphlet says "a paper read before the Royal Astronomical Society"; De Morgan, then Secretary, wrote that no account appears in the Notices and that he read some of the arguments aloud "for your amusement" [web: Schadewald Ch.1]; this is a critic and an officer's statement; the deciding record, the RAS minutes, is not obtained); the Gleason patent; the lecture trail 1849-1882; the absence of the Jones event in the record found (negative search). The Investigator's geometry checks are right (I re-derived them). Two items in the Investigator's text need the Step 1 correction: the "43-mile" sight is 4.5 miles.

Absence of evidence: Rowbotham's flat-Earth lecturing winds down in the mid-1870s while the Zetetic Society continues (1883) and the Universal Zetetic Society (1893). The record does not go dark; no analysis of a disappearance is needed. The Jones pendulum event is the one place where the record is silent: the only source is the Manchester Examiner reprint in the book. Competing explanations: it was reported only locally; it was not noteworthy; the report may be inaccurate. Deciding record: the Manchester Examiner of 24 May 1851 and the Manchester Philosophical Society minutes.

How the claims were rejected (the Mallove questions)

• Rowbotham's claims were tested on his own ground (the canal, 1870), by a method agreed beforehand, with both sides' referees. The negative result was disowned by the party, who published a "swindle" pamphlet; the umpire's finding for curvature was upheld in the sense that the libel conviction followed. The contested parts (Hampden and Carpenter's objection to the telescope diagrams, the Field's claim that the referee knew the earlier result) are not resolved in the folder; the full pamphlets should be read. Both sides had stakes: Hampden and Carpenter as the wager's party, The Field's editor as umpire.
• The mainstream side was not neutral either. The Royal Astronomical Society episode (1848) is described only by De Morgan. Critics such as Proctor and Schadewald are partisans of the globe, and the Wikipedia articles are secondary. None of the negative tests I found was a modern, instrumented, refraction-measured repeat. That is the real gap in the record.
• No evidence of data being omitted or funding being blocked appears in the folder or in the Investigator's finds. I looked for it and did not find it; absence in this record is not proof of absence.
• Rowbotham's own handling of data is the weaker side: figures from newspapers used as measurements (Grimsby), a unit slip (air-gun), contradictory accounts of the founding experiment, an RAS credit that the Society's secretary did not support, unnamed observers for the key southern and Southampton data, and the use of "perspective" as a rescue for each failed prediction. The same standard applies to the mainstream gloss "it is just refraction" when refraction is not measured.

What would settle it

1. A modern repeat of the canal sighting with a temperature profile on the line and a long-focus camera at several heights (the Blount/Clifton design with k measured), done on calm summer mornings and repeated across seasons.
2. A three-station simultaneous noon-altitude set on one meridian (for example from public sextant or astronomical data), checking one Sun height.
3. The Ordnance Survey source for the "Southampton 800 mile" data, or any record of it.
4. A Foucault pendulum 10 m or longer, launched by burning a thread, run for hours at two latitudes, with its Airy precession fitted.
5. The southern degree of longitude measured by geodesy at 45 S (about 49 miles on the globe, 163 on Rowbotham's picture).

Sources and tags

• [read] Book pages cited (PDF numbering); OCR corrected from page images at PDF pp.164-165; Step 1 deep read for pp.138-159.
• [web] https://en.wikipedia.org/wiki/Foucault_pendulum; https://en.wikipedia.org/wiki/Michelson%E2%80%93Gale%E2%80%93Pearson_experiment; https://en.wikipedia.org/wiki/Neptune; web-search results on falling-body deviation (Reich, Hall; e.g. https://arxiv.org/pdf/1112.5408) and on the Airy precession formula (https://arxiv.org/html/2502.12230v1). Wikipedia pages and search summaries are secondary; the primary papers were not read. Web calls used: 6 of about 6.
• [web] via the Investigator's notes (not independently re-fetched): Schadewald, The Plane Truth; Welsh Newspapers (Cambrian 1870, Denbighshire Free Press 1882); Wallace Online S179aa; Google Patents US 497,917; Wikipedia Bedford Level experiment.
• [memory] Stellar parallax (Bessel 1838): high; sextant noon-sun navigation: high; refraction at the horizon about 35 arcmin: high; Sydney/Santiago/Perth/Johannesburg coordinates: high; flight times: medium (not checked); Antarctic coast length: medium; inversion-induced large k: medium; Moon/Sun irradiance ratio: medium; Coriolis projectile formula: medium.
• Calculations: [calc] run with numpy in the project venv; assumptions stated in the text.