DIO and Dennis Rawlins:

A Few Successes & Vindications

A sample of the decades of DIO & DR vindications that have made DIO a respected journal among able scientific scholars (as against the phalanx of cemental-case pols, pop-writers, and cult-goons whose several anti-DR crusades have so consistently backfired) will be set out below:
[DR does not pretend to be always right. To the contrary, he has made a point of highlighting his very, very few errors — only 2 of substance (neither debuting in DIO) throughout a 4-decade research career — adding severe criticism of his slips. (Even poking fun at himself for one of them in boldprint on the cover of his own journal.) This is not a virtue which has proved particularly contagious among DR's detractors.]

  1. In the 1960s, the official US Naval Observatory mass of Pluto was c.1 Earth (defying valid 1930s reasoning by Bower, Brown, & Baade, etc.), and the Percival Lowell mathematical prediction of the place and orbit of Pluto in 1915 (long before its 1930 discovery) was still thought to have merit. But in Sky&Telescope 38:160-162 (1968 March), DR contended — against a then-majority of scientists (e.g., Eckart, Brouwer, & Clemence used USNO's 0.91 Earths) — that the famous, remarkably correct Lowell orbital prediction was a complete accident, because Pluto's mass was greatly too small to cause sufficient perturbations on Uranus' orbit to justify a prediction that was supposed to have been based on such perturbations. The truth of DR's 1968 position is now totally undisputed.

  2. Following up on this in top journals of the Amer Astr Soc (Astronomical Journal 75 [1970 September] pp.856-857) and (also 1970) the Royal Astronomical Society of London, DR ran a perturbational study finding that measuring Pluto's mass via perturbations on Uranus & Neptune was too insensitive. Also accounting for Pluto's recent unexpected failure to occult a star, DR concluded that the best method for mass-measure was to use Pluto's various resemblances to Neptune-satellite Triton, which indicated that the two bodies had similar masses. Not an entirely new idea but now more discernable as the preferable approach, thus for the 1st time producing a specific mass-estimate. So DR's final estimate was 1/40 of an Earth (MNRoyalAstrSoc 162 [1973] pp.261-270). The matter was definitively settled in the mid-to-late 1970s (D.Cruikshasnk 1976 & R.Harrington 1978), and it turned out that, of all the many estimates of Pluto's mass ever previously published, DR's was the closest to the truth.
    (DR-haters have doubtless been searching for a better one for years. Lotsa luck.)
    [DR's achievement in this regard has occasionally appeared in the Wikipedia article on Pluto's discovery — but has always been eliminated immediately, despite the (of-course-establishmentAryan) monitor's inability to cite a better pre-1976 value. Because there isn't one.]

  3. The 1973 estimate would have been much better had the mass of Triton not been so over-estimated at the time. It is now known (via Charon and Voyager 2) that the two bodies do indeed have very similar masses. Thus, decades later, DR's preferred method for finding Pluto's mass has been validated.

  4. In 1972 the sensational Jovian-sized “Brady Planet” was proposed out of the famous Livermore Lab (Univ Calif Berkeley). DR was the 1st astronomer to computationally check the matter (using math he'd developed in MNRoyAstrSoc 147 [1970] pp.177-186) and publicly announce the body's non-existence: Baltimore Evening Sun (1972/5/1). Within a year the argument was over.

  5. In 1973, DR published the book Peary at the North Pole: Fact or Fiction (Luce, Wash DC), showing that the US' greatest Arctic explorer, Rob't Peary, faked his 'til-then-universally-accepted 1909/4/6-7 attainment of the North Pole. At pp.151-153 it was revealed for the 1st time that Peary's sole civilized companion, Matthew Henson, in his only detailed statement (Boston American 1910/7/17) of activities at the Pole camp, reported that upon arrival at the Pole camp Peary took observations of the Sun to find position and was disappointed: “his face was long and serious. He would not speak to me.” Peary suddenly for days stopped talking to his diary and to Henson, his faithful exploring companion of two decades. This new evidence, along with navigational analyses published by DR in the US Naval Inst Proceedings (1970 June), Dartmouth College's Polar Notes (1970 Oct), & Oslo University's Norsk Geogr Tiddskrift (1972), plus Fiction's publication of Henshaw Ward's 'til-then-establishment-suppressed discovery of the Bowdoin College navigation-math expert whom Peary secreted in his home for weeks before producing his easily fakable sun-shot “proofs” (Fiction p.286), convinced the great majority of reviewers that Peary's claim was dubious. This included the prominent 4pp review in the 1975 March Annals of the Association of American Geographers 65:79-82. Given the fact that the New York Times was Peary's top newspaper fiscal backer from 1909 and decades after, the Peary claim's present status is best understood from the 2008/1/12-13 p.1 International Herald Tribune obit for E.Hillary, excerpted at the News Notes of DIO 14 [2008] p.2 and from the 2009/9/7&8 New York Times Science assessment of The Polar Controversy.

  6. In his 1973 book, Fiction, DR said at p.140 (see also p.87) that Amundsen checked his steering (left-right course errors) — a log-sph-trig procedure in those days — en route to the South Pole in 1911. This position was later attacked by Drewry&Huntford, the Pres. of the Univ. of Alaska, and (1990) National Geographic's NavFou. But a few years after that, Amundsen's longitude observations were discovered by Ted Heckathorn and (at Wm.Rawlins' instigation) Norwegian archivists. See Washington Post 1993/6/1, Science 1993/6/11. In DIO 2.2 [1992], the Norwegian and British 1911-1912 South Pole expedition-navigators' log-sph-trig math is fully set out, with detailed samples of each party's calculations.

  7. In 1973, in Fiction's final chapter, DR made the then-apparently outrageous assertion that the 1st three claims to the North Pole (F.Cook 1908/4/21, R.Peary 1909/4/6, R.Byrd 1926/5/9) were all fake, thus the 1st genuine claim (1926/5/12) was that of the FOURTH claimants, the Amundsen-Ellsworth-Nobile Norge dirigible trans-Arctic expedition. The Norge's having the 1st solid claim to attaining the North Pole is now the general opinion among exploring professionals. (Further polar-history vindications below.)
    Not that the usual forceful public apologia won't continue (to try breathing life back again into the Peary claim's mummy). But the Cook, Peary, & Byrd claims are effectively dead; and DR is the prime reason for the last two funerals. The first funeral is primarily due to R.Bryce (DIO's Editor and member of its Induction Award committee), climbers Belmore Browne & Hudson Stuck, and the Boston Science Museum's late President-Emeritus (and double National Geographic medalist) Brad Washburn, both involved (also Keith Pickering & DR) in DIO's famous issue debunking Cook: DIO 7.2-3 [1997]. (See also Bryce & DR DIO 9.2-3 [1999].)

  8. In Peary … Fiction 1973 pp.72-75, DR was 1st to detect (even while barred from access to the primary source, the Peary Papers in the National Archives) that Peary had in 1907 faked his claim to have seen the summits of non-existent “Crocker Land” on 1906/6/24&28. On the transit data which societies assumed Peary had taken during his sighting of this “discovery” when in 1913 launching the Crocker Land Expedition, Dennis Rawlins wrote unambiguously in 1973 (again, without access to the diary at that time) “No such measurements ever existed.” (See Fiction p.74.) When the Peary Papers were subsequently opened, DR found (Washington Post 1989/4/20 p.22) that Peary's diary entry of 1906/6/24 — written upon the exact spot later claimed for the Crocker Land discovery of that date — states (see photo of diary-page): “No land visible”. Vindications don't (can't) get much firmer.

  9. At 1973's Fiction p.80 DR sided with the establishment position, agreeing with those who have long doubted 2nd Explorers Club Pres. Frederick Cook's alleged 1st ascent of Mt.McKinley (1906 Sept), there noting (as B.Browne & Washburn had also) that the Cook “summit” photo published in his 1908 book (opp. p.227) accidentally included in its distant background a bit of Mt.Grosvenor at an angle impossible from Mt.McKinley (but identical to that from the molehill now called “Fake Peak”, right where Cook's companion said the photo was taken). Only a fragment of the photo's background got into his book because he had deliberately cropped off almost all of it. (The Mt.Grosvenor sliver slipped through accidentally.) But, thanks to Rob't Bryce, the full original “summit” photo was unexpectedly recovered and debuted as DIO's 1st centerfold: DIO 7.3 [1997] Fig.18 [pp.68-69], with clear blow-up analyses by Keith Pickering (Figs.6&8 [pp.52&54]) of several giveaway background features. Bryce's find so definitively ended the Cook-McKinley controversy that it was reported (with credit to DIO) on the front page of the New York Times: 1998/11/26. Finally, don't miss Bryce's latest articles, in DIO 21 [2017].

  10. Fiction p.25 located for the 1st time the actual farthest north of Isaac Israel Hayes' 1860-1861 expedition (backed by an array of US academic societies unequalled before or since in eminence, for a polar expedition): Ellesmere Island's Cape Collinson, barely past 80°N, c.100 mi south of his claimed farthest, 81°35'N. Subsequent much more intensive, pioneer examination of his record-book provided a perfect match for Cape Collinson by three independent criteria: the compass bearings of distant capes (recorded at farthest), his hitherto-unexamined drawing's match's of the scene, and his coastal-sketch's match to internet-map images of the spot.

  11. DR has induced a simple hypothesis that fits the 1°1/2 exaggeration: Hayes created his 90-nautical-mile latitude-enhancement on Ellesmere Island by simply flipping a digit! He just inverted a nine into a six (merely nine seen-from-a-different-perspective, after all!) at the degrees place in his farthest-north's unshared meridian sextant-shot. Halving this double-altitude's 3°-enhancement produced a latitude error of 1°1/2 or 90' or 90 nautical miles, lifting him from 80°05'N actual latitude to 81°35'N reported. The fact that Hayes' announcement of his Farthest gave EXACTLY the correct longitude for his Cape Collinson position is confirmatory: the 19th century polar explorer's standard sphtrig method of finding longitude from non-noon solar sextant-data requires knowledge of latitude (found via noon solar sextant-data) as part of the calculation, so Hayes knew his actual latitude was 81°05'N, evidencing conscious fraud. Did he deliberately leave his accurate longitude as a clue-message to that effect — and to show that he was indeed an expert at genuine navigation? (As shown by his fine 1854 Ellesmere maps for E.K.Kane's 1853-1855 expedition — before he joined the mutineers against Kane in 1855.) Finding latitude was mere arithmetic, while standard longitude-determination required logs & spherical trig in those days.

  12. In 1973, DR published (Mon. Not. Roy. Astr. Soc. 1973) a novel perturbational study (the 1st ever that melded special and general perturbations for planet-searching) to show that new planets beyond Neptune must be modest in mass and that if a (particular specified) slice of the zodiac yielded none (it didn't, as Charles Kowal verified optically at Mt.Palomar) then the serious masses of the Solar System ended at Neptune. This unsensational result was the 1st study that based such a prospect upon gravitational analysis, not conjecture. The truth of this proposal has subsequently been established by ultra-sensitive space-craft probes.
    [Thus, optical discoverer J.Galle's 1846/9/25 proposal to Leverrier of the name “Janus” for the then-new planet is redeemed: “the most ancient deity of the Romans, whose double face signifies its position at the frontier of the Solar System.” Quoted by Nick Kollerstrom JAHH 12.1 [2009] p.66.]

  13. In the late 1970s, DR investigated the mystery of the ancients' two standard but quite disparate Earth-sizes (differing by c.40% !) and realized that neither was based upon the almost universally accepted Alexandria-Aswan legend (promoted by, e.g., Carl Sagan's popular Cosmos TV-series) but rather upon clever stay-at-home methods which were much simpler physically, using lighthouses or sunsets. DR's analyses of atmospheric refraction's effect upon results obtained by such methods showed for the 1st time that both methods' results would be off — multiplicatively (lighthouse) or divisionally (sunset) — by factor 6/5, so the atmospheric-refraction theory for the lighthouse and sunset methods predicts 20% high and 17% low, respectively. Now, according to the standard definition of the Greek stade (185m): Eratosthenes' original value is 19% high.
    Further (astonishing) confirmation of the match waited 26y. (See below.)

  14. The Poseidonios value (used in the Ptolemy Geography) is 17% low, exactly the atm-refr theory's prediction for the double-sunset method. I.e., the agreement of theory with the two prime actual ancient values is good to c.1%.

  15. The attractiveness of the sunset method (discovered in 1978 by Barbara & Dennis Rawlins during a La Jolla beach sunset) was vindicated when the well-known referee (Jearl Walker) for the Amer J Physics said he'd never had such fun refereeing a paper, and agreed that the idea was true mathematically and probably historically. The American Journal of Physics (American Physical Society) published it as its lead article in 1979 Feb (AJP 47.2:126-128). It shortly went into Scientific American (May), and then (starting in the 1990s) was featured for years in a standard college textbook intimately known to thousands of physicists: Halliday, Resnick, & Walker. The book's opening photo was a sunset, and the DR article was explained with generous credit in the 1st few pages of the book's main text.

  16. The atm.refr. theory's fit to both ancient C-values and to the standard 185-meter stade ultimately became a cover story for Griffith Observer 82.8:9-16 (2018 August).

  17. In the mid-1970s, DR entered the already-hot controversy over whether 2nd century AD astrologer-mathematician Claudius Ptolemy faked his observations, as centuries of astronomers had suspected. (See, e.g., Tycho Opera Omnia 3:337.) Owen Gingerich defended Ptolemy from the charge for decades, promoting any available alibi to fend off ever-accumulating evidence of Ptolemy's theft of the entire Ancient Star Catalog from 2nd century BC astronomer Hipparchos: 1025 stars, which Ptolemy claimed (Almajest 7.4) he'd entirely observed outdoors. That at least a large part of the Catalog was stolen is no longer denied by anyone, and virtually all historians now believe the fraction was nearly 100%. But public acknowledgement is sparse.

  18. Further, when DR noted that Ptolemy had goofily claimed seeing the same greatest elongation of Venus at two differing elongations, on two separate occasions 37 days and 37° apart (136/12/25 & 11/18: Almajest 10.1&2), Gingerich was finally reduced to claiming (Isis 93:70-74 [2002]) not that Ptolemy didn't cheat but that, in order to get Venus' orbital elements, he was FORCED to fake these data because of a Venus near-resonance. (The Venus-made-me-do-it defense.) DIO 11.3 [2002] immediately published 3 methods by 3 different well-known scientist-historians (D.Duke, D.Rawlins, H.Thurston) showing how Ptolemy could have gotten Venus' elements easily & honestly. (No error has since been found in any of the 3 methods.) Vindications don't get much funnier. (There is no longer any serious scholar who argues that Ptolemy did not fake data; only the extent of the fraud is quibbled about by a few die-hards. Mainly James C. Evans, Editor of the Journal for the History of Astronomy, who is never wrong about anything — e.g., DIO 16 [2009] ‡1 §A2 [pp.3-4], ‡4 §G2 [p.46].) As Gingerich noted aloud a decade ago: the implicit victory of Ptolemy-skeptics was iced when modern star-catalogs were successively named “Hipparcos” and “Tycho”, skipping Ptolemy. Yet virtually all prominent institutions (1979-to-date) continue to protect Ptolemy by publishing promotions while refusing to publish a coherent review of the many obvious evidences indicting him. (Because interested parties have purveyed to institutional chiefs the crock that an ASTROLOGER's criminality is an embarrassment to SCIENCE?)

  19. DR's much-resented “sTARBABY” (Fate 1981 Oct) revealed — along with a mass of dirty establishment politics — that the Committee for Scientific Investigation of Claims of the Paranormal (CSICOP) had screwed up its initial Scientific Investigation (testing M.Gauquelin's neo-astrology) and tried by threat, bribe, expulsion and post-hoc sample-splitting to cover up the fact. Though it has become a test of loyalty among CSICOPpers to promote the lie that there was (and is) no coverup, no one denies that [a] the experiment was a disaster; [b] DR had warned CSICOP in writing (1975/11/15) and by phone (1975/12/6 & 1976/3/8) of the experimental flaw that ultimately sank its test; [c] DR was first to insist upon telling the public the embarrassing truth (and to explain the statistics in detail) — for which insistence he was ejected from CSICOP's board. (By unannounced “election”.)

  20. When the 1613 drawing of Neptune's position near Jupiter in Galileo's records was announced, DR immediately contributed to Nature 290:164 [1981/3/12] mathematical analyses showing that its discrepancy versus modern orbital theory was not significant. The leading figure in the field, CalTech-JPL's Myles Standish checked the matter by independent reasoning and shortly concurred (idem). And the discoverer himself, Chas. Kowal (STSI), has recently joined the majority and made it unanimous: DIO 15 [2008] p.6. (All three of these scientists are now with DIO.)

  21. In 1982, DR was 1st to publish (in the world's most prominent history of science journal, Isis) the date of ancient astronomer Aristyllos, by running a least-squares with his date and latitude-error as simultaneous unknowns. Result: c.260 BC (overturning the previous generally accepted estimate: c.300 BC) and virtually null latitude error. Y.Maeyama later verified DR's Aristyllos date (Centaurus 27:280 [1984]) and Jack Brandt did likewise in JAHH in 2014. Similar inductions for all ancient star observers: DIO 4.1 [1994] ‡3 Table 3 [p.45]. The happy result was to elevate Aristyllos from his previous status (as one of the worst ancient observers) to one of the very best of all Greek star-transit astronomers.

  22. In 1982, DR built upon his prior Amer J Physics success in ancient geodesy by publishing a paper, backed by the eminent mathematician B. L. van der Waerden, in the [then] Johns Hopkins University journal Archive for History of Exact Sciences 26.3:211-219 [1982] p.212, a (superficially speculative-looking) analysis which concluded that a map attributed (Strabo 17.1.2) to Eratosthenes showed that his over-large empirically-derived Earth-circumference was actually about 256000 stades, not 252000 or 250000 as had hitherto been universally believed. Twenty-six years later: precisely vindicated, to ordmag 1/10th of a percent, in DIO 14 [2008] (‡1 eq.11 [p.6]), by the long-overlooked testimony of Eusebius. See also below.

  23. In 1982 DR published (Geophys J Roy Astr Soc) the 1st analytic method (as against previous authors' inelegant trial&error forays) of instantly computing for the many-body case, in 3 dimensions, the magnitudes & axes of symmetry of a tidally distorted star or planet or any other near-spherical body. (An easily usable computer program accompanied the more challenging text.) This was accomplished via Legendre polynomials, Lagrange multipliers, & eigenvectors. In 2000 May, the method was vindicated when Sky&Telescope published a cover story that unknowingly (and over-laboriously) got exactly the same results, for the decades-long span common to both studies: 2000 Sept S&T letters pp.14-16.

  24. In the Baltimore Evening Sun (1984/11/14), DR computed the astronomical odds against the peculiarity that (since 1955 when TV revenue took over the game) the baseball World Series had been [a] getting longer and [b] ever more enlivened by dramatic comebacks. Seven-game Series' frequency, previously 25%, jumped to 50%. Comebacks from 0-2 deficit (which had never previously happened in a best-of-7 Series) were now so common that it actually became an advantage to be so handicapped! From 1955 to 1984, 8 out of 15 teams behind 0-2 won the Series (all in seven games).
    In the two Series immediately following the article, the team behind 0-2 ended up winning in 7 games. [Thanks to Don Denkinger and Mookie Wilson.] Thus, by the end of 1986, teams behind by 0-2 had won 10 of 17 Series.
    [Explanation: Umpires massage the strike zone in favor of trailing teams.
    (Whyelse MLB's eternal refusal to adopt an electronic strike zone?)]

  25. In 1985, DR reconstructed (BullAmerAstronSoc 17:583) the hitherto-unknown hour of the −329/6/28 Kallippos Summer Solstice as dawn. Six years later, the EH orbit's elements unevadably underlying Hipparchos eclipse trio B, were shown (DIO 1.3 [1991] §K [pp.142-143]) to be based upon Kallippos' solstice for this very time of day.

  26. In 1986, when the maximum length of CDs was 74min (to fit Beethoven's Ninth), DR predicted that the max would go to about 80min. As it ultimately did.

  27. In several publications 1984-1991 (starting in Queen's Quarterly), DR showed that the yearlength on the famous Babylonian cuneiform text BM55555 was based on well-known GREEK Summer Solstice observations: Meton 432 BC & Hipparchos 135 BC. Thanks to the late John Britton's verification and championship of the discovery, it was rapidly agreed to by all sides. (Even including anti-inductor text-clingers and outright DR enemies.) Explicitly on this basis, BM55555 is now on permanent display at the British Museum in Room 52.
    since it is the 1st and only firm proof that Babylonians used Greek astronomy instead of entirely the other way about (as had hitherto been rigid orthodoxy in the field). This finding triggered DIO's growing realization that Babylonian astronomy in general was derivative. See discussions at DIO 1.1 [1991] ‡6 §B13 [p.54] & Isis 93.1 p.58. DR's view on this larger question has been endorsed in some degree by such eminent scholars as Dicks (U.London), Thurston (Springer's Early Astronomy author), and Walker (British Museum). Indeed, Walker may have intuited the point before any of us.
    See photo of the Museum's tag on BM55555, twice adopting DIO inductions:
    [1] BM55555's “Babylonian Month” came from Aristarchos,
    [2] BM55555's yearlength was Hipparchan.

  28. The BM55555 finding permitted fixing the hour of Hipparchos' well-known 135 BC S.Solst, vindicating Willy Hartner's skepticism regarding Almajest 3.1's failure to provide its hour, which DR now revealed was dawn not noon: DIO 1.1 [1991] ‡6 eq.6 [p.51].

  29. This SS was then used to discover a lost solar orbit employed during Hipparchos' lunar calculations near the end of his famous career, his ultimate “UH” orbit: DIO 1.1 [1991] ‡6 eqs.13,17-18,29 [pp.55-56&58]. In 2000, this DR discovery was entered into the Hipparchos article in the Encyclopedia of Astronomy & Astrophysics.

  30. After R.Newton discovered that Ptolemy's planet mean motions were not mathematically based upon arc/time ratios as Ptolemy claimed, DR found that three planets were based upon attested period relations instead (A.Jones & D.Duke Centaurus 47:226-235 [2005]). Two other planets' speeds were miscontrued by DR (his error jocularly announced on the cover of DIO 11.2 [2003]) but the correct solutions (by NYU's A.Jones & FSU's D.Duke) verified DR's period-relation theory more thoroughly than DR had (see idem).

  31. The Journal for the History of Astronomy ignored & resented DR's well-intended 1982 advice on refereeing. When DR informed JHA Editor Michael Hoskin that a paper in the 1982 Oct JHA was invalidated by a fundamental error, Hoskin responded with threats of non-publication, libel suit, and exile. His bad luck: the paper's honest author agreed with DR. (And the paper was recomputed for JHA 15:134-135; 1984 June.) Which only enraged Hoskin the more.

  32. So Who's the Liar?:
    DIO 1.2 [1991] §B2 [pp.97-98], prints DR's response to Hoskin-JHA threats — and His charge that DR's suggestion of inadequate JHA refereeing was a “damned lie”. DR's letter (1983/3/14):

    What most disappoints me about your [1983/]3/3 reply is that it indicates you've learned nothing from this [editorial] disaster…. I have pleaded with you privately [see DR 1980/7/30 letter to JHA on its refereeing: ibid n.8] for years to improve your process of evaluating and filtering incoming mss (specifically, to replace on obsession with superficialities by attention to substance). In vain….
    … If you knew me at all, you would realize that threats neither intimidate nor rile me. Their only effect is the suggestion that you wish to suppress open discussion….
    … I continue to wish you well.

    Years later, confirmation of DR's assessment arrived via the most authoritative possible source — a JHA insider, boasting of the JHA's refereeing efficiency (similar to that of another careless establishment's Efficiency: DIO 1.1 [1991] ‡8 §B2 [p.78]):

    it is quite common for an article received at breakfast to be refereed during the morning in some remote region of the globe and the verdict sent to the author by lunchtime.

    Author of the above 2003/6/21 letter? Michael Hoskin….
    [Decades of inevitably-resulting tragicomic JHA pseudo-scholarship are cataloged elsewhere on this site.]

  33. DIO 3 [1993] was the first critical edition ever of Tycho's 1004-star catalog. It contended: [a] Tycho's accuracy was better than previously realized and (for singly-observed stars) was magnitude-independent down to 5th magnitude. [b] Ten stars were faked in whole or in part. Contention [a] was accepted and [b] not challenged in the expert review of the book in Annals of Science 53.4:423 (1996 July). And no challenge to either conclusion has since appeared in any refereed journal.

  34. In 1982, DR demonstrated (P.A.S.P.) that Ptolemy's Almajest 7.5-8.1 star catalog missed all deep south stars that were invisible from Hipparchos' Rhodos (latitude 36°) but visible from Ptolemy's Alexandria (latitude 31°), suggesting plagiarism (as Delambre had pointedly hinted in 1817 at 2:284 of his HistAstrAnc). In 1987 & 2001 appeared massive JHA papers (totalling over 100pp!) challenging the small atmospheric opacity (for minuscule aerosols) DR had applied. Vindication occurred in 4 steps:
    [a] It was shown in DIO 3 [1993] §§L8&11 [pp.25-27] that Ptolemy had reported bright stars visible on the horizon, impossible for the JHA 1987 opacity, which would have made 1st magnitude stars look 12th magnitude on the horizon.
    [b] K.Pickering in DIO 12 [2002] ‡1 §B1 [p.4] showed that Hipparchos' Commentary had the same locus of lowest stars visible as Ptolemy, though if Ptolemy observed the Catalog these loci should differ in declination by 5°, the latitude difference of Rhodos' 36°N (Hipparchos) minus Alexandria's 31°N (Ptolemy).
    [c] Specifically (Pickering op cit §B2 [p.4]), the star γAra would have been invisible to Hipparchos if JHA 2001's opacity were valid, yet he records it at Comm 3.2.6.
    [d] JHA 2001 promoted the Muffia's insistence that heliacal rising/setting data were not for the horizon but for first/last visibility at whatever altitude. This was shot down by the unexpected KP-DR phonechat-realization (Pickering ‡F11 [p.19]) that Ptolemy's opposite phenomenonon, acronycal rising/setting, cannot even be defined at all unless referring to the horizon. Pickering's analyses of both types of data on this basis confirmed the dominance of very clear air in antiquity.

  35. The 1982 P.A.S.P. paper proposed an odd theory: that the Catalog's longitudes and latitudes were observed by different sweeps for the zodiacal stars. In 1994, independent chi-squared tests (DIO 4.1 [1994] ‡3 §§C4-C5 [pp.38-39]) on the Catalog proved that only the zodiacal stars showed incompatibility between latitudes and longitudes.

  36. Additional confirmation of Ptolemy's Catalog-theft appeared in the same DIO issue's article ‡2 (p.13 Table 2), as Dennis Duke built on Gerd Graßhoff's 1990 proof of the dependence of the Almajest star catalog upon the positions in Hipparchos' Comm, pointing out that many of the stars believed (by the JHA 2001 thick-atmosphere attack on skeptics) to be most in favor of Ptolemy's authorship were demonstrably connected to Hipparchos.

  37. In 1992-1997, DR continued in DIO his then-alone longtime contention that U.Leverrier not J.C.Adams deserved prime credit for the discovery of Neptune. That view is now generally accepted (e.g., Scientific American 2004 Dec), since the revelations of the long-stolen RGO file. (First publication anywhere of details from that file: DIO 9.1 [1999] ‡1 [pp.3-25].)

  38. Back in the 1990s, DIO publicly branded Britain's Neptune-discovery claim as robbery of the French. No other journal did so. Vindicated right on the cover of the 2004 December Scientific American: “Stealing a Planet”, with DIO 9.1 [1999] cited at p.98 as the source of the key evidence (Adams' circular orbit) which proved the truth of the charge.
    [Specific DIO charges prior to 2004: “claimjump”, “robbery”, & “theft”; “scheming to grab Leverrier's planet for England”. (See, respectively, DIO 2.3 [1992] ‡9 §C3 [p.124] & §D2 [p.126]; DIO 9.1 [1999] ‡1 §B3 [p.6] & §I1 [p.21].)]

  39. DIO 4.2 [1994] ‡10 [pp.92-102] outted Olin Eggen, the powerful figure who hid the Royal Greenwich Observatory Neptune file for over 30y. No other journal did so. On his 1998 death in Chile, the entire file was found in his home. (DIO 9.1 [1999] ‡1 pp.3-4.)

  40. DIO 2.3 [1992] ‡9 n.12 [p.118] (also (DIO 7.1 [1997] ‡5 §A5 [p.25]) predicted that the doubly-“disappeared” 1846/12/8 letter from Astron Royal G.Airy to Cantab A.Sedgwick had lambasted Neptune-controversy Brit-hero Adams. When the letter was doubly-recovered in 1998 (after Eggen's death), it confirmed that theory resoundingly: Airy's scathing sarcasm on “baby” Adams can be found at DIO 9.1 [1999] ‡1 §H8 [p.20]. A photograph of the precious original of this letter is viewable on DIO, which is exclusive host to the Royal Astronomical Society-funded gleanings from the long-unavailable RGO Neptune file — thanks to Nick Kollerstrom.

  41. DIO 2.3 [1992] ‡9 §B4 & n.21 [pp.120-121] had dropped the bomb that Adams (whose entire claim was based on his alleged 1845 deduced ELLIPTICAL orbit for predicting Neptune's place) had been so unsure of his work that as late as 1846 July he was calculating using a simple circular orbit (with elements virtually identical to those already published on June 1 by Leverrier). Point made quantitative in detail at DIO 9.1 [1999] ‡1 §E, n.21, Table 1 [pp.13-14]. Used as the centerpiece scientific evidence for the Leverrier claim's primacy in Scientific American 2004 Dec p.98.

  42. In 1973, there were almost no documents available to evaluate airman R.Byrd's long-suspect 1926/5/9 N.Pole claim. But DR (Fiction 1973 p.263) found his story's coincidences too incredible for acceptance, and deemed it probably fake. In 1996, the R.Byrd 1926 “North Pole” diary was finally unsecreted. As a specialist in the mathematics of navigation, DR was invited by Ohio State University to examine it. OSU's Byrd Polar Research Center itself sent DR's report to the New York Times which went page-one on 1996/5/9 (triggering coverage on all 3 networks' evening news that day) with DR's finding — not a digit of which has since been overturned — that, despite being shot into equatorially opposite hemispheres of the sky (1st north, 2nd south), the two sextant data in the diary both consistently put Byrd over 100 mi south of where his later official report placed him at the corresponding times. Both DR calculations of position from the sextant data were later verified on the nose by CalTech's E.Myles Standish, the most eminent of the world's positional astronomers, who later joined DIO's board.
    [For the last 1/4 century, Standish has been designer of the world-standard Astronomical Almanac orbits of the Sun, Moon, & planets, used by ships at sea and NASA-craft in space as their guide.]

  43. Shortly after the New York Times story, DR noticed (what he and all other reviewers of the Byrd official 1926/6/22 report had missed for over 70y): that the consistent sextant-data precision (1") of Byrd's official 1926/6/22 report to SecNavy & NGS was (DIO 10 [2000] §G6 [pp.39-41]) wildly impossible on his sextant. An ironclad vindication of the DR 1973 & 1996 negative verdicts, which had previously been arrived at on quite independent grounds.

  44. Vindicating this finding: Byrd covered up his blunder by hiding the original report — with NGS connivance to this day — instead issuing (e.g., to the American Geographical Society) a later 1926/11/24 revised report with all the indicting raw data removed. Detailed bowdlerization example at ibid Fig.7 (p.34), comparing the secret June report to the November report sent to geographical societies.

  45. The finding was among the more startling new evidences appearing in DIO 10 [2000], co-published with the University of Cambridge (accompanied by the University's special note on the article's import to the polar community) in 2000 January to kickoff the new millennium, in the journal of the Scott Polar Research Institute.

  46. Nature is the world's #1 science journal. Its 2000/11/16 cover story was the sensational claim (prefatorially backed by O.Gingerich) that the Giza pyramids were oriented north-south by using the fact that in 2467 BC, the line connecting stars Mizar & Kochab ran through the celestial pole, so when one was atop the other visually, this line gave true north. DR and Keith Pickering immediately realized that the sph trig mathematical development defending the theory was miscalculated. The correction was published in Nature 2001/8/16. (See also [at same link] the sadly chauvinist reply-comments by Gingerich's debunked author.) The two DR-Pickering theories (both involving the hitherto-neglected star, 10i Dra, the nearest star to the celestial pole of usable position & brightness, when Khufu's pyramid was designed) were soon after picked up by the NY Times and Astronomy. DR&KP published the details of their new stellar methods at Nature loc cit and DIO 13.1 [2003]; both would work only c.2600 BC, approximately the conventional date. While not abandoning her theory, the author agreed to the validity of the DR-KP correction of her sph trig (Nature 212:699-700). Her 2467 BC theory, widely promoted in 2000, has long since become almost universally defunct.

  47. On 2005/1/12, the American Astronomical Society gave the biggest publicity boost it had ever provided to an alleged historical discovery: the supposed detection of the stars of Hipparchos' catalog in the marble Farnese globe (Naples), the only sizeable celestial globe surviving from the ancient world. Six referees were said to have reviewed the paper, which was promoted by the AAS-Hist.Ast.Div's top guru, O.Gingerich (a dedicated slanderer of DR for the last 40y: see. e.g., DIO 4.3 [1994] pp.133-134) as proof-AT-LAST of the existence of Hipparchos' star catalog. The existence of which had actually been well known to genuine experts for a few years — like since Pliny's 77 AD Natural History 2.95. Gingerich's at-last announcement was his way of — after for decades denying Ptolemy stole Hipparchos' star catalog — half-admitting the theft (long asserted by R.Newton, D.Rawlins, & G.Graßhoff) but salving his pride by now claiming that his clique was the 1st to convincingly prove it.

  48. On 2005 April Fools Day, DR posted an appropriately sober satirical demonstration that no one at AAS or its Historical Astronomy Division (HAD) or JHA had bothered to read critically Schaefer's above-cited JHA paper before promoting it to the world as a sextuply-refereed sensational discovery.
    [DR's target was not the author but the pols who were simply rewarding said author for smearing DIO in Sky&Telescope (2002 Feb). DR's much-resented intent for the posting was to wise observers up to the slack (and purely political) criteria that held at the AAS regarding promotion of historical scholarship, thanks to the AAS' unsupervisedly leaving HAD dominance to mostly mediocre-scholar pols for decades.]
    DR has been vindicated in that, in a field known for seething disagreements, there is now no disagreement at all on the fact that the Farnese-Hipparchos theory was unoriginal, invalid, and not effectively refereed — and that DIO was 1st to publish (2005: aptly AllFoolsDay) demonstrations of these facts. One positive upshot was the JHA 2006 Feb publication of DIO Editor Dennis Duke's non-smartA undoing of the 2005 JHA Hipparchan-Farnese connexion (no mention of JHA bungling, or farcical refereeing, or DIO's priority in debunking this prank), with Duke joining the JHA board. But another result was a vindictive ratcheting-up of now-yet-further-embarrassed AAS-HAD pols' well-known (see Sky&Tel 2002 Feb p.40) shunning of DR, which was increasingly resorted to in desperation after DR's repeated counter-debunkings of these same funds-controlling dictators' earlier censorial pretenses to expertise (latest flock of shirt-unstuffings: DIO 16 [2009] — further exposures of same mis-scholarship, including repeated, systematic data-tampering at DIO 22 [2018] ‡3 §§B5&D&F-G [pp.53-69]) — exposures so uniformly accurate, central, and revealing that they cannot be answered by any tactic but shunning. I.e., fleeing, threatening, and-or censoring. Some vicious cycles are genuinely vicious.
    [Suppression and intimidation of dissent in history of astronomy began long before DR's entrance into the field. Systematic non-citation has been stifling heretics in ancient astronomy at least since 1934, e.g., Aubrey Diller, Robert Newton, and now DR. Little wonder that DR (with apologies to Mary McCarthy) spoofs the ongoing show as (DIO 16 [2009] ‡3 §E [p.25]): “The Grovels of Academe”. (See also “White Affidavit”: DIO 1.3 [1991] ‡10 [pp.176-177].)]

  49. In a paper written earlier and originally submitted elsewhere but published in 2006 at DIO 13.3, Duke at p.33 n.18 was still holding out (long after Toomer gave up the Catalog controversy) in favor of the Toomer 1984 Almajest pp.329-330 n.56 translation of Almajest 7.3's statement that Ptolemy-era stellar latitudes agreed with those (Heiberg 1898&1903 2:18) anagegrammenais kai synagomenais by Hipparchos. Toomer makes it: as “computed from the records of Hipparchos” rather than DR's “recorded and compiled” by Hipparchos (DIO 1.3 [1991] I1 [p.127]; also §E2 n.66 [p.111]), the disagreement originally arising out of skeptics' proofs that Ptolemy's Ancient Star Catalog (Almajest 7.5-8.1) was just a trivial precessional update of Hipparchos' ecliptical catalog, a charge which Muffiosi countered by claiming there never was an ecliptical Hipparchan catalog to steal (see, e.g., Neugebauer History of Ancient Mathematical Astronomy (HAMA) 1975 p.280; also DIO 1.3 loc cit), so that only a computation from non-ecliptical data could provide Hipparchan stellar celestial latitudes.
    As noted at DIO 13.3 n.18, Toomer's wrenched rendition contradicts not just DR's but every previous expert's translation. Manitius' classic 1912-1913 edition 2:17 has “aufgezeichnet und zusammengestellt”. The lesser but unprejudiced Great Books 16:228 version has “recorded and brought together”.]
    So why in 2006 raise this embarrassment from the dead?! An attempted resurrection which seems all the weirder when we note that 12y before 2006, DIO 4.1 [1994] ‡3 §E4 [p.40] had made it undeniable that the equatorial-frame-observations portion of the Ancient Star Catalog was transformed to ecliptical coordinates in Hipparchos' era, not Ptolemy's.
    In any case, Pickering delivered the final quietus to the matter by showing, e.g.:
    [a] Star π Hya was infected with a huge 5° error that can only have been equatorial (and is identical to the Hipparchos Commentary error for the same star), though Ptolemy claimed he observed all 1025 stars on an ecliptical astrolabe. (DIO 12 [2002] ‡5 §E [p.66] & n.4.)
    [b] The coordinates of 39oOph (PK251) obviously derive from an ecliptical scribal error only possible for Hipparchos' era (Ibid §C6 [p.61]).
    [c] The position of ζCnc (PK448) is a sph trig sign-error also only possible for Hipparchos' era (ibid §C12).
    [Die-hards might protest that Ptolemy could have transformed equatorial positions into ecliptical ones in the Hipparchos-epoch frame before then precessing the longitudes (reasonable procedure). But we can test the idea (as usual, though cultists never seem to anticipate this, when launching rear-guard defenses of dying orthodoxy): it is the southern part of the Ancient Star Catalog that was originally observed & recorded in equatorial coordinates (DIO 4.1 [1994] ‡3); if Ptolemy or a contemporary were the sph-trig-transformer (of southern-sky equatorial data to ecliptical), he had no reason to round the precise results before adding 2°40' to the longitudes, which would thus be rounded to ancient convention after the addition. So the resulting mass of southern longitudes in Ptolemy's catalog would display a full spectrum of ancient-standard fractional endings, including quarter degrees. It doesn't. Out of hundreds of Ptolemy southern stars, not a single longitude ends in 15' or 45'. And the endings-frequencies are consistent with Ptolemy's slide&hide procedure: see idem.]

  50. In early 2008, DR learned that Eusebius had preserved for us Eratosthenes' Earth-radius, 40800 stades. (Ancient geographers almost always rounded distances to the nearest 100 stades.) This precisely matches the hitherto controversial 256000 stade circumference which DR had back in 1982 published as the true empirical value (versus the hitherto-iconic values: 250000 & 252000 stades). Simple multiplication by 2π will readily confirm (DIO 14 [2008] ‡1 eqs.6-18 [pp.6-8]) another spot-on vindication, to the precision provided. Further confirmation appeared unexpectely in 2014.

  51. Following up on this, DR published in 2008 March (DIO 14 ‡1 [pp.3-12]) a completely novel reconstructive theory (leaping beyond the above-cited 1982 work & 2008 match to it) that Eratosthenes' Earth-size estimate was accomplished via not just any lighthouse but the obvious choice (given his time and place): Alexandria's world-wonder then-new then-record-tall Lighthouse on Pharos Island. (The word “pharos” eventually became a synomym for “lighthouse”.)
    DR's novel theory was that builder Sostratos would likely make his record-setting building's height a round number of feet. The indicated number of feet was obviously 300 (DIO 14 [2008] p.2 n.1, ‡1 eq.4 [p.6]) which then (given that a stade = 600 ft) suggested that the way to measure the Earth was super-neatly elucidated (for public science-education) by Sostratos' placing of the Pharos' flame exactly 1/2 stade high, thus startlingly simplifying the method's equation (in stades), for finding Earth-radius r from flame-visibility-distance v and flame-height h:

    r = v2/2h

    to merely (since 2h = 1 stade)

    r = v2

    (See DIO 14 [2008] ‡1 eq.21 [p.9].) I.e., the induced Earth-radius r equalled simply the square of the visibility distance v of the Pharos at night, which must have been measured as 202 stades, the trivially & conventionally-100-stade-rounded square of which indeed neatly matches Eusebius' value, 40800 stades. This theory was first put online (DIO 14) for internal refereeing on 2008/3/12, published online (encouraging general refereeing) shortly thereafter, and mailed out in 2008 December. In 2009 January, DR encountered the sole 1st-hand account, in unambiguous units, of the Pharos' three sections' heights, up to the flame (1165 AD report, published in Proc Brit Acad 1933): 31 fathoms & 15 fathoms & 4 fathoms. (These proportions are consistent with the best surviving image of the Pharos.) The sum is 50 fathoms. Fathoms have always been defined as six feet (the span between middle-finger-tips of outstretched arms); thus the height of the flame was 300 ft, exactly the value gotten via mostly theoretical DIO reconstruction in 2008. (For further details that multi-confirm 300, see DIO 14 [2008] p.2 n.1 [2009 rev].)

  52. Aubrey Diller's 1934 Klio paper on eleven Hipparchos-Strabo klimata showed that Hipparchos had used sph trig, in the 2nd century BC, long before the 100 AD date hitherto accepted by orthodox scholarship. (E.g., O.Neugebauer HAMA 1975 pp.305-306 & 335-337.) A few of the fits were slightly inexact, though the theory was obviously true. In DIO 4.2 [1994 & 2002 revision] pp.55-57, DR brought in two new data — both fitting the Diller theory on the nose — and altered the theory by introducing conventional ancient 5' rounding at a key stage in the ancient math computation of the klimata. This showed (contra Neugebauer's abuse of Diller, to promote his own far-inferior scheme) that the Diller theory fit all but one of the data at issue. On 2009/4/1, DR found that even that one glitch was simply from a self-evident Strabo misinterpretation-ambiguity (see DIO 5 [2009] §D3 item 7 & n.25 [p.9]; or DIO 16 [2009] §B5 eq.3 [p.21]) and the obvious correct reading gave precisely the value (for the klima in question: Meroë) that Diller had predicted back in 1934. Thus, the Diller-DR fit became literally perfect: 13 hits for 13 data. DIO announcement (DIO 16 [2009] cover): “DR to Muffia: Is 13-for-13 Enuffia?”
    [Later addition of the Equator to the sample made it 14-for-14.]

  53. DIO 11&13 (2001&2003) solved by attested ancient method, all three hitherto-unexplained ancient lunar motions: System A anomalistic (3rd century BC), Hipparchos' draconitic (2st century BC), Plan.Hyp  anomalistic (2nd century AD). Each of the three motions was anciently expressed as a ratio of two 4-digit integers; thus a total of 24 digits required solution. The DIO papers showed how all 24 were simply, automatically recoverable, on the nose, by 1st grade arithmetic: founded upon eclipse cycles, using now-lost eclipse data from the 13th century BC. The outraged Muffia, unable to point to errors in DR's math, unable to find eclipses from any other century that would solve the motions, and unable to find attestation (or show such precision and accuracy) for any other method, were left sputtering on about [a] speculativeness (this, in the context of Muffiosi's own fantastic speculations via unattested method), and [b] the data's remoteness, a point soon after shot down by adducement (DIO 16 [2009] p.2) of the ordinariness of the belief that Babylonian observational astronomy began c.1350 BC: Isis 83:474.

  54. The recent realization, that Hipparchos' 600y tables (noted by Pliny) could be used for eclipses backwardly from Nab 1 (747 BC) as easily as forwardly, added extra indication of Babylonian astronomy c.1350 BC.

  55. The System A case has a remarkable vindication by temporal match: the most likely and last of the classical-era eclipses that were proposed by DIO 11.1 [2002] ‡2 (§B4 & eq.8 [pp.13&17]) as founding System A occurred on −262/1/26. According to the Muffia's own expert, John Britton, the earliest firmly identified System A tablet calculation is for later during the very same year: ibid §E6 [p.18].

  56. At DIO 1.1 [1991] ‡7 §C1 [p.69], and DIO 1.3 [1991] n.272 [p.168] item[b], DR originated the theory that Aristarchos' famous 87° figure for half-Moon elongation was not an exact value but a lower bound. (See also DIO 8 [1998] ‡4 n.4 [p.37].) In 2008, surprise (if speculative) support for this theory came out of recent realization that Eusebius had revealed that pseudo-Aristarchos' distance to the Moon was 19 not 20 Earth-radii, which required calculating with 90° (not 87°) half-Moon elongation, the obvious calculational choice if one didn't know where the truth lay in the range 87°-to-90°. See development at DIO 14 [2008] ‡2 §C5 [p.21], eq.5 vs eq.6.

  57. At DIO 1.3 [1991] n.288 [p.173], DR revealed that Hipparchos (twice for Spica: Almajest 3.1) and the JHA's now-Editor J.Evans had used the wrong sign when applying parallax corrections to their determinations of stellar longitudes via lunar eclipses. Correcting the positions on that assumption, all 3 huge longitude errors (ordmag 1° each) virtually vanish. Recent vindication: Hipparchos' other main fundamental star was Regulus. Besides the two Spica eclipses, the only remaining eclipse (of which we have an extant Hipparchos report) occurred near Regulus, whose position error was long as mysteriously huge as Spica's eclipse-based two: Regulus' error = −35', the worst of all Hipparchos' fundamental stars. But when DR (DIO 16 [2009] ‡1 §E [pp.8-10]) applied the parallax sign-mixup theory to Regulus' position thus (mis-)computed from a perfectly accurate measure via the nearby 141 BC eclipsed Moon, the resulting longitude error was −0°.6, just the error in Hipparchos' record. Thus, the sign-slip theory fits all 4 cases examined: each's seeming ordmag 1° error shrinks to ordmag 1'.

  58. The New York Times Science section celebrated (2009/9/8 p.D2) the 100th anniversary of the Cook-Peary N.Pole Controversy by publishing a thoroughly researched article agreeing that the Amundsen-Ellsworth-Nobile Norge dirigible expedition had the 1st credible claim (of four) to have reached the Pole (1926/5/12), adding that only Ptolemy's fakes had lasted longer than Peary's. The 1st scholar to allege Amundsen's priority was DR, Peary at the North Pole, Fact or Fiction? (Wash. DC, 1973), pp.274&280. The New York Times article also analyses in detail how the various hoaxes' defenders have fallen into a familiar mental cycle of evidence-denial. Some journals allow calling it chauvinism.

  59. For decades, DR has argued the obvious: that J.C.Adams' final 1846 prediction of Neptune's position was an arithmetic extrapolation from his Hypothesis 1 and Hypothesis 2. Craig Waff has dissented (2004-2010). But on 2010/10/25, DR discovered the exact extrapolation ratio, 14:11 (and how it was derived) — which, when applied, produces exactly the results Adams announced to the Astronomer Royal (1846/9/2) for his ultimate Neptune-place prediction: longitude 315°20' and orbital mean-distance ratio 0.57.
    (This DR discovery could have been discussed at Waff's Seattle 2011/1/9 HAD session on Neptune's discovery. But after DR's 2010/12/27 mass-mailed postcard pointed out Waff's exclusion of all scientific experts on the math of the discovery, Waff fled his own meeting!)

  60. In Isis 1983/12, DIO 1.2 [1991] n.53 [p.107], DIO 4.1 [1994] ‡3 n.41 [p.44], and DIO 14 [2008] ‡2 n.24 [p.19], DR argued (contra several Princetituters) that outdoor Greek astronomers were using degrees from at least c.300 BC. In 2011, DR discovered that Archimedes' conventional unit-fraction expressions for the lower and upper limits of his outdoor measurement of the Sun's diameter (Sandreckoner) — 1/200 and 1/164 of a right angle — were merely a standard-pedantic format for expressing his actual sexagesimal angular measuring-practice: his original (pre-conventionalized) solar-breadth limits were 1°/2 ± 10% or 1°/20 (i.e., 9 and 11 twentieths of a degree, resp.); or just 27' and 33' — which, when he'd converted them to fractions of a right angle, had become 1/200 and 1/163.64 of a right angle, resp. Simple rounding of the latter figure then produced the numbers we now find in the Sandreckoner.

  61. In 2011 November, the question was raised as to why Hipparchos would claim (Commentary 1.6.14) that the Pleiades group is seven stars when there is so little difference in magnitude between the 7th (magn 5.06) and 8th (magn. 5.46) brightest stars in the group that observers could record 8 as easily as 7 (or even 6). Resolution: DR had in 1982 published the 1st frequency function for the 1025-star Ancient Star Catalog of Hipparchos (PASP v.94 p.363); this predicts that a 5.06 magn star was 70% likely to be captured; and a 5.46 magn star, 30%. Thus, Hipparchos' statement on the Pleiades is confirmatorily consistent with the 1982 function.

  62. On 2005/4/1, DR suggested (and see DIO 16 [2009] ‡3 n.4 [p.19]) that the mysterious, hitherto-unidentified line-segment (see DR's 1st-hand photo) attached to Cygnus on the famous ancient Farnese Globe (Naples Archaeological Museum) was a surviving fragment of a galactic circle (Milky Way) on the original Greek globe (of which the Farnese is a Roman copy), with the galactic circle mostly removed — the little CygSeg's survival being due to the copyist's confused belief that the segment was a leg of Cygnus.
    [Greek astronomers called this constellation simply the bird. Rome later converted that into a swan.]
    In 2011 November, DR received from Ulrich Kuehne the information that the ancient celestial globe fragment SK1050A (at Berlin's Neues Museum) is adorned with a galactic circle, proving that such a circle was indeed displayed on ancient globes — and that it passed right through Cygnus' wing & Cassiopeia's middle, as does the Farnese CygSeg's extrapolated great circle.

  63. At DIO 7.3 [1997] ‡9 n.4 [p.83], it was suggested that the reason Frederick Cook's 1907-1909 “North Pole” trip had started by going west for hundreds of miles was that he intended to get to the Pole via Peary's 1907-reported Crocker Land, NW of Ellesmere Land.
    [That Cook was planning to get north by land as far as possible makes sense to any scientist who understands how little navigation Cook knew. (And if Cook could not reach the Pole, exploration of Crocker Land and a possible unknown continent beyond could make his expedition a success. See R.Bryce Cook & Peary: the Polar Controversy Resolved 1997 pp.326; also Cook's feint at ibid p.331.) When Cook found in 1908 that Crocker Land did not exist, and thus that the only path to the Pole was over rough sea-ice (more than 1000 miles, round-trip — mostly far out of sight of terra-firma), our non-navigator explorer was forced to either face career-disastrous failure or fake a trip to the Pole.]
    On 2011/12/4, DR received a phone call from Rob't Bryce, on his great pleasure at coming upon Cook's handwritten plans for a trip to the pole via Crocker Land.

  64. In 2010 DR posted on www.dioi.org website the argument (eventually published in DIO 18 [2014] §W12 [p.62]) that Henry VI's performances, before the 1593 debut of Shakespeare's 1st work, were evidence that Marlowe wrote the work. In 2017, the new published edition of Henry VI co-credits Marlowe.

  65. For two millennia, the only solstice known from Hipparchos' observing career was from −134. But in 1991, from analysis of Hipparchan eclipse-trio B (Almajest 4.2), DR was 1st to propose that Hipparchos had fixed a solstice in −157 (DIO 1.3 [1991] §K8 [p.143]), inducing that he had in −157 used it to found his early (EH) solar theory: a Summer Solstice which he did not observe but computed indoors from Kallippos' calendar, i.e., his theory of the motion of the Sun. Fourteen years later, a 2nd century AD papyrus P.Fouad 267A was examined by Anne Tihon and found (Archimedes 23:2-10; 2010) to cite a hitherto-unknown Hipparchos S.Solstice. Its year? —    −157. The probability that this hit is an accident is (since Hipparchos observed during periods totaling at least c.1/4 century) less than 5%, i.e., statistically significant.
    [The 1991-hypothesized date was 6/28 6h, while the papyrus date was 6/26 at a missing number of “hours of the day” (due to that datum's having flaked off the document). In any case, we now have utterly unexpected new evidence confirming that Hipparchos indeed sought a −157 S.Solst, the very date 1st appearing at DIO 1.3 [1991] §K8 [p.143].]

  66. The long-lost, flaked-off time of day was recovered through induction as 18h at DIO 20 [2012] ‡2 §§K4-K5 [p.15], implying the S.Solst's time was

    Hipparchos' P.Fouad 267A S.Solst = −157/6/26 3/4 (evening)

    This speculative hypothetical reconstruction of a supposedly-lost-forever datum leads on — with a fruitfulness so characteristic of reasonable hypotheses — to solving the papyrus' next mystery:

  67. Besides a Kallippic column, the papyrus (P.Fouad 267A) also bears a “tropical” column, based upon the previously unexplained yearlength, 365d1/4 − 1/309. DR's solution was published at the 2015-revised version of DIO 20's ‡2 §K5 [p.15] eq.25: the papyrus' 130 AD astronomer uses a yearlength Y computed from the 274y interval between Meton's −431 S.Solst and Hipparchos' −157 S.Solst, but with the effect of seasonal hours included, for the nearest klima (14h3/4 for Meton's Athens):

    Y = (100077d + 14h3/4)/274 = 365d1/4 − 1/309

    which matches the papyrus' table, thus solving for Y, as well as validating the 18h hypothesis of the previous paragraph.

  68. The papyrus' ephemeris also bore a Hipparchan column (Tihon op cit Table p.2) for Kallippic solar speed (360° per 365d1/4), confirming the (entirely unprecedented) proposal — published years ago at DIO 1.3 [1991] §K9 [p.143] — that the young Hipparchus was in −157 temporarily using Kallippos' solar theory.

  69. Contra Muffia ultimo wisdom, DR realized in 1985 from mathematical analyses, rejected without referee report by a Brit journal at the time (detailed later in DIO 20 [2012] ‡2 §J2 [p.13], Table 3 [p.21]), that ancient Greek solstices' accuracy was ordmag 1h (BullAmerAstronSoc 17:583). In 2005, papyrus Fouad 267A was examined and found to report a Hipparchos −157 S.Solstice correct to ordmag 1h. Physical analyses showing how 1h-accurate solstices were accomplished in antiquity are found at DIO 20 [2012] ‡2 §§H-J [pp.12-13], culminating in eqs.19-21.

  70. Aside from theories of methodology, there is a collection of all four recoverable outdoor ancient solstices at DIO 20 [2012] ‡2 Table 3 [p.21]: rms error c.2h.
    Ancients' convention of rounding to the nearest quarter-day introduces rms 1h.7 mean error. See discussion at ibid §B4 [p.9].

  71. When DR elicited the elements of Hipparchos' “Frankenstein” orbit (DIO 1.3 [1991] §M4 [p.147]), which satisfied the other Almajest 4.2 eclipse trio (Trio A), it turned out to contain the two non-tabular elements of the EH orbit, thus re-confirming the validity of the prior Trio B-based induction of same.

  72. The other two PH elements could not be adopted until tables were prepared. The pace of adoption of tabular and nontabular elements is correctly sequenced — yet another point in favor of the DIO's hypotheses here. See DIO 20 [2012] ‡2 §L3 [p.16].

  73. Further, the above-cited 1991 DIO inductions from the two eclipse trios concluded that the EH and Frankenstein orbits were each based upon Kallippic solar mean motion (the 365d1/4 year). As noted above, this motion was not previously known to have been used by Hipparchos, but later (2005), when the 2nd century AD papyrus was examined, its mean solar table was found to be equivalent to Kallippic motion, consistent with both of DIO's two distinct 1991 orbit proposals.

  74. Almajest 4.2-3 provides the highly accurate monthlength that was used by Hipparchos, good to a fraction of a timesec (then&now), as not a single historian-of-science besides sharp-eyed Olaf Pedersen seems ever to have noticed: 29d31'50''08'''20'''' (commonly mislabeled the “Babylonian month”), while also providing a saros equation which DR in 2002 traced to Aristarchos by a route quite different from pioneer Tannery's: the saros = 223 months = 18y10°2/3 = [18+(10+2/3)/360]·365d1/4 = 4868/270 Kallippic years, the numerator matching Tannery's crucial prior discovery (next paragraph).

  75. In 1980, DR elicited Aristarchos' Metonic year, 365d1/4 − 15/4868, via continued fraction analysis, from Vat. gr. 191 fol. 170v, and on 1980/6/15 submitted the discovery to the Journal for the History of Astronomy, resubmitting a fuller version on 1981/8/7. Hoskin's subsequent tantrum, threat, and blackballing suppressed publication for years: history chronicled at DIO 9.1 [1999] ‡3 §F [pp.39-42], along with the paper's 1981 edition. Its Table 1 extracted 4868 from the Vatican ms. This datum is validated by our previous paragraph here, & by P.Tannery's much earlier finding (T.Heath Aristarchus of Samos 1913 pp.314-315, Neugebauer HAMA 1975 p.603) of Aristarchan intervals of 2434y & its double 4868y, from Aristarchos' exeligmos (ibid §C3 [p.33]).

  76. In 2002, DR discovered that 4868 Metonic years of 235/19 months each, according to the iconic Metonic-Easter relation, equal 4868·(235/19)·29d31'50''08'''20'''' = 1778022d, which divided by 4868 (to compute implicit yearlength) produced 365d1/4 − 15/4868 (see DIO 11.1 ‡1 eqs.9-12 [pp.7-8]), independently confirming the Vatican ms' value (previous paragraph). Textbook theory-fruitfulness and predictivity.

  77. In 2002, DR computed the monthlength determined by the above saros equation:
    monthlength = saros/223 = {[18+(10+2/3)/360]·365d1/4}/223 = 4868·(365d1/4)/270/223 = 1778037d/60210 = 29d31'50''08'''04'''' which differs from the “Babylonian” month (above) by 1 part in 24 million. The difference is obviously a mere rounding, so it's safe to conclude that Aristarchos' mathematically-grounded 280 BC monthlength was ancestor to Babylon's 200 BC monthlength, for which no Babylonian ancestral context exists, as can be seen from, e.g., the discussion by University of London's D.R.Dicks at DIO 4.1 [1994] ‡1 §C4 [p.10]. Unlike Greeks: nowhere in the cuneiform literature is there a hint of how the Babylonians arrived at their astronomical elements. This situation is consistent with DR's Muffia-hated heretical-suspicion (shared also by Dicks, Christopher Walker, & Hugh Thurson) that Babylonian astronomy is derivative.
    The point is driven home in more detail at DIO 13.1 [2003] ‡2 §H [p.18].


    The same 2002 paper realized that the interval from Meton's canonical −431 S.Solstice to DR's 1991-published Hipparchos Ultimate Orbit's epoch, −127/9/24 noon Nab 621 Thoth 1 (DIO 1.1 ‡6 eq.28 [p.58]), was exactly 1/16 of Aristarchos' 4868y Great Year.

    DIO 14 [2008] ‡1 showed that only the 185m stade could satisfy the two grossly unequal atm-refr-affected Earth-size estimates of Sostratos-Eratosthenes (R = 40800 stades, 19% high) and Poseidonios-Ptolemy (C = 180000 stades, 17% low.
    Eratosthenian chauvinists have attacked the 185m stade for over a century (lately insisting on polluting Wikipedia's pages with fantasies masquerating as facts), but maybe (very maybe) the seductive speculative reconstruction which follows can finally entice even them. On 2014/4/29, six years after DIO 14's double-verification of ancient use of the 185m stade, unexpected independent support for that value appeared when it was realized (DIO 20 [2012] ‡1 n.2 [p.4]) that the unit-fraction-bound and fractionally-sexagesimal Greeks c.300 BC (under emperor-pharaoh Ptolemy I) had apparently standardized the formerly unstable stade by redefining it scientifically (prototype for the nautical mile's modern redefinition of the mile by ordmag 10%) as ≡ C/216000, which we will call an “Alexandrian” stade (generally miscalled “Attic”) as a perfect sexagesimal unit-fraction of C (40 million meters):

    1 Alexandrian stade ≡ 1/60th of 1/60th of 1/60th of C = 185m

    This three-step sexagesimalization's step 1 (which determines the following two steps by mere Greek-conventional sexagesimal fractionalization) IS EVEN ANCIENTLY ATTESTED — by Strabo 2.5.7 — more at Neugebauer HAMA p.590 n.2. In modern standard sexagesimal notation, with superscript C to denote units of Earth-circumference C, the stade is PRECISELY:

    1 Alexandrian stade ≡ 0;00,00,01C = 185m.