One of the most transparent of arctic exploration-exaggerators was politician-explorer Isaac Israel Hayes (1832-1881), whose present obscurity is one of the most fascinating, instructive, and Orwellian facets of the detective-mystery you are about to read.

No other arctic explorer was ever so unanimously — nay, flagrantly — endorsed by US academe and wealthy patriots.. If ever there was an Establishment Arctic Explorer, Isaac Hayes was it. For over 1 1/2 decades (1857-1873), Isaac Hayes was universally considered the United States' leading arctic explorer and authority.

A veteran of the late martyred Kane's 1853-1855 expedition in the ship Advance, Hayes assumed the halo left by Kane's 1857 death. And he shortly had convinced bigbuckbackers to fund an expedition of his own, in the subtly re-named ship: United States.

Following close upon the US' expansionist war with Mexico, the 1850s-1860s polar expeditions of Elish Kent Kane and Isaac Hayes can be interpreted as among the 1st symptoms of nascent US imperialism.

Describing his 1861 trip, Hayes claimed a record farthest north land, and (while evidently going for the Bulwer-Lytton Award for record-longest sentence of the 1860s) spoke ever so inspirationally of his emotions upon leaving his sacred [alleged] farthest-north-ever turf (HO351-352, preserving [as throughout here] Hayes' arcane punctuation):

I quit the place with reluctance. It possessed a fascination for me, and it was with no ordinary sensations that I contemplated my situation … in that hitherto untrodden desert; while my nearness to the earth's axis, the consciousness of standing upon land far beyond the limits of previous observation, the reflections which crossed my mind respecting the vast ocean which lay spread out before me, the thought that these ice-girdled waters might lash the shores of distant islands where dwell human beings of an unknown race, were circumsatnces calculated to invest the very air with mystery, to deepen the curiosity, and to strengthen the resolution to persevere in my determination to sail upon this sea and to explore its furthest limits; and as I recalled the struggles which had been made to reach this sea; — through the ice and across the ice, — by generations of brave men, it seemed as if the spirits of these Old Worthies came to encourage me, as their experience had already guided me; and I felt that I had within my grasp “the great and notable thing” which had inspired the zeal of sturdy Frobrisher [sic], and that I had achieved the hope of matchless Parry.

Unfortunately, Hayes prose-purpularity ascended far higher than his latitude.
His farthest was a conscious fraud.
As will be variously demonstrated below, beyond the slightest doubt.

Hayes' 1860/7/7 departure for the arctic was blessed by every relevant US academic society. (An extensive list is provided here.) The president of Harvard was at the wharf in person. With such certifications, how-could-anything-go-wrong?
[More seriously: if anything did go wrong — would anyone ever know how wrong?]

The only catch was that, amidst the classic coagulative suckup-rush to get behind and in-good-with the hero anointed by the political moguls who controlled exploration-funding, no one had bothered to investigate little matters like:
[a] whether Hayes knew navigation, and
[b] whether he was an honest person — e.g., whether he had (as persistent rumors were claiming) secretly mutinied against Kane in 1854 (an executable offense) and later conspired to lie about it.
[The able Kane expedition member, Johan Carl Christian Petersen of Denmark, highly expert at every aspect of arctic survival (Geo.Corner Dr.Kane of the Arctic Seas Temple Univ 1972 p.132) told the truth. (Prof. Oscar Villarejo's Dr.Kane's Voyage to the Polar Lands [UPa 1965] is primarily based upon Petersen's account of the mutiny.) Which proved — in case his foreign-ness was not sufficient in itself — that Petersen was unqualified to lead a US polar expedition.
(Spain's Ferdinand & Isabella were not famous for tolerance, but even they didn't mind sending an Italian across the Atlantic in 1492. Granted, nothing much came of the idea….)]
The funniest thing mutineer Hayes ever said (HO318; 1861/4/27), fully worthy of DIO's Doubletakes column: “My men have failed me … as those of Dr.Kane did before me.”
[Disbelieving that there was a mutiny, Amer Philos Soc chief Corner (1972 p.290) attacks his colleague and predecessor Villarejo for erroneously charging that the official USS Advance ship's “log” (Hist. Soc. Pa. archives) of the expedition was mutilated (to hide the Kane mutiny) — declaring instead (Corner pp.278 & 290 vs. Villarejo 1965 pp.25f & 172f) that the supposedly destroyed section is simply part 1 of the Kane “journal” (second part at Stanford Univ archives), and thus that Villarejo had erred on whether there was a hidden mutiny. But it is Corner who has erred. (DIO thanks Stanford archivist Patricia Palmer for verifying this by direct examination, and for sending photocopies of the disputed records.) A close comparison leaves no doubt that Villarejo was correct (the log and journal are utterly different, as a comparison of the 1855/5/1 entries will readily show), and thus that the chief of the most venerable US academic institution falsely denigrated the valid work of a fellow dedicated Kane historian. (More on this matter will appear in DIO 6.2.) Not that Corner ever had the integrity to publicly admit it. (DIO's publisher was told several falsehoods by Corner in connection with his bowdlerization of a paper which he feared would upset the National Geographic Society.) As for whether the Hayes-Sonntag defection was mutinous: Villarejo was a colleague of several admirals in the U.S.Navy and knew perfectly well what constituted a mutiny.]

Upon his return, hero Hayes went forth to thrill a super-patriotic nation (NYTimes 1861/11/15:3:1):
“The land was taken possession of in the name of the United States [DIO: though the states were rather less than “united” at the time], and the flag which was used on the occasion has covered the most northern known land upon the globe. [Prolonged applause.]”

But the war diverted attention. And, as time passed, it gradually (culminating in 1873) became apparent to the mestablishment's aghast ultra-socialites that the explorer they'd in 1860 lauded, funded, fan-fared, and ceremonially seen-off to reach the North Pole, had instead led a disastrous expedition by any measure (science or latitude-record) and had perpetrated a fake farthest-north-land claim, adorned with altered dates, north latitudes never remotely attained, inventions of non-existent geography (fantasy bay, capes, peak, Open Polar Sea, etc), even corruption of (his own) existent geography — all to set up a false claim to have found the northern-most land on Earth.
Why? Frankly: to make a buck. (His arctic-predecessor-martyr and former colleague Kane had [Corner 1972 pp.237f] gleaned a fortune with his hit 1856 best-seller on his 1853-1855 expedition.)
[This wouldn't be a unique instance of an arctic explorer lying for gain. But Hayes was the hardy pioneer of what ultimately became a durable tradition.]

Because Hayes hid his sins and destroyed his diary, it has generally been believed that his 1861 farthest-north point was an insoluble mystery. E.g., Sir Wally Herbert Noose of Laurels 1989 Chap.4: “How far Hayes went no one now will ever know”.
However, in what follows, we will discover that long-elusive point to remarkable precision: within ordmag 100 meters.

Upon realizing they'd been snookered, the very same mestablishment (that had foisted Hayes upon the community of genuine scientists) conspired to protect its own rep for judicious trust-worthiness — by betraying the scientific community's and the public's trust: covering up Hayes' sins, just letting him (and thus its own folly) fade quietly down history's memory-hole.
[Reminds one of how corporations prefer to handle embezzlers found in their midst: nothing said publicly, just a smooth divorce — on the quiet, to keep the firm's reputation from being damaged. Such priorities are obviously selfishly dangerous, since the perp is then passed on to his next victim as blemish-less.
The Hayes case well illustrates the point: AGS-backed Kane's assent to hushing-up the 1854 Hayes-Sonntag-etc mutiny handed Hayes to the AGS as a seemingly ideal next US polar hero.]
It is one of the purposes of the present paper to undo that all-too-typical exercise in institutional dishonesty.
[Not the last time that one institutional polar cover-up led directly to the need for yet another. See the Cook-Peary-Byrd triple-hoax chain at DIO 10 [2000] pp.4-5.]

[In what follows, Hayes' 1867 book The Open Polar Sea will be abbreviated “HO” so that page x will be written as “HOx”. His original ms record, “Bearings” (American Geographical Society archives), will be similarly abbreviated, so that page z in it will be referred to as “HBz”.
We will generally measure distance in nautical miles (15% larger than statute miles), abbreviated “nmi”; so 1nmi corresponds to 1' of great-circle distance on the Earth's surface. A degree of latitude equals 60' or 60nmi. But a degree (or 60') of longitude equals only c.10nmi near 80°N, the approximate latitude we will be visiting below.
For the actual geographical coordinates of sites, capes, camps, etc, Yahoo was adopted here as the most trustworthy of the various internet maps, since its latitude (& NASA's) for Cape Jesup (83°38'N) closely matched the real latitude of that well-measured spot, the northernmost coast on Earth, discovered by the greatest US arctic explorer, Robert Peary 1900/5/13.
However, there is no guarantee that the Yahoo maps do not contain small but non-trivial systematic errors. The various internet maps disagree with each other by ordmag 0'.1 (gt-circ) in the region of the globe we will be investigating below. Note: if these contain common errors, the accuracy could be worse than that.]

The enormity and sacrilege of Hayes' imposture is best précised by his own lying boast (HO374-375):

With [Sir Edward Parry, who in 1827 reached record-latitude 82°3/4 N over sea-ice north of Spitzbergen] I will now divide the honors of extreme northern travel; for, if he has carried the British flag upon the sea nearer to the North Pole than any flag had been carried hitherto, I have planted the American flag further north upon the land then [sic] any flag has been planted before.

Hayes seemingly had all the attributes that mattered. An Ivy League M.D. (UPenn) and pioneer 1854 Ellesmere explorer with the Advance Expedition (1853-1855) of Elisha Kent Kane (another Philadelphia-area M.D.-explorer), he was: an inheritor of the glorified Kane's mantle, on the American Geographical Society's Council (see John Wright's centenary history of the AGS 1851-1951 [1952] p.52), Smithsonian lecturer (HO5), and a genuinely durable traveller (as was fellow faker F.Cook), who'd lost some of his toes to frostbite (Villarejo 1965 p.148) — among myriad other sufferings, sacrifices, awful disappointments, and wearingly strenuous & dangerous strivings (e.g., HO301, 366, & 369) in the service of exploration and ambition. (He is sometimes referred to as the 1st non-Eskimo to set foot on Ellesmere Island.) His false reports are all the more tragic because he possessed above-average if not extreme shares of intelligence, skills, and admirable qualities.

If one accepts the 1861 story he told, Hayes was apparently an amateur — both technically and conceptually, regarding serious mathematical navigation.
[By contrast, such achieving and heroic explorers as Peary, Amundsen, & R.Scott were adept at the use of spherical trig-based navigation.
Note: If Hayes' bumbling 1861 yarn that his watch stopped accidentally were true, he was obviously an amateur in being unable to effect remedy. But its falsity (which will be established below) is far more indicting, since his patched-together & inconsistent tale (meant to alibi-cover for his exaggerated north-latitude claim) is even bumblier, thus hardly a credit to his science or cleverness.]

Unfortunately, such trivia mattered far less than Hayes' high political associations and skills. Even in remote Greenland in 1860, he still had the touch, setting out for the Upernavik locals a formal meal (HO41-42)

to the representatives of King Frederick the Seventh, at this most northern outpost of Christian settlement. Accordingly I sent my secretary, Mr.Knorr, out with some formal-looking invitations, gotten up in all the dignity of Parisian paper and rose-scented wax. … clean white table-cloth …. noble salmon — an excellent punch from Santa Cruz….

And Hayes' mutinous history was unknown because of a previous cover-up as air-tight as the one that later protected the public from knowing what fools Hayes had ultimately made of all his ultra-eminent backers.

Both Kane and (much more so) Hayes exaggerated their latitudes to claim new farthest-north-land-reached records, launching a trend in US polar fakery that ultimately culminated in the 1908-1926 triple-hoax chain of Cook-Peary-Byrd.
[Which we have discussed elsewhere: in DIO 10 [2000] pp.4-5.]
Adding Kane and Hayes to the more famous case of Frederick Cook, M.D., we have the extraordinary spectacle that the three clumsiest fabricators in US arctic history were all M.D.s (a point we will return to) — which doesn't say much for antique US medical ethics.
[Additionally, there is the case of Hayes' own thieving doctor.
Note: back in the era when a general practitioner's ministrations were as likely to harm as help his patients, perhaps bedside-manner-bluff was the prime key to success in the field.]
It is also enlightening to note that the only one of the three ever attacked (e.g., Geographical Review (AGS) 5:140-141, 43:129-130) in US geographical journals was also the only one who publicly criticized the societies. (See, e.g., F.Cook My Attainment of the Pole 1911&1913 pp.543-544.)

After his service with (and mutinous betrayal of) Kane, Hayes then headed his own expedition (1860-1861), aiming to cross straight to the North Pole, via the mythical “Open Polar Sea”, supposedly semi-verified by Kane's 1853-1855 expedition. (The idea of an open polar sea long [Corner 1972 pp.108-109] pre-dated Kane & Hayes, whose alleged sightings were merely feeding the prejudices of moguls who already believed in it.) Note the clarity of Hayes' intentions as revealed by letterings on the map published with his 1860 book, An Arctic Boat Journey.
[Which told the story of the 1854 Kane Mutiny. Was the 1954 H.Wouk novel's title, Caine Mutiny, a hint that Wouk knew who played intolerable Queeg in the only USNavy mutiny? But, unlike Wouk, Hayes left out the mutiny part.
James Cook-protégé Capt. Ned Bligh (on whose greatness as a navigator, see C.Nordhoff & J.Hall Men Against the Sea 1934), was an earlier (1789) object of a mutiny, this in the British navy. Coincidence dep't: both mutinies took place shortly after seamen mingled for months with a people of looser, more hedonistic mores than those of WASP civilization. DR will typically endear himself to PC anthropologists by commenting that his 1996 March visit to Tahiti impressed upon him the unlikelihood of anyone achieving much, who has long lived amongst the natives of such civilizations. Paul Gauguin is not an exception but indeed the perfect example. Robert Louis Stevenson comes nearest to providing the rule-proving exception.]
Probably the looniest item on the Hayes map he published with his 1860 An Arctic Boat Journey is his huge “Probable Northern limit of the ice belt in the Summer”. I.e., if you want cold, forget about the Arctic Ocean, and instead make for the map's “Approximate American Pole of cold” in Canada, the coldest spot in the American hemisphere, at about 78°N, 95°W. Hayes even asserted that the Earth's cold pole was not the geographical but the magnetic pole, and the Royal Geographical Society actually printed this stuff. (Hayes 1858/5/23 letter, Proc Roy Geogr Soc 3:148.)
Keep in mind: this was the top US polar scientist in the eyes of the world scientific community's politicians for the next 15y. (Indeed, it was the sci-fi just cited that got Hayes his backing.)
[As DIO readers are well aware, there are academic fields today that exhibit like acumen and priorities when gauging scholarly talent. Generally speaking, science is happily no longer one of them.]

Never wanting in the patriotism dep't, Hayes named his ship (a schooner formerly called Spring Hill): the United States. (Re-named so by an act of Congress: Hayes 1861 p.151; HO8.) He went north more unanimously and flag-wavingly backed by US academic societies than any arctic venture before or since. (THose of NYC, Philadelphia, Boston, Washington. DR is happy to note that the only major US cultural center having nothing whatever to do with helping put over Hayes' fake was Baltimore.) This included the blessing of the US' leading geographical figure, Henry Grinnell (head of the young American Geographical Society of NY), for whom he & Kane tried to claim&name northern Ellesmere Island. (See on left of Hayes-Smithsonian map: [Schott 1867 p.i opposite.] The name ultimately didn't stick.)
[An observation regarding the entire history of US polar exploring: faking tended to occur more in connexion with privately-funded expeditions. By contrast: despite its many deaths, the gov't-backed 1881-1884 U.S.Army expedition under Adolphus Washington Greely produced accurate reports, solid science, and new geography — including the most undubitable of all of polar history's Farthest-Norths (1882).]

Among other committees, academic societies, associated luminaries, & (notably) publishers subscribing to or assisting Hayes' expedition (listed at HOxi-xvi & 5-12 & Hayes, Smithsonian Annual Report 1861:149-160 pp.149 & 157):
American Geographical Society (NYC): ultra-mogul of US geography Grinnell, able astronomer (soon-to-be Major-General in the upcoming war) Ormsby Mitchel, Harpers Bros, G.P.Putnam;
American Association for the Advancement of Science;
American Philosophical Society (US equiv of UK's Royal Society);
American Journal of Arts & Sciences (NYC);
Academy of Natural Sciences (Philad): Childs & Peterson, J.B.Lippincott & Co, A.Bache (US Coast & Geodetic Survey head);
top US scientist Jos.Henry (Smithsonian Institution head);
Academy of Arts & Sciences (Boston): Louis Agassiz (Harvard), Benj.A.Gould (founder of the still deservedly prominent Astronomical Journal), for whom Hayes named Gould Bay (HO336n1), Edward Everett (top US academic of the day [i.e., automatically doomed to be as forgotten as Izzy Bowman]), even the marvelous Nathaniel Bowditch.
Boston Society of Natural History;
Academy of Natural Sciences of Philadelphia.
And: The Bible Society

The ship was fêted in Boston harbor on its scheduled departure-date, 1860's Independence Day — a touch of patriotism that has been blamed for causing the ship to arrive in the north too late in the Summer for breaking through to the Arctic Ocean, beyond Smith Sound. The July Fourth speakers included (HO12) Harvard's president & the Governor of Massachusetts, among other “renowned statesmen, orators, divines and merchants of Boston, and by savans of Cambridge [Harvard]”. After 3 more days of delay, the ship finally sailed on 1860/7/7 (HO13).

The Hayes expedition resulted in the most disgracefully bungled arctic chart in the history of US science. Click link to view the Smithsonian Institution's 1865 map of Hayes' fantastic alleged 1861 explorations and discoveries on Ellesmere (north Canada). (Charles Anthony Schott, Smithsonian Contributions to Knowledge #196 [1867] Physical Observations in the Arctic Seas by Isaac I. Hayes.)
[It was perhaps the eventual awareness of Hayes' unreliability that educated the AGS: note that it never for a moment fell (as National Geographic eagerly did) for the later fake N.Pole claims of able engineer Peary (1909) and able politician Byrd (1926), who had been a congressional lobbyist before he became a polar hero (DIO 10 [2000] §B7 [p.16]), even while justly and generously honoring both explorers with AGS medals for their considerable genuine polar contributions: 1898-1902 and 1929-1930, resp.]

It will be instructive to compare Hayes' map with Kane's, as rendered by the same USC&GS astronomer, Chas. Schott in 1860, so we provide the Kane map, too.

Given that the actual east coast of Ellesmere trends far more northeastward, it is immediately obvious that Hayes (in the Hayes-Schott map or opp HO72) has largely copied Kane's coastline — including its dominant errors. A plagiarist's nightmare.
[Note that in the later Hayes map, Cape L.Napoleon has been moved to replace Cape Prescott. In the Kane-Schott map, the Ellesmere (“Grinnell Land”) capes up to Cape Frazer (spelled “Fraser” today) are Hayes' 1854 May discoveries. Those beyond Cape Barrow are based upon Kane steward-valet Wm.Morton's 1854/6/24 sightings (with Eskimo Hans) and thus are based merely upon guesstimates of the positions of far-off lands, the most northern being those only barely seen from Greenland's Cape Constitution (80°.6 N, 67°W), itself grossly mismapped (see Schott 1860 chart) at 81°N, 66°W. (Kane initially put it at 81°22'N or even higher, 81°44'N; see Rawlins 1973 p.22.) Thus, the very base-point of the northern Morton sightings was seriously in error.
Morton being Kane's valet, it is an oddity that the sole non-Eskimo witnesses to both the 1854 & 1861 exaggerated farthest-norths were the personal servants of the expedition leaders: Kane's W.Morton & Hayes' G.Knorr, resp. This tradition was later extended by Peary's man, Matt Henson, for Peary's 1906 & 1909 faked latitudes.
The Morton claim of farthest-north-land-trod is still widely believed, though it is possible that in 1773 Constantine Phipps and even (young) Horatio Nelson set foot on Spitzbergen-area land that was further north. (North of Spitzbergen, the Phipps expedition sailed to 80°48'N.) And returning members of the E.Parry 1827 expedition (which got to 82°3/4 N over the ice north of Spitzbergen) probably stood on land further north than Morton's 80°.6 N.]

During his remotest 1861 travels (5/14-18), Hayes got only about 20 nautical miles north of his 1854 farthest-north point, Cape Frazer.
[Here, throughout (unless otherwise noted), references to geographical capes, bays, lands, etc will refer to modern appellations. Comparing the Hayes-Smithsonian chart to a modern map will shock any reader — not only at the audacious degree and folly of Hayes' fraud but at the extent to which the science establishment put aside even international competitiveness to paper-over his deceits by retaining many of the names of Hayes' wildly mis-located or never-seen capes etc, while shifting them (sometime amusingly) far out of their originally mapped positions. Wryly commenting upon such mis-geography is early Hayes-disbeliever Greely (1886 1:73 on Hayes' Carl Ritter “Bay”): the agreeable mapping by the 1875-1876 Brit expedition under George Nares (who saw through both Hayes & Cook) of “the indentation at that point [81°.9 N on Ellesmere's east coast] as a bay would seem to be a courtesy on the part of our English cousins toward Dr.Hayes, who located there [see Hayes-Smithsonian map] an inlet some twenty-five miles deep. The actual indentation is so slight, and the curve so great, that it is a bight rather than a bay.”
(In 1909, expert navigator [now Admiral-Sir-George] Nares, whose maps [of the region that Kane & Hayes had messed up] were highly competent, summed up the N.Pole claim of Cook — a doctor, backed by gambling-den proprietor J.Bradley — with incomparable contempt: it must be “either an American gambling scheme to make money or a medical project to test the stupidity of the public.” See Rawlins 1973 p.200.)]

Cape Frazer had been Hayes' genuine and well-mapped discovery, made on 1854/5/27-28. (Mis-printed on the Hayes-Smithsonian chart as 1854/5/8.) But in 1861 he stretched his 1861/5/14-17 advance of c.20nmi beyond Cape Frazer into over one hundred nautical miles — map-displaying Kane's long fantasy Canadian coast running virtually north-south (merely 12°-15° E of north, whereas the real Kennedy Channel runs about 30°-35° E of north): “Grinnell Land”.
[The error can be largely explained by the 18° error in Hayes' chronometer. (But it is remarkable that Kane's map should make much the same error years before Hayes' watch stopped!) Of course, Hayes (unlike Morton in 1854) never in his life got into Kennedy Channel at all; but he did get a roughly accurate azimuth — as seen from Cape Collinson — of Cape Lawrence, the western of Kennedy Channel's southern portals. Thus, despite the false (nearly N-S) direction of the coast from Cape Frazer to Cape Collinson, Schott was enabled to get a pretty good idea of the off-north slant of Kennedy Channel as seen from Cape Collinson. By contrast, Hayes' own map (opp HO72) has the same slant way more nearly due north (only c.15° east of), which is consistent with his erroneous watch, but conflicts with his own computed true azimuth.]
“Grinnell Land” is displayed to the left (west) of Kennedy Channel in the chart. Hayes placed his alleged 1861 farthest-north-land-reached right on the Ellesmere (“Grinnell”) east coast at latitude 81°35'N, longitude 70°30'W — barely exceeding the Kane expedition's own exaggerated claim of having reached 81°22'N on 1854/6/24.
[Hayes asserted that Morton in 1854 didn't get past 80°56'N, the exaggerated latitude shown on the Kane-Schott map. (See Hayes 1858 p.147 and NYTimes 1861/11/15:3:1.) But Hayes reported his own claimed 1861 latitude just high enough that it was #1, no matter the prevailing opinion on Kane-Morton. So the ambiguity regarding Morton's highest latitude probably forced the Hayes exaggeration's ultra-ludicrousness (80°07'N reported as 81°35'N) — a way-overdone stretch-try at putting beyond dispute that he had achieved the highest latitude ever on land. This leap-frogging fabrication-farce was finally cut short by the accurate 1871-1882 work of the US' Hall, Brits Nares-A.Markham-Beaumont-Aldrich, and the US' Greely-Lockwood.]
But the spot at the given geographical coordinates is deep-inland not coastal — which is a prime reason why none of his latitude claims are now taken seriously by anyone.
[By far the best modern account of Hayes' 1860-1861 expedition — and the genuine agonies he endured during it — is that of Canadian historian Pierre Berton Arctic Grail 1988 Chap.9 Pt.2. Note that we are not covering here Hayes' 1854 & 1861 crossings of the hummock-packed Kane Basin, from Greenland to Ellesmere & back. He compares the ice-chaos he met (see illustration opp. HO322) to “a thousand Lisbons crowded together and tumbled to pieces by the shock of [a meta] earthquake” [HO312] and despairs [HO314] of the impression that he must travel 5mi to make 1mi of northing. Do not fail to realize that this was the worst of his travails.]

Nonetheless, the questions remain:
[a] Is there an innocent explanation?
[b] Did he merely miscalculate? — as some have suggested.
[c] Did he commit fraud?
[d] Did he fake his farthest north Sun-sight sextant datum?
Our respective answers below will be:
[a] At the outset, yes — in part.
[b] No.
[c] Yes.
[d] No. Technically, anyway.

The crucial portion (1861/4/10-5/29) of the relevant diary is conveniently lost. But decades ago DR consulted, via the expert assistance (1971/9/20) of AGS Librarian Lynn S. Mullins, Hayes' 1861 survey-book, “Bearings”. (As noted earlier, this ms will here be abbreviated as just “HB”.)
[HB is item#8 of the AGS holdings of Hayes material. The AGS archival list calls it “copied from field notes” — but it has all the earmarks of an original field document. But he may well have copied material into HB. After all, if if he had a field-journal (HB) called “Bearings” (for [mostly time-independent] compass azimuthal data), wouldn't he have a companion called “Altitudes” for recording sextant data and their times, for finding latitude and longitude? Note: all HB's altitude sextant look (see reproductions here) as if they were not in the original HB but were taken from “Altitudes” were later just tucked into blank spots Hayes found here&there on HB's pages: virtually all sextant data in HB are at the bottom of a page, and not always chronologically quite right. (This may also be true of compass variation observations: HB22&38, Schott p.86.) Among the mix-ups on HB40 is a suggestion of mis-copied material.) This point and the subsequent disappearance of the “Altitudes” journal suggest that all altitude sextant data in HB are non-primary. They were selectively copied from “Altitudes” into HB before he disappeared the original “Altitudes” journal. Thus, HB is the sole known ms relic of his 1861 Ellesmere trip.]

This material permitted DR's solution of Hayes' actual whereabouts on 1861/5/17, and below reconstruction in detail of Hayes' trip.
As announced for the 1st time in Rawlins Peary at the North Pole; Fact or Fiction? [1973] p.25, Hayes' true 1861/5/17 farthest north was Cape Collinson (Ellesmere Island, Canada), barely past 80°N.
Later-claimed latitude: 81°35'N.
[For the claim of farthest-north-land-reached at 81°35'N., see New York Times 1861/10/11 pp.4&9 or Isaac Israel Hayes The Open Polar Sea (HO) 1867 HO351 — a book which (Rawlins 1973 p.24) got Hayes the gold medal of the Royal Geographical Society. Just in time. Hall's expedition was the 1st to see (1871) that Hayes that had invented the geography of east Ellesmere, and the Hall survivors reached civilization in 1873.

After departing his Greenland base-camp (“Port Foulke” 78°17'.4 N, 72°38'.6 W, about 2nmi from the well known Eskimo village of Etah), and crossing the Kane Basin's ice-hummocks — shedding some men en-route — on a path virtually due north (presumably by compass-course, if his chronometer was already off, as he indicated), he and 3 companions (dog-manager [HO40] Peter Jensen, seaman [HO10] John McDonald, and Hayes' sec'y [HO10&41] Geo.Knorr) reached Canada on 1861/5/11 near Ellesmere's Cape Hawks (79°32'N, 73°W).
[On the left find a narrow map of the Ellesmere coast from Cape Hawks (bottom) to Cape Lawrence (top), the latter being Hayes' eventual furthest-north-land-seen.
Every major point on the coast is linked to glowing citations of it in the text, so that clicking on the citation will swiftly bring up the map — and to precisely such vertical location that the clicked coastal feature will be nearly due left of the screen's center.
On the map, Up = nearly northeast, since this is a 45°-tilted piece of one of several splices (more below) which DIO's Keith Pickering has accomplished from Geological Survey of Canada color topographical (“topo”) maps. Details regarding all these maps (including the present one) are found below.]
The Hayes party then sledged along a coast that trended somewhat east of north-east at first (until he rounds Cape Frazer). Hayes' 1st Sun-sight (Table 2 below) on Canadian soil since 1854 was taken on 1861/5/13 at what he called “Foggy Camp”: a double-altitude via pocket sextant (Gilbert's #3 [Schott 1867 p.20n]), with mercury (Hg) reflecting artificial horizon.
[This he estimated was c.1/4 mi SW of Point Joy. (Though Hayes' distance estimates are usually exaggerated.) See the tiny triangle near that feature on the Hayes-Smithsonian map. (Schott misplaces the camp SE of Pt.Joy. The original HB23 sketch makes it SW.)]
It was a longitude observation. Which should have instantly clued him to the fact that there was a huge error in his allegedly lone pocket chronometer.
[The compass' direction at chronometer-“noon” had also not already given him analogous pause: a virtually (perhaps really) — incredible symptom of apparent navigational obtuseness. Hayes alibi-comments on such matters in his book's preface (HOviii) provide yet another example of his acting as prototype for F.Cook: “entire accuracy was not attainable in the field, inasmuch as I had neither the leisure nor the facilities for reducing the magnetic [compass] variation, nor for obtaining the absolute time.”
What an ideal choice to lead an expedition universally backed by US scientific societies!]
Shades of R.Byrd's 1926 N.Pole hoax, which crucially exploited the ludicrous claim that he had carried but one sextant on his journey, and (a-là Hayes' non-winding his watch) it “broke” during the trip. This, though Byrd is known to have carried multiples of every other portable navigation-related instrument. See DIO 10 [2000] end-note 8 pp.91-92.]
[A conventional sextant time-check by Hayes would have required spherical trig. (Though a simple equal-altitudes procedure would've sufficed. And perhaps did.) But Dr.Hayes evidently didn't know such navigationally-essential math. (Not a scrap of it appears in HB.) I.e., thanks primarily to Hayes' political connexions (built upon honed skills at buttering-up those in power), the US science establishment had exalted and sent-north a supposed exploring-expert who didn't know navigation past 1st grade arithmetic. (And that's the least of Hayes' pretensions.) This is on the level of the American Museum of Natural History in 1913 sending out Peary-1909-expedition veteran D.MacMillan to search for Peary's non-existent Crocker Land — without even bothering to check Peary's records for the equally non-existent data showing he'd ever seen this perhaps most northern land on Earth. (See Rawlins 1973 p.73.)]

On 5/14, the party passed Cape Frazer (78°3/4 N, 71°W), his farthest north in 1854, camping just NE of there, at 78°47'N, 71°.1 W, where he took a latitude observation that disagreed seriously with the latitude he'd obtained for the same spot in 1854. Proceeding in a more northerly direction than previously, the explorers camped the next day (5/15) at what Hayes privately called “Tired Dogs Camp” (HB25&34), suggesting transport problems. Before crossing Scoresby Bay, he realized all his men were worn out (HO342), so he left the injured Jensen, his strongest man (HO342-343) and dog-manager, with McDonald on the bay's south shore (on the north shore of what is now called Cape Knorr: see above-left Canadian GPS Survey topographical map), telling McDonald (HO343) that he expected to be back within 5 days. He then struck northward with only his sec'y Geo.Knorr as companion. By 5/16, matters had worsened to “Bewildered Camp” (HB27).

On 5/16-17, they cleared 80°N, which extremely few other Europeans had done up to that time. (Eskimos may've. Hayes found traces of Eskimo camps near 80°N: see, e.g., HO337&341 and the Hayes-Schott map. Morton had, too, virtually at his 1854 farthest: Kane 1856 2:377.
Hayes took compass bearings of northern capes as seen from the east coast of Cape Collinson's southern extension (at a place we'll later see was Hayes' Cape#8): 80°03'N, 70°.5 W. Low on hale men & dogs, short on provisions, rightly fearing that melting ice would lengthen bay-crossing times (esp. the Kane Basin return's), a tired and bitterly disappointed Hayes was forced to make his last camp there. According to the innocent-error theory of the expedition (which we will ultimately argue was deliberately staged by Hayes): after a “noon” sextant shot of the Sun at (see Table 1) about 36m past his slow-chronometer-noon (an impropriety — possibly from variable weather [and perhaps not] — which he may (if we assume — contra strong evidence — that he still didn't know correct time) initially have regarded as minor), Hayes started at 2PM by his watch (HB31), towards the northern part of Cape Collinson (see topo and Cape#11 on HB31). He claims he found by trial that (what is now called) Richardson Bay was impassible due to unsafe ice. He then (HB31) returned to the last camp, lunched, “Displayed flags”, and headed south. (Hayes considered naming the bay “United States Bay”: see HB28. It was eventually instead identified with Kane's Lady Franklin Bay, placing it at c.81°3/4 N.)
[See both the Kane-Schott and the Hayes-Schott Smithsonian maps. Curiously, Captain Edw. Inglefield (the 1852 discoverer of Ellesmere Island) had placed a “Lady Franklin Bay” on the east side of Smith Sound, on the west coast of Greenland in the 79th degree of latitude.]
When later explorers found a bay at roughly the Kane-Hayes latitude-guess (though far different longitude), they called it: Lady Franklin Bay.
[Consider the resultant oddity that Greely's 1881-1884 expedition in that region became known as the “Lady Franklin Bay Expedition”, thus acquiring its name from the false Kane-Morton-Hayes reports; yet Greely's was a geographically honest and highly productive endeavor, which achieved history's most impregnable Farthest-North claim, in Greenland (83°24'N, 41°W), reached on 1882/5/13 by Greely's James Lockwood. (A genuine arctic martyr, who died in the north and is buried beneath an imaginatively rendered tombstone at the US Naval Academy: a ruled solid globe whose axis is tilted 83°24'.) His cairn-record was later recovered by, ironically, Greely's most undeterrable detractor, Rob't Peary. (Rawlins 1973 p.29.)]

Rawlins Peary Fiction [1973] p.25 found Hayes' 1861/5/17 farthest position initially by counting deep-indentation-bays-crossed in HB. (Hayes' published map shows 2 such bays, each miles-wide, between Cape Frazer & farthest. But HB shows only one. Note Greely's comment, above.)
[Hayes was an able artist. And not just at the con. In addition to his ability to draw scenes, he sketch-mapped the coasts he visited, reasonably-well converting horizontal experience into vertical depiction. He was also an engaging writer, whose works signify a person of reflectivity, sympathy, and some humor.]
But the Cape Collinson solution is further iced-confirmed by Hayes' set of compass-bearings (augmented by HB28's excellent labelled scene-sketch) taken on 1861/5/17 from HB's Cape#8 (80°03'N, 70°.5 W, on the southern part of Cape Collinson's easterly extension). The sign-less bearing-data (HB28) were measured with respect to compass-south (the true azimuth of which was c.70°), where we include in brackets Hayes' own politically-canny names for these capes (which he sets out at HO372-374, mapping them opp. HO72).
[Does the repeated kissing-up to foreign biggies (which we're about to see here, below) hint that Hayes' claims were becoming suspect in the US even before 1st hand witnesses' dis-confirmations arrived back from the arctic in 1873? (No foreign-name suggestions appear in HB.) Hayes was still internationally pristine at least as late as 1867. But, after 1873, when Hall-expedition members began returning home, it was all downhill for Hall's long-time nemesis Hayes.
The long-delayed moment of truth is recorded, live, in Hall expedition survivor G.Tyson's diary (G.Tyson & E.Blake … Drift … 1874 p.148) for 1871/8/28, in Kennedy Channel (moving northward on Hall's ship USS Polaris, into the unknown): “We have now gained lat. 81°35'N. Can't make any thing out of the charts.” (Based upon the maps of Kane and Hayes.) Later in the day (TD 148): “Here should be the open sea, but there is land on both sides of us!” (Mortified Morton was on the ship at the time. Which argues in favor of his at least partial innocence of deliberately exaggerating.) See also G.Nares Narrative … Voyage to … Polar Sea 1878 1:101.]
Hayes usually measured azimuth eastward from compass south (Schott 1867 p.84). The capes' HB28 compass azimuths, as seen from Cape#8 (with [in brackets] Hayes' names as found at HO346, the Hayes-Schott map, and-or the map opp HO72):
Cape Lawrence (HB Cape#14 [Cape Union]) 38°1/2;
Cape Joseph Good (HB Cape#13 [Cape Frederick VII (Danish King)]) 41°;
Cape Wilkes (HB Cape#12 [Cape Eugénie (French Empress)]) 42°1/4;
Cape Collinson (HB “Cape 10” [Cape Cracroft]) 51°1/2.
Cape McClintock (HB Cape#7 [Cape Back]) 227°;
Cape Knorr (HB Cape#6 [Cape von Buch]) 222°1/2.
(Note: Hayes accidentally wrote the azimuths for Capes#6&#7 in reverse.)
[Capes Cracroft, Back, & von Buch were named by Kane-Morton: see Kane-Schott map.]

Comments:
[a] Hey, where did Cape#8 disappear to? (According to the combined coast-sketches of HB27 and HB31, Cape#8 obviously should be more visible than Capes#7&#6.)
[b] Cape#11 [Cape Lieber (AGS: HOxii&6)] was merely the [here-invisible] other [north] side of Cape Collinson.
[Note: we are throughout calling Hayes' farthest point Cape#11, on the north side of the Cape Collinson east-point bulge. Careful distinctions on our part are here necessary because Hayes' HB31 confusingly labels the bulge AND the north part together as “11”. (Contra this, the internet maps make it clear that the farthest-north tip [supposedly Cape#11] is invisible from the southern part of Cape Collinson and HB28's scene-sketch confirms this.) Further confusion, the east bulge is called cape “10” in HB28's scene-sketch, which brassily moves Cape“10” from the HB31 coastsketch's placement of it (on the south side of Cape Collinson) all the way northward 2nmi across the cape and converts it into the east-tip-bulge, which is (see topo) on the north half of Cape Collinson.
This ploy presumably grew out of his sly double-use of the quarter-circle bay between Cape McClintock (Cape#7) and the southern part of Cape Collinson (Cape#8) — amidst the pretense that HB31's re-cycling of this bay can explain why Cape#11 can't be seen from “Cape 9” — forgetting that, from HB31's “Cape 9”, one can't see Capes#12-14, either!]
The compass variation in this region was then about 110°W. This crucial datum can be ascertained from modern models. Or roughly from nearby PFoulke data, or by correcting the Hayes expedition's own magnetic observations: Schott 1867 pp.83f.

But one does not even need the exact 1861.38 compass direction at Cape#8 in order to find the near-coastal point from which the differences between the foregoing bearings will match those measured off a modern map.
[DIO's Keith Pickering has scrupulously created a splice of several Canadian topo maps. The coordinates of the topos agree so closely with those of Yahoo that we will ignore minuscule discrepancies.]
Testing the azimuthal-differences (of capes seen by Hayes from Cape#8) on the topos or on Microsoft's maps along the Ellesmere coast by trial, one finds a best fit (for the position from which the azimuths were measured) slightly inland on Cape#8, just off the east tip of which (80°02'43"N, 70°30'.0 W) Hayes camped late on 5/16. (This is our 1st hint suggesting Cape#9's non-existence, though Hayes repeatedly alters the record to say that these azimuths were made from a “Cape 9”.)

Inland makes sense, because an experienced examination of HB28's scene-drawing proves it was made from a high vantage point.
[HO348: “I determined to climb the hill above the [farthest] camp”. Hayes' 800-foot climb for a view from a cliff above his final camp (HO348-349, falsely dated 5/18), looks initially like a temporal and spatial transplant of this precisely-located Cape#8 5/17 HB28 vista-event — until we here learn that cape “10” (the site of his true farthest camp) WAS Cape#8.
(Common sense: where's an explorer going to climb highest for a view? Any old place? Or virtually his farthest? See analogous discrepancy regarding Byrd: DIO 10 [2000] §C16 [p.22].)
Given that he can see past Cape Joseph Good, well out into Rawlings Bay — roughly to the foot of Cape Lawrence [c.23nmi away] — Hayes was likely well over 100 meters above sea-level when he made the HB28 drawing of the vista seen from above Cape#8.
(Thus, he could see the bay's surface out to more than 20nmi — and mountains over 1000' high would be visible for another c.40nmi, for a total of roughly 60nmi of visibility over the Earth's curvature, correcting for refraction.)
Note that the Hayes book's romantic rendition of the same scene makes it look (due to artistic insertion of two human figures into the foreground) as if the viewer is but 10 meters above bay-level. Similar analysis at DIO 7.3 [1997] ‡9 n.65 [p.140] regarding F.Cook's photo of his non-existent “Bradley Land”.]
And it would be impossible to satisfy the azimuths of Cape Collinson, Cape Wilkes, & Cape Joseph Good and still see Cape McClintock (Cape#7) at all — unless one were on the heights.
[See topo, where you can verify this point. And you can use the map to measure for yourself all the azimuthal fits. (Whatever tiny absolute errors exist in our maps tend to be pretty constant throughout the region, so azimuths are virtually identical on all maps.) On the topo, Cape#8 (the east tip of the southern part of Cape Collinson) is at 80°00'N, 70°.8 W. Subtracting the foregoing (compass-oriented) data from 70° will translate them into azimuths measured familiarly eastward from true north (not magnetic north): Cape Lawrence 31°1/2, Cape Jos.Good 29°, Cape Wilkes 27°3/4, Cape Collinson 18°1/2, and (adopting the correction cited earlier) Cape McClintock −152°1/2 & Cape Knorr −157° (where negative simply means azimuth west of true north).]
The distant capes' azimuthal matches are so remarkably close as to leave no doubt whatever of the already obvious place of Hayes' ultimate 1861 latitude: Cape Collinson, of which azimuths-observation-point Cape#8 is the southern part.
This is the camp (80°03'N, 70°.5) where he took the “noon” Sun-sight which “proved” that he was then at 81°32'N.

Hayes later alleged in detail (HO346-347) that he had on 1861/5/18 made several harrowing attempts to cross Richardson Bay, claiming (HO347) to have achieved a 4 mi northward sally out onto the bay. However:
[i] From Cape Collinson's northernmost point, Richardson Bay is only 4nmi across.
[ii] His coast-line-travel sketch (see HB31) places the “highest point reached” not out on the bay but upon the north-east part (HB31's Cape#11) of Cape Collinson itself, at a position we now know was near 80°07'N, 70°1/2 N.
[This coastal area is more clearly visible on Microsoft's maps than Yahoo's, a problem for several of our other positions as well. In each such case, the precise position was measured off Microsoft maps, and then translated to Yahoo's coordinate system (by amounts determined by comparison of identical nearby points' coordinates). In the Cape Collinson region, this was effected (2007/6/3) by subtracting 9" in latitude and adding 1'.4 in longitude.]

The peculiar triangular shape just to the left (west) of Cape#11 (“Highest point reached” on HB31's sketch) turns out to be a the delta of an arroyo-valley (perhaps glacial or morainal), which is strikingly visible on most of the internet maps. HB31's crude mapping of this valley proves that Hayes (hugging the land-ice) rounded Cape Collinson's east tip-bulge (80°05'10", 70°27'.1 = Cape “10” of HB28's scene-sketch), ultimately traveling NW for 2nmi. He would not otherwise have known of the valley at all.
[It might be suggested that Hayes could have seen the valley while out on Richardson Bay, as HO351 says he was. Problems:
[a] The HB31 coast-sketch contradicts that, placing the farthest upon a protruding mini-cape just east of the valley.
[b] If, he'd gone his alleged 4nmi onto the bay (HO349), he'd have seen that Richardson Bay's westward extention angles somewhat southward.
[c] And he would have been all the way across the bay.
[d] Despite his story, Hayes may not have turned back entirely due to Richardson Bay's “rotten ice and cracks” (which were likely similar to negotiable [if difficult: HO366] Scoresby Bay's) — but from rotten circumstances regarding dogs, men, provisions, risks of getting back to PFoulke across Smith Sound ice in Summer, etc. (Indeed, his initial public account [Hayes 1861 p.157] says he was stopped when “our provisions became exhausted”.]

HB31's coast-sketch shows Hayes stopping at a mini-cape on Cape Collinson's north-east part, jutting north-eastward just short of a triangular shape, which we already found was a valley recognizable on internet maps — where we see that it is just east of the tip of a very small NE-jutting mini-cape. So we can pin down his northernmost position with gratifying precision.
[And hopefully accuracy — depending on Yahoo maps' trustworthiness.]
Hayes' farthest-north was at the mini-cape's tip, which is precisely at:

Reviewing the simple logic here:
[1] Traveling along the land-ice, Hayes could not have seen the valley unless he reached this tip.
[2] And HB31 shows he stopped before going on into the valley.
Brackets [1]&[2] have narrowly fenced-in this expedition's long-unknown farthest-north location.
[Note also that the HB31 coast-sketch shows no awareness that Richardson Bay's interior curves distinctly to the south of due west. (HB31 depicts the bay as strictly east-west.) As already mentioned, had Hayes been around the north tip of Cape Collinson or where he claimed (HO347) he ultimately got (4nmi north of Cape#11), out onto Richardson Bay's ice, he would have known that — and been on the south coast of Cape Wilkes.]

So, after 146y of explorers' and historians' guesswork, this finding solves for Hayes' 1861/5/17 northern-most position, to a precision of about 30 meters, and (assuming the several internet maps are trust-worthy in this region) an accuracy of ordmag 100 meters — i.e., comparable to the length of a football field.

Rounding Hayes' farthest-north to 80°07'N, it's 88nmi — more than 100 statute miles — south of his claimed 81°35'N.
[By contrast, his claimed Cape#8 longitude [70°30'W] is almost exactly correct. Given his problems of latitude, chronometer, & math, this is presumably just a huge errors-cancelling-out coincidence.
(Unless a smiling Hayes knew where he was all along — and decided to create an innocent-cover for his hoax, so that when the truth came out it wouldn't look deliberate. A bizarre theory? Well, this was a bizarre expedition. In any case, we will later present coherent evidence in favor of something like this at-first-incredible idea.)]

Hayes was hoping (see HO351) to try sailing his ship north from Port Foulke the following Summer, but that proved to be impossible. (No one ever reached the Arctic Ocean by this route until 1871, when it was done by C.Hall, the explorer whose AGS backing Hayes had grabbed.
[The feat was still so difficult even years later that it took three tries (1882, 1883, 1884) by the US to get a relief ship to Greely's 1881 expedition. (The successful 1884 rescue was by W.Schley, of Frederick, MD, home-town of DR's mother, who remembered its pride in his [passing] glory.) And in 1907, lacking a ship capable of the passage, F.Cook had to try reaching the Arctic Ocean by going west across Ellesmere.]
Hayes had only 5 dogs left, and his able astronomer (and 2nd-in-command: HO10) August Sonntag had died the previous winter, allegedly on a vain search for more dogs (from Eskimo settlements) via ultra-risky night-dash south, a (superficially) demented mis-use of Hayes' top scientist.
[One more reason to re-christen Port Foulke as Port Foulup.
(Opting for an unwontedly decent choice-of-retention for the mid-consonant.)
But perhaps Sonntag had his own reasons for leaving the expedition. On 1854/8/28, he and Hayes had both departed from Kane's expedition in an also vain mutiny, despite Kane's (vain again) threats of execution. (See O.Villarejo Dr.Kane's Voyage to the Polar Lands UPa 1965 pp.24-25, 160-164, & esp. pp.27 & 150!) Was Sonntag history's only double-mutineer? (Sky&Telescope 1974/11 p.284 wished that an account by Sonntag might be found, unaware [having let one of its authoritarian snits cut itself off from expert advice in this area] that 60pp of such had already been published: see Villarejo 1965 pp.87-146.)]
Hayes quickly awoke to the realization that his whole 1860-1861 expedition would be rated a career-snuff failure if he did not report a record northing. He could not return to the US and then get back north in 1862 without backing — so a fake farthest was just what the Doctor ordered.
[In 1906, such grantmanship-desperation was replicated twice simultaneously by funds-hungry explorers F.Cook (fake Mt.McKinley attainment) & R.Peary (fake Farthest North and fake Crocker Land).
Peary of course ranks far above Hayes in polar history. But are we being circular here? Suppose Hayes' fraud had been on water and thus not detected, and suppose the War Between the States had not come on, would hero Hayes have returned with now-gloriously-massive backing to open up the Arctic? The exaggerations of Peary and of Byrd both helped lay the fiscal basis for later legitimate and (especially in Byrd's case) epochally pioneer geographical work. (See DIO 10 [2000] n.10 [p.13].)]

Having made his misleading “farthest” 5/17 sextant observation and (as we'll see below) having begun to manipulate his account's times and distances, Hayes removed (he probably had scissors on hand) the HB29-30 leaf containing data and-or tale-versions not agreeing with his eventual story.
(Or possibly the excision and serious re-write occurred when he realized upon returning to PFoulke that his ship was too damaged for the expedition to continue north.)
He then simply post-composed new entries upon HB31.
[Due to an extremely important discovery by Wally Herbert (1989 Chap.11), we know that fellow-partially-toeless-but-suddenly-superswift-when-convenient-and-unaccompanied-by-fellow-navigators explorer R.Peary found himself gummed up in Hayes' dilemma on 1906/4/20, somewhere south of c.86°30'N, just one back&forth march short of his own faked 4/21 record-Farthest, 87°06'N — a situation which implies at least 72 round-trip bee-line nautical miles over rough pack-ice, in one sleepless to&fro. And Peary solved it like Hayes had: suppression. (DIO 1.1 [1991] ‡4 §B3 [p.22]. Peary's 4/20 Sun-sight resembled Hayes' 1861 work in another way: non-noon “noon” solar altitude data. See ibid n.6 [p.23]. The alleged 4/20 data and the 1906/4/21 “Farthest” data were never seen and were later thrown out by the Peary family.) Result: Peary's 1906 “Farthest” and 1909 “N.Pole” alleged sextant fixes are isolated: no other data survives within 100nmi. Just like Hayes' 1861 “farthest”. Similar isolation of unshared data likely for the false farthest-north claim of Austria's Julius Payer (1874) (who shared Hayes' folly of exaggerating on a later-checkable coast-line — and claimed seeing non-existent northern-most “Petermann Land” extending beyond 83°N), and certainly true for the “Farthest North” of Italy's Umberto Cagni (1900). See Rawlins 1973 pp.27&65, respectively.]

Hayes' leaf-excision may also have eliminated a meridian sight(s), from either noon or midnight — not to mention timed longitude sights — that were inconsistent with his later ludicrous 81°35'N claim. Perhaps he'd made a slip in carrying off his calendar-shift (see below) and was forced to a re-write. But the most tempting speculation is that he had written (upon this lost leaf) that Greenland was visible — which un-opened the Open Polar Sea.

As we see from HB27, there is a peculiar squeezed-in 5/17 entry at the bottom of the page. (Keep in mind that, since HB28 is full, this is the nearest prior open space he could find, to insert a replacement for his scissored-out original H29 entry for 5/17.)

The next sextant shot is 5/20, 3d after the 5/17 “farthest” shot. This neatly insulates the key 5/17 record from obvious contradiction by sextant data from nearby sites. (Between the 5/14 and 5/20 shots at sites he placed at c.80°N [see Hayes-Schott map], Hayes claimed to have travelled over 200mi, but took just this one single 5/17 shot during the entire period.
[Note that Hayes' dead-reckoning distances are usually off [on the high side] by a factor of merely 2 — until he's decided on fraud.) Similarly, no estimated daily distance estimates survive near Capes#8&#11, though many are found elsewhere in HB, and for 5/20&21 (HB34), we find — now that Hayes is committed to fakery — enormous exaggerations of southward distances achieved: the 9nmi from Camp Jensen to Cape Frazer he triples to 27nmi: HB34.]

Note: for his final 5/17 burst, up to the “farthest” sextant-data site, Hayes gives (see HB27) the march as from “ [small dash] P.M.” to “ [blank] P.M.”.
[Compare to Peary's dashed blanks for his final latitude: Rawlins 1973 p.229, W.Herbert Noose of Laurels (1988) p.257.]

An evidence-cohering theory:
[1] Knowing that he was claiming enormous distances, Hayes inserted a fictional day of travel near his farthest-north.
[2] Hayes' problems then were to stretch his reported schedule, to justify — by fiddling the total travel-duration in his post-Cape#8 records — the ridiculous latitude he got via computing (as if not late) the (late) Sun-shot taken there. So he applied simple addition (1d padding, dittoed quarter-circle bay, multiplying deep-indentation bays, invented capes), and subtraction (scissors & blanks).

Indicia:

1. As soon as Hayes knows (5/15 HB25: Tired Dogs Camp and Jensen's Camp) his northward thrust is crumbling — “(dogs used up)” and Jensen breaking down — he ceases (all the way until returning to Jensen's Camp: HB34) his hitherto-unbroken habit of writing estimated mileage achieved, at the end of each march.
   [The only 1861 Hayes inter-camp mileage-estimates north of Jensen's Camp are found in his 1867 popular book.]

2. On HB27 (5/16), just as he begins omitting to write estimated march-mileages, there is an extremely thorough inking-out of two lines, right after mentioning that by 8:30PM he'd reached a point about 1/2 way between Capes#7&#8, marked in HB27's coast-sketch there by an “x”.
   [Much larger than adjacent “x” marks, thus possibly later-added, either innocently or to pseudo-inflate the northing effort.]
   These lines would perhaps describe when he arrived at Cape#8. The east point of Cape#8 (where the HB27 sketch's “x” puts him) is the very place (80°03'N) where he is at last within sight of the east tip (80°05'N) of Cape Collinson (which is not numbered by Hayes, except wrongly during a shuffle), and very close to not-yet-visible Cape#11 (now merely 4nmi distant at 80°07'N), the north-east part of Cape Collinson, his eventual northern-most point.
   [Part of the 2nd deleted line is a time, as one may see from the surviving super-scripts. The hours part of the deleted time had two digits, and that time was probably 10:30PM. (The very bottoms of both the “1” and the “3” seem to have survived.) Perhaps Hayes originally wrote that he lunched at 10:30PM (at the 1/2 way “x”). If so, then he could have reached Cape#8 at 2AM, the time of day given atop HB31 for arrival at Cape 910 i.e., Cape#8 (allegedly 5/18).]

3. The odd blanks for 5/17 departure&arrival times on the lower half of HB27 suggest that Hayes was trying to get his story straight on what exact hours to insert — but later forgot to get back to this. I.e., the 5/17 passage at the bottom of HB27 reeks of material moved from scissored-out HB29-30 onto the nearest previous open page-space.

4. After the farthest (not before), we find Hayes crossing out numerous dates in HB and replacing them with dates a day earlier. (These alterations start at his [alleged] 5/22 entry. That particular date's significance will become apparent.)

5. The most glaring oddity of all is, of course, the missing leaf (HB29-30) — right in the midst of all the other oddities we've just cited.

From modern internet maps (Microsoft's is very clear), it is obvious that from the east point of Cape#8 (the southern part of Cape Collinson) to Cape#11 (the east-tip at the north part of Cape Collinson), there is no serious cape. (This is even discernable on the topo reproduced here. Between Cape#8 (80°03'N) and the easternmost bulge (80°05'N) of Cape Collinson, the main feature is a low valley.) We already found that the bearings attributed by HB28 to “Cape#89” were observed from ordmag 100m above above Cape#8. (Stretching distances and times naturally required extra geographical features.) HB28's dramatically jagged and obviously later-interpolated fantasy coast-sketch (which doesn't even look like the other such sketches) is the purest art.
[Also, in the HB28 coast-sketch, Cape#8's genuinely roundish east side has just acquired a (non-existent) dagger-like sharpness that was lacking one page earlier in the rather accurate HB27 rendition. Compare HB27 & HB28. The sharp fantasy version ends up on the Hayes-Schott map: Cape R.Baker.]

Obviously, the farthest camp was originally placed at Cape#8 — before re-write. Note that Hayes wrote “9” over “8” twice at the top of his “Cape#9” page, HB28, and wrote “10” over “8” in the same place — and wrote “10” over “9” in HB28's bearings and atop HB31, when specifying the number of Furthest Camp. And he doesn't even mention passing Cape#8 or Cape#7 during the return south — presumably because he's by now re-named these as Cape#10 & Cape#9, resp. Nor is Cape#8 to be found in HB28's bearings-list — for the same obvious reason. (Capes#8&#9 are doubling as already-listed Capes#10&#7, respectively.) Note that the camp at Cape#8 is the only camp in HB that [seemingly] doesn't have a name.

So the bottom-of-page HB27 (blank-times-of-day) entry for 5/17 is a pretense that there was substantial geography here that required the extra 1d of his altered calendar. Recall that the (real-world) distance from Cape#8 to Cape#11 is just 4nmi! The suggestion is therefore strong that the allegedly 5/18 times on HB31 were actually 5/17 — and may include the true “blank” times for 5/17 on HB27.

Wilder yet: compare the Hayes coastal sketch at HB27 to that at HB31, using the width of each bay (Scoresby Bay & Richardson Bay, resp) for scale, and comparing to a modern map (e.g., the topo here) — and you will find that HB27's Capes#7&#8 have become in HB31 transformed into Capes#9&10, respectively!
[The HB27 coast-sketch's quarter-circle curved bay (really more like a third of a circle: from 8 o'clock to 12 o'clock) between Capes#7&#8 has has become the quarter-circle curved bay (Joiner Bay) between “Cape 9” & “Cape 10” in the coast-sketch on HB31.
(“Cape 10” takes on yet another life in HB28's scene-sketch. We already briefly sorted out that joke above.)
Hayes' pretense that the two bays are distinct geographical features is amusingly and definitively ash-canned below. On the topo this is the quarter-circle curved bay (just above the map's 80°N parallel) between Cape McClintock (Cape#7) and Cape Collinson's southern-most roundish eastern extension (Cape#8). On the Hayes-Schott map, it serves twice: as (HB27) from Cape G.Back (Cape#7) to Cape R.Baker (Cape#8) and as (HB31) from Cape Defossée (Cape#9) to Cape Cracroft (Cape#10), just short of Cape Lieber (Cape#11). Note: the scene-caption opp. HO346 and the Hayes map opp. HO72 both show Cape Lieber as the east-most tip of Cape Collinson and ignore Kane's Cape Cracroft. Given that this is near the 1861 farthest, it presumably reflects one of the key 1866 map-disagreements between Hayes and the Smithsonian. (Capes Defossée and Cracroft are both from the Kane-Morton-Schott 1860 map.)]
So, Capes#8 & #10 are the same spot — just the southern part of Cape Collinson (at the 80°N parallel on the topo), where Hayes' HB28 scene-sketch and compass bearings of distant capes were accomplished from a high cliff.
[This single point (Cape#8) was expanded into a fantastic jagged line, by the fraudulent later-inserted coast-sketch of HB28.]

Confirmatory: upon investigating the coast-sketches, it becomes quickly obvious that the HB28 scene-sketch and bearings must have been made from cape“10” of HB31's coast-sketch; yet, according to the coastal profife we find from melding the HB27 and HB28 coast-sketches, there is no way an observer at the latter's cape“10” (or even its cape“9”) can see Capes#7&#6, especially while missing cape“8” — yet that is what the HB28 bearings list does. None of this tangle makes sense until one realizes that Cape#8 of HB27's coast-sketch is the same as cape“10” of HB31's, and that HB28's coast-sketch is just a later interpolation of imaginary coast, drastically-carelessly transforming the shape of Cape#8 (HB27 coast-sketch vs HB28 coast-sketch) and the azimuth of cape“10” as seen from cape“9” (0° in HB28 coast-sketch vs 45° in HB31 coast-sketch).
[Comparison of the coast-sketches of HB27 and HB31 to a real map shows genuine resemblance to reality (requiring only that they be over-lap-knitted-together — with Capes#7&#8→“9”&“10”, respectively), while HB28's coast-sketch resembles nothing real.]

All of which answers some questions:
[a] We now know why the “8” is written-over by a “10” at the top of HB28.
[b] There don't seem to be enough hours (in the real-time schedule during the HB27-31 period) to arrive at Cape#8 at 5/16 10:30PM, climb for sketches & bearings, then go right on to reach Cape#10 at 5/17 2AM. Now: no need, since Cape#8 is Cape#10.
[c] One recalls that the cliff-climb described at HO348-349 seemed at first to be temporally out of place, since this climb is specified (HO348) for Furthest Camp, even though HB28 places the obviously high-viewpoint scene-sketch and azimuthal bearings there at Cape 8#9, which is in fact HB27's (and consistently our) Cape#8, the southern part of Cape Collinson. (Obviously, it was also originally HB28's Cape#8, before the “8” was stricken-out.) Now the whole problem vanishes since, Cape#8 is also Cape#10, Furthest Camp. Henceforth, unless quoting Hayes, we should try to skip straight from Cape#8 to Cape#11 (only a 4nmi distance, anyway: 80°03'N to 80°07'N), since distinct Capes#9&#10 are simply Hayes' cape-shuffling fakes.
[On HB28's scene-sketch, Hayes does temporaraily label the east tip of Cape Collinson as cape “10”, a shuffle noted earlier.]
[d] On reflection, it's obvious that an explorer who was stretching a 20nmi trip beyond Cape Frazer into 112nmi (beyond his former Cape Frazer's latitude) would have to describe something more than 92nmi of smooth coast: so the two faked capes help explain how Hayes filled that gap.
[Keep in mind that Hayes' 1861 arctic base was far south of Kane's base, from which Hayes had failed even to cross 80°N in his 1854 thrust into the same region he was exploring in 1861 — which made it all the more incredible on its face that he could enormously better his previous latitude record. But note that it is a testament to his determination and endurance that he in fact did go about 20nmi further in 1861 than in 1854.]

We will now reconstruct the true-calendar journey beyond Scoresby Bay:
HB27 records that, at 3:20 PM, Hayes left Bewildered Camp. (North part of Scoresby Bay: see “x” in coast-sketch on HB27.) The arrival at Cape#8 is preceded by two heavily scratched-out lines on HB27: the 1st such oddity since arrival on Ellesmere.
[There's a light scratch-out on HB22, but it's readable: just a bearing-datum he was innocently moving down a few lines for chronological reasons. No alteration.]
These are followed by one line stating: “Camped at Cape 8 at 10h30' P.M.” Natural question: how does this revise what's been suppressed? Aside from the possiblity of innocent re-write or suppressing mention of discouraging events or inconvenient observations, recall our earlier suggestion: the original version perhaps said he started north from the “x” between Capes#7&#8 at 10:30PM. He would thus reach his farthest camp (Cape#8) shortly. And, indeed, HB31 has him arriving there at 2AM, which would be about right — except for the fudged date: 5/18.
[Hayes had done a similar nearly-as-long march (HB22-23) from 5/13 18:45 to 5/14 2AM (with two stops en-route, as evidently here also) from Foggy Camp to Camp Frazer, at least 12nmi actual distance made good. By comparison, from Bewildered Camp to Cape#8 is only 6nmi, with more time (than the 5/13-14 march) to make it: 10h2/3 vs 7h1/4. And 5/18's southward march (HB32) was even longer than 5/17's: 14h. If one questions the suggestion here that Hayes simply marched 10h2/3 (including eats-breaks) from Bewildered Camp to Furthest Camp (Cape#8), then one must contend with the fact that Hayes himself said that the daily travel-times for the northern-most marches were 9h, 10h, & 12h. He even (falsely) claims a 22h march during the return.]
Hayes arrived at Cape#8 on 5/17 2AM and camped there. HB31 says he left there for Cape#11 at 5/18 (read 5/17) 2PM (right after his Cape#8 latitude Sun-sight: double altitude 56°52') and took 3h (HB31) to get to Cape#11.
[Keep in mind that Hayes has effectively confessed the 5/17→5/18 date-fudge in (HOvi-viii) assenting to and admiring Smithsonian publication of the Schott (USC&GS) reduction of his results, which included restoration of the farthest's actual date. (And, indeed, of all four altered dates: 5/18-23→5/17-22: Schott 1867 pp.20-22.) No other date will computationally yield (from the Sun-shot at HB31) Hayes' announced 81°1/2 N latitude. In addition, observing on 5/18 was probably impossible from bad weather. Jensen at nearby Cape Knorr 5/18 recorded (HB33): “wind and snow throughout the day”. This is the storm whose onset Hayes tries to switch to the start of 5/19.]
He presumably returned to Cape#8 late on 5/17 and (HB31) “lunched”.
[Recall that “lunch” does not mean mid-day: indeed, 5/13 “lunch” was at 11:15PM: HB22.]
After rest, he then set out for Cape#7, Snow Storm Camp (79°59'1/2 N, 70°40'W), 3nmi distant, arriving midnight 5/17-18. (HB32 falsely calls it 5/18-19.)

Hayes' obviously-padded account has him (HB27 to HB32) taking two days (5/17&18) to go north from Cape#8 (80°02'.7 N) to his farthest (Cape#11: N.tip of Cape Collinson: 80°06'.7 N) and back south to Cape#7 (“Cape#9”), Snow Storm Camp — a distance that totalled merely c.11nmi.
HB31 says it took just a few hours to go the 8nmi from Cape#8 to Cape#11 and back to Cape#8. So did Hayes require all the rest of the two days to go the 3nmi from there to Cape#7?
[On the modern topo, Cape#8 is the right-angular mini-cape roughly 1/2 way between Cape McClintock (79°59'1/2 N) & the east-tip bulge (80°05'.2N) on the northern part of Cape Collinson. Cape#8's east tip is where HB27 shows Hayes camped. Its Yahoo position is 80°02'.7N, 70°30'W.]

The disproportionality of the above item starkly reveals Hayes' pad-ploy. But his deceit had a complicating downside: having inserted a non-existent day of marching to reach his record latitude, Hayes was forced to alter HB's calendar by +1d for awhile.

He carries the padding right into his book. From 1861/4/24 (HO315) through 1861/5/11 (HO332) arrival on Ellesmere, Hayes' book gives dated diary excerpts for every single day of his sledge dash for a farthest: “my last throw” (HO343). From that point on, he gives only a 5/15 entry (HO342) — then we are given no dates until he quotes the alleged 5/19 farthest-cairn-record (HO351), and then no more dates until 6/3 (HO363 & 368) when he's back on board ship! — writing up a dateless account of the return trip, claiming at HO365 (1861/6/4) he made no entries for the return trip. (Reminiscent of Peary 1906 [Rawlins 1973 p.69] & Byrd 1926.) Hayes there describes his “field-diary”: “That water-soaked and generally delapidated-looking book”. He then quotes (idem) from the last entry, at Snow Storm Camp, and at last provides the march-distance estimates that were missing from HB: Snow Storm Camp is “about ten miles” south of Cape#8 (real distance: 3nmi), and “forty to fifty” miles north of Jensen's Camp (real distance: 6nmi) in 22h (vs. HB32: 14h).
[The exaggeration's asymmetry was perhaps due in part to the horrid difficulty (HO366) of crossing Scoresby Bay.]
Which puts Jensen's Camp c.0°.9 south of Cape#8, at c.80°2/3 N.
[Cape von Buch on the Hayes-Schott map, which places it rather nearer 80°3/4 N, presumably because HO365's 10nmi was taken to be from Cape#11.]
At this point Hayes alleges (HO365) he stopped writing in the diary: “There is no record after we had turned our faces homeward.” Given the 12h→22h exaggeration just noted, it's understandable that he doesn't mention that HB32ff records page after page of entries. (And that, unlike Cook, Peary, & Byrd, he took sextant observations on the return journey — though none anywhere near his farthest.)

So, when examining the book, one must (as in HB) carefully count days and travel. The post-Jensen's Camp trip starts on 5/16: 9h of travel claimed (HO344), vs barely 7h claimed at HB27; next day (5/17), 10h (HO346). He claims 12h total travel on 5/18, much of it in a (fictional) vain attempt to get past Richardson Bay's crumbling ice.
[Hayes' favorite expression for such was “rotten ice” — a phrase echoed throughout the works of his 20th-century re-incarnation, Doc Cook.]
This is followed by “a most profound and refreshing sleep”, after which (is it now supposed to be 5/19?) he makes an 800-foot climb up a cliff for the view (HO348-349). He leaves a cairn-record (HO351), dated 5/19, stating he and Knorr had visited Cape#11 on 5/18&19. So there is no question that the extra day is embedded in his public account, even as the Smithsonian was simultaneously (1867) publishing a navigational record placing him at Furthest Camp on 5/17 (Schott 1867 p.20).

So what eventually went wrong? Simple: Hayes forgot that since the 1d shift put his farthest on 5/18, the 1d variation (13') in the solar declination messed up the 81°1/2 N latitude he'd deduced in the field and announced to all upon his not-so-triumphant return in 1861 Oct. The same declination factor would obviously also set off alarms with Schott (who appears to have worked from HB, the same ms we are presently analysing): the Camp Hawks longitude observation, if computed for 5/23 would create a glaring discontinuity in the deduced chronometer-rate: 1h18m! — instead of the 1h12m+ found upon return to PFoulke (and established here for 5/13 at Foggy Camp, before any date-confusion). One can speculate that when Schott pointed out that all would be well if the Camp Hawks observation was actually 5/22, Hayes went back to HB and scratched out or wrote over the false dates, restoring the real ones. (So these are the dates ultimately used in Schott's calculations. And ours.) Note that the restorations begin at HB36 which was originally (and falsely) written as 5/22. This temporal coincidence is nicely consistent with our theory that it was Schott's bad-news on the 5/22 Cape Hawks longitude shot's incompatibility that panicked Hayes into un-altering dates in this part of HB.

But, classic frying-pan→fire: Hayes' discontinuity problem then merely transfers from chronometer-rate to calendar. If one simply counts marches and dates in HB27ff, this re-do leaves an obvious 1d discrepancy (the inserted day) in the period 5/16-5/20 — coincidentally near the time of Hayes' farthest-north — as well as leaving the embarrassment of his inserted HB27 march-times (both AFTER-noon on 5/17, before arrival at Cape#8) — contradicting Schott's 5/17 date for the Furthest Camp (Cape#8) sextant-shot (supposedly AT-noon) that “proved” his attaining record-north land.

To reveal the calendar-fudge that KOs Hayes' 1d-fudge, one need only count days in HB, as we will now proceed to do. (While additionally counting suspicious features in passing.)
[Times are off Hayes' pocket chronometer. And characters shown here as stricken-out were usually just written-over by the replacement-characters.]
We will simultaneously note the altered cape-numbers that litter the record, as Hayes' tale kept evolving — live — right in the pages of HB.
HB21: “Cape Hayes Camp” near Cape Hawks 5/11-12.
HB22: “May 13. Camped 2 ock A.M. (weather very thick) Dist travelled about 12 miles …. Foggy Camp [near Point Joy] … about 1/4 mile from the land.” [Longitude observations c.4AM.] Left 6:45 PM; reached Cape Leidy 9:45 PM. “Est dist 12 miles … Cooked 2 dogs…. Halted for lunch 11 AM. Started 12h.5m. A.M. (14th)”
HB23: “Frazer Camp” (just north of Cape Frazer) arr 5/14 2AM; noon latitude observation, double altitude 58°16', index error (generally abbreviated “I.E.”) 1°28'.
[The enormity of this I.E. is highly unusual. Possibly Hayes arranged the sextant that way in order to have one more innocent-looking foul-up alibi for later.]
HB25: “Tired Dogs Camp” arr 5/15 1AM; depart 4:30PM (“Started 4 1/2 P.M.”); “reached Cape 6, 6 ock [oclock] P.M.”; “left Jensen & Jensen's Camp” 11:45PM.
HB26: “Cape 6.” Followed by bearings, then a coast-sketch showing Capes 4-6, with a note beside a tiny “x” atop Cape#6 marked “Jensen's Camp” and to its left a very tiny scrawl: “Left Jensen 15th”.
Careful examination reveals that a leaf between HB26&27 has been scissored out of the record. (See left side of HB27.) The hand-written pagination is unbroken (proving that Hayes was carrying scissors — unless HB was entirely a post-trip concoction); so either the excision was innocent or he caught a slip before paginating the next leaf. (He was more impetuous in paginating the leaf following excised HB29-30.)
HB27: “May 16th. Camped in [Scoresby] bay at 4 ock. A.M. Bewildered Camp”; depart 3:20PM. Reached a point 1/2 way between Capes#7&#8 at 8:30PM. The next two lines are very thoroughly scratched-out. They are followed by what is evidently a revision of them: “Camped at Cape 8 at 10h30' P.M.”.
A coast-sketch covers from Cape#6 (Cape Knorr) to Cape#8 (southern part of Cape Collinson). Beside Cape#7 (later Deep Snow Camp) is a note on the cold there. HB27 bottom: “May 17th.
[Entry does not start at the page's top — a rarity in HB (though see also HB34).]
Started      -       ock P.M.
Halted at Cape#9            ock P.M.”
HB28: “Cape89. Three very low headlands [Capes #12, #13, #14] are visible from Cape 89. A large bay opens above Cape 8 10.” In the list of distant capes' bearings, we find 1112 and 910. Then to the left, we see a minuscule note: “115 var”. Then the data 38.30 E, 141.30 E, −26.30 W. These highly revealing numbers will be explained below.
In HB28's scene-sketch, Hayes correctly shows Cape#11 as invisible from his Cape#8 viewing point, but mis-labels Cape Collinson's east point (whose the just-around-the-bend north part is Cape#11) as Cape#10 — even though he's standing on HB31's Cape#10 (i.e., HB27's Cape#8) as he draws. This beaut is just a botched extrapolation from his cape-shuffle, as we will now see. We've already noted that Hayes' HB31 coast-sketch over-laps with the HB27 coast-sketch, showing the same quarter-circle bay from Cape McClintock to the southern part of Cape Collinson (remember: HB27's Capes#7&#8 equal HB31's Capes#9&10, the respective bounds of the quarter-circle bay) — though Hayes tries to invent an artistic HB28 fantasy coast-sketch, to pretend that the HB27 & HB31 quarter-circles bays are at different places (which the fantasy-coast is supposed to knit together). This deceit is undone by the obvious fact that Capes#12-#14 (shown in HB28's scene-sketch) are not visible from Cape McClintock (“Cape 9” of Hayes' HB31 coast-sketch) — one may readily see (from the topo) that all are blocked by Cape#8. (The same point is equally obvious even from Hayes' own rough HB31 coast-sketch, where Capes#12-#13 are invisible from “Cape 9”.) So, again we find: the HB28 scene-sketch was made from above Cape#8 (Cape#10 of HB31).
HB29-30 removed by scissors.
HB31:“May 18th. Reached Cape 910 at 2 oclock A.M. Furthest Camp”; noon latitude observation (crowded onto a corner of a large coast-sketch — obviously a later transfer from the missing leaf), double altitude 56°52', I.E. 1°31'. Coast-sketch shows Capes#9-#14, but with some alterations: 134, 123, 112. Running through Cape#12 is a short burst of faint backwards-script. We will discuss this below.
HB31 bottom: “Started north at 2 ock P.M. travelled 3 hours. Returned to Cape 10 and lunched. Displayed flags. Returned to Cape 9 for observations”; at very bottom of HB31 is the bold header-caption (for the entry of HB32): “Snow Storm Camp”.
HB32: “May 19th. Reached Snow Storm Camp about midnight [5/18-19 by by Hayes' already-suspect calendar].
[Long crossed-out line.]
Thick snow falling and blowing a gale from the north. No chance for observations. Started south, 10 oclock A.M. Snow deep. Dogs exhausted …. Reached Jensen's Camp at midnight [5/19-20].”
HB33: weather records at Jensen's Camp “during my absence” 5/16 to 5/19 noon.
HB34: “May 20th Started south at 5 oclock P.M. Reached Tired Dogs Camp 7 1/2 P.M.”
HB34 bottom: “May 21st Camped in [Gould] Bay above Cape Leidy 2 1/2 A.M. …. Camp Leidy”
HB35: “Camp Leidy” data for noon latitude observation, double altitude 61°14' ([May] 21st), I.E. 1°30'.
HB36 [where the date-“corrections” commence]: “May 22nd Camped above C.[Cape]Napoleon 3 ock A.M. Deep Snow Camp. Started [south at] 7 ock P.M.” Noon latitude observation, double altitude 61°48' (221st) I.E. 1°32'. “Latitude 80°05'”. [This is the only latitude computed on HB's Ellesmere Island pages. Note that it is computed for 5/22 (solar decl 20°29') — accurately on the nose if r&p were ignored. (Schott 1867 p.20 re-works it for 5/21 [solar decl 20°17', r&p = 1'.7, solar semi-diameter [ssd] 15'.8, instead finding [since decl was 12' less on 5/21] a latitude slightly under 79°55'.)
[Since a sample latitude calculation will be instructive, we will re-do what Hayes' calculation for May“22” should have been (and nearly was), using the above-supplied double-altitude, I.E., r&p, ssd, & solar decl: 90° − (61°48' − 1°32')/2 + 2' − 16' + 20°29' = 80°07'N.]
If (as our theory proposes) Hayes had jumped his calendar by 1d, he must have been delighted to find that this in itself added over 10nmi to latitudes computed from his “noon” sights.]
HB37: at Camp Hawks “May 22nd 23rd [the only positive alteration (and by far HB's most thorough strike of a date — a complete ink-out, not the usual mere write-over) — presumably resulting from a momentary in-the-field neglect to stick to the altered calendar] Camped 5 ock A.M. …. Started 8:20 P.M.”
[There is an observation written on HB37 that was later laboriously erased.]
HB38: Cape Hawks data “(232rd)” ... Latitude [May] 22nd [this line a possible later insertion, since the next line is] Mer al [meridian altitude] 232rd ar.h. [artificial horizon] 62. 34 I.E. 1. 32. [Double altitude 62°34', index error 1°32'. Data at Schott 1867 p.21, rightly treated as for 5/22.]
[If we take seriously the dates written beside the three noon shots at HB35-38, we find that: though Hayes took too few observations near his farthest, he certainly made up for the deficit in a big way on 1861/5/21-22, when he became the first explorer in history to make three distinct noon Sun sights in two days. Which perhaps implies he went over the Pole and back — but later neglected to recall this epochal feat.]
HB39: Cape Hawks data “Longitude [obs] 22nd”. [Data for c.7AM at Schott 1867 p.22, rightly treated as for 5/22.]
HB40f: continuation of −1d date-alterations.

Conclusions from the evidence:
Starting at HB31 (that is, immediately following the lost leaf),
[a] Two non-existent capes have been invented.
[b] Most dates have been enhanced (at least temporarily) by +1d.
Thus, we should restore the real situation. (As Schott forced Hayes to do — though Hayes' book sticks with his padded calendar.)
[Hayes' stubborn insistence even 5 years later on the validity of his farthest's date, latitude, and data (though they cannot be reconciled) proves that this golden boy of the academic societies was either incompetent, demented, or dishonestly stonewalling. (All of the above? Perhaps not probable. But possible — after all, DIO readers are familiar with modern society-sweethearts who fill all three categories simultaneously.)]
The required corrections to HB follow:
HB27: Scratch the interpolated & blank-ridden 5/17 fantasy at the bottom of the page.
HB28: Forget the interpolated sketch of the non-existent stretch from Cape#8-to-Cape#10 — i.e., from Cape#8 to Cape#8. No coast in this region remotely resembles this entirely invented profile.
[It is uncertain whether arrival at Cape#8 occurred at 5/16 10:30PM (HB27) or 5/17 2AM (HB31) if either. The latter seems preferable. Regardless, the arrival was roughly 5/16-17 midnight.]
HB31: For May 18 (header) read May 17. So at Cape#8 (Furthest Camp): “Started North [for Cape#11] at 2 ock P.M.” (Hayes' chronometer).
HB32: For May 19 (header) read May 18. So: returned to Cape#9=#7 at 5/17-18 midnight and named it Snow Storm Camp. Departed 5/18 10AM, spent day crossing Scoresby Bay, arr Jensen's Camp (north part Cape#6) 5/18-19 midnight.
HB33: Temperature records every 4h (12AM, 4AM, 8AM, 12PM, 4PM, 8PM) were being kept at Jensen's Camp while Hayes was to the north; and these data were copied by Hayes onto HB33. The last entry is for 5/19 noon, meaning that the data-recording was cut off by Hayes' return (followed by hasty preparations for all 4 men starting south) between 5/19 noon and 4PM. A glaring slip-up by Hayes, fatal to his calendar pretense, since HB32 has him back at Jensen's Camp at 5/19-20 midnight, and HB34 says that departure from this camp was 5/20 5PM.
HB34: So, for May 20 (header) read May 19. Depart Jensen's Camp 5/19 17h. Arrive Tired Dogs Camp 7:30PM. Est dist 15mi. Depart 9:15PM. Arr Cape Frazer 9:15PM. Est dist 12mi.
For May 21 (sub-header) read May 20. Arr bay above Cape Leidy 5/20 2:30AM.
HB35: Latitude obs noon. For parenthetical 5/21 read 5/20. Cape Leidy bearing 207° by compass.
HB36: For May 22 (header) read May 21. Camped above Cape Napoleon 5/21 3AM. Latitude obs dated in parenthesis 5/21 noon (corrected from 5/22). Departure 7PM.
HB37: For May 23 (formerly written 5/22 but totally inked-over) read 5/22. So, arr 5/22 5AM; and depart 5/22 8:20PM. Est dist 20nmi.
HB38: Latitude obs 5/22 noon, marked as such in parenthesis. Longitude obs 5/22 c.19h. (Marked 5/22 in perhaps-later-added line above. Originally dated 5/23 on next line but written-over as 5/22.)

Proof of calendar alteration: if one follows the pre-restoration HB headers (HB31f) then there are latitude obs on 5/21, 5/22, 5/23 plus longitude obs on 5/23. The unbroken string of noon shots allegedly from 5/21 to 5/23 eliminate any possibility of claiming an accidental 1d-omission in the 3 days, so when Schott's math rightly found that only 5/22 fit the Cape Hawks longitude observations, the whole daily string of latitude data (allegedly 5/18, 5/21, 5/22, 5/23) were then moved back to their real dates: 5/17, 5/20, 5/21, 5/22.
[Even superficially, we can tell that the farthest was reached on 5/17, simply by noting the symmmetry of time of leaving and returning at such places as Jensen's Camp (depart 5/15-16 c.midn [HB25], ret 5/18-19 midn [HB32]). Also, Hayes claims (HB27) he reached Cape#8, very late on 5/16 (which has to be close to the truth), which we now know was the site of his Furthest Camp observation. (Thus ending the attempted lie that this “noon” Sun-shot was 5/18 — an implicit claim of over a day of virtual immobility.) He was then only 4nmi from his farthest north point-reached, Cape#11 at 80°07'N. He'd gone further (6nmi) in c.7h the same day (HB27): Bewildered Camp (in Scoresby Bay) to Cape#8, so it would hardly take long (HB31 says 3h) to go the 4nmi from Cape#8 to Cape#11 — which obviously contradicts the HO351 lie that he was at Cape#11 on 5/19.]

Was a slow chronometer deliberate? Keep in mind that in this region a 1h.2 chronometer error can add a fake half-degree to a “noon”-shot-based calculation of latitude. And, due to the quadratic growth (of said padding) with time-past-noon, a surprisingly minor delay can roughly triple the advantage to about 1°1/2 — as Hayes was spectacularly to prove.
[Note in Table 1 that, for the four latitude observations other than the farthest, Hayes does not take full advantage of the half-degree potential in his slow chronometer, since he always starts tens of minutes before chronometer noon. This looks so natural that it may have helped fool the many commentators who regard him as non-fraudulent. But to put the sham across convincingly he had no choice but to start shots before clock-noon, while he cannily reserved the slow-chronometer latitude-lift advantage for the one big throw where it counted: the farthest, where he springboard-tripled the latitude-boost, in the manner just described.]
So perhaps Hayes started preparing for a tall-latitude tale even before 5/13, this being the date of the Foggy Camp longitude shot that proves (unless he altered the true times by −1h.2 before copying them into HB [doubtful]) that the chronometer he was using for HB was by then 1h.2 slow.

But for an unambiguous signal of sneaky thinking, one of our earlier items suffices: from the moment his strongest man breaks down — dooming Hayes' hope of a genuine record — he instantly snuffs his hitherto unbroken practice of writing estimated distances in HB. So, there is no doubt that by 5/15 he was preparing to stretch his distances: not committing in ink to anything that could contradict whatever story he might have to tell — a concoction that was obviously still in-flux.

By good luck and detection, we can show that an original written record at now-missing HB29-30 for the days near Hayes' farthest was removed and that Hayes then just boldly wrote, upon the virgin pages of HB31f, a “revised” version of events.
[A-là F.Cook: see R.Bryce Cook & Peary: the Controversy Resolved Stackpole 1997 Chap.28, e.g., pp.835f or DIO 7.3 [1997] ‡8 [pp.77-82].
Victor Borge (My Favorite Intervals 1971 Chap.10): Modest Moussorgsky “ left bits & pieces of a dozen unfinished operas …. Another famous Moussorgsky piece was “Night on Bald Mountain”. He managed to not finish that one four times. Moussorgsky's greatest achievement was his opera “Boris Godonov”, and one of the remarkable things about it is that he really did finish it himself. It made him feel so good that two years later he finished it all over again. Rimsky Korsakov couldn't believe it, so he finished it a third time, just to make sure.”]

The unexpected new evidence follows.

A typical HB entry-caption of course starts an entry and thus was written in fresh-from-the-inkwell wet ink & usually bold to the eye. Thus, e.g., we find the bold-ink caption “Snow Storm Camp” at the bottom of HB31, representing the header to his entry for that camp, the text for which appears on HB32.
But, thanks to the good fortune of Hayes having closed HB right after writing the original version's identical caption on the upper half of now-missing HB30, HB31 became a blotter for HB30: the undried ink imprinted “Snow Storm Camp” upon HB31's upper half in reverse and this can be read there today with a mirror.
Try it: the short faint backward-slanted line at Cape#12.
Hayes never repeated headers other than to enter bearings-data under the 2nd header (e.g., HB35). So there is little doubt that HB32's Snow Storm Camp text is a re-write of the excised entry of HB30.

Note that the vertical line on the left in our reproduction of HB31 is the scissor-sever that removed leaf HB29-30. A tiny jagged flaw in the scissoring is visible directly to the left of “Ar. hor.” (artificial horizon). Hayes claimed (HO351) that “tearing a leaf from my notebook”, he wrote the record left at his farthest. If that was ever used to excuse the missing HB29-30 leaf, it won't wash: the leaf was neatly, carefully scissored-out, not torn. And: how could HB30 have born the caption “Snow Storm Camp,” well before Hayes had even (2pp later at HB32; or see HO365) experienced (while fleeing southward) the storm that caused the name, much less arrived back at that camp (Cape#7). Note that “Snow Storm Camp” (a returning-south event) tells us by simple chronology that missing HB29-30 contained a record of events at the farthest camp and point — now permanently destroyed.

Hayes' own 23nmi Ellesmere-coastal travel (both 1854 and 1861) between Cape Hawks & Cape Frazer (79°43'N) was greater than the allegedly-record-setting northward distance from there (Cape Frazer) to Cape#11 (north Cape Collinson), a distance of (at most) merely 21nmi. I.e., unless his dead-reckoning ability had suddenly dawned into a warped universe, he had to know that he had not traveled over 100 mi (!) north of Cape Frazer to Cape Collinson. This is plain, whether or not his 5/17 sextant reading's invalidity was or wasn't innocent. (Even if it was at-first innocent, the missing leaf indicates that the proposed innocence didn't last long.)
[The Hayes record is variously confused and confusing. (HB27 names his 5/16 site [in Scoresby Bay] “Bewildered Camp”.) Among the symptoms: between Schott's 1860 map (of the Kane-Morton-Hayes explorations of 1854) and HB, Hayes reversed the 1854 names of Cape Hayes and Cape Hawks: see HB38; also HB21 & HB37-40. (Cape Hawks is next to unmistakable Washington Irving Island, which the Smithsonian map called “Irwing Id.”, proving that most of the fiction Schott&co read that of Kane & Hayes.) Perhaps Hayes wished to honor his present 1861/5/11 landfall by naming the he-hoped-immortal spot for himself. The two names were later re-reversed back to the 1854 situation (HO326): see Schott's map of Hayes' 1861 work (submitted 1865, published by Smithsonian 1867). By subsequent nomenclature, Cape Hayes (if the name is still used at all) is his 1854 landfall; Cape Hawks, his 1861 landfall. So we here throughout refer to his 1861 “Camp Hayes” as Camp Hawks.]

On 5/17, at Cape#8 (Cape Collinson), latitude 80°03'N, longitude 70°.5 W, Hayes' measured (HB31), via sextant with artificial horizon (“Ar. hor.”), a solar double-altitude “(double)” of 56°52', with index error (“I.E.”) = 1°31'. If the data [altitudes] are real (we are proceeding according to the assumption that they are), then his Local Apparent Time was about 2 hours past Local Apparent Noon. How could such a disaster happen without Hayes realizing it?

To play god's-advocate here, let us try an innocent explanation and see how far we can go with it. HB33 refers to fog and snow on the afternoon of 5/17, so let's grant that fog could have interfered with a noon sight on 5/17 but allowed a Sun-shot a little later. Then we can ask: what time did Hayes think it was when he made the shot? Hayes' chronometer had stopped for over an hour (he said he'd forgotten to wind it), sometime between (Schott 1867 p.84) 4/25 & 5/13, probably before he even reached Canada (5/11). Following the theory of innocence: unbeknownst to Hayes, the chronometer was slow by 1h.2 (vs PFoulke time) throughout his journey in Ellesmere as he drove for his farthest-north. Thus, we know from this error and his measured solar altitude at the Furthest Camp “noon” sight (which, via sph trig, tells us the real time there) that his chronometer read c.12:36 P.M. when the shot was performed.
[Astronomical calculation tells us the Local Apparent Time was 14:01. Correcting for the Equation of Time and for Cape#8's longitude being east of PFoulke's, we have 13:48 PFoulke mean time (PFMT). Subtracting 1h12m chronometer slowness, we find that Hayes' slow-chronometer read 12:36 (lower Farthest Camp time in Table 1) at the time of observation if the altitude was observed after noon; if before noon, we may similarly compute that his accurate chronometer read 9:48 (upper Farthest Camp time in Table 1).]
From the slow time-piece's presumed error and rate (measured at journey's start: Schott 1867 pp.18&22), Hayes could have by our fading innocence hypothesis believed it to be 10m or 11m ahead of PFoulke Mean Time. If he then ignored 5/17's 3m51s Equation of Time and his being east of PFoulke (c.8m.6) — factors which in sum virtually cancel his watch's pseudo-fastness — then he could figure it was only 36m −11m = 0h.4 after Local Apparent Noon, and he perhaps knew that (in these latitudes) taking a meridian shot 0h.4 hour after (or before) Loc. App. Noon would cause only a trivial 3nmi (3') error in deduced latitude. Even 36m lateness (after Loc. App. Noon) in his 5/17 Sun-shot would only cause an 8nmi (8') error. But since, at the moment of his 5/17 shot, the Sun was (if we round the Table 1's over-precise 14:01 to 2PM) actually two hours past Local Apparent Noon: the latitude error (which grows nearly quadratically) caused by such lateness in late May at c.80°N is 84nmi, ten times or more what Hayes may (on the innocent hypothesis here) have thought was the error from non-noon-ness. Adding this to the c.20nmi actually traveled north of Cape Frazer (his 1854 farthest), his false ssd's 3' error, and Hayes' alleged 4nmi 5/17 walk north, we have accounted for virtually all the sham in Hayes' implicit claim that he went 112nmi beyond where his 1854 survey had accurately put Cape Frazer: 79°43'N, 71°17'W (his 1854 farthest-north). (See E.Kane Arctic Explorations 1856 2:369, 385, & [note misprint] 389. It should be pointed out that the position of Camp Frazer in Table 1 is marked on Hayes' sketch-maps [HB23 & HB25] as a few miles north & slightly east of Cape Frazer. Such small discrepancies between the positions of capes and Hayes-camps named for them also apply elsewhere in Table 1.)

If one has a genuine Local Apparent Noon solar observation, the math for finding the observer's latitude is merely elementary arithmetic (as already seen), which is what Hayes and Schott used, to reduce his purported latitude observations. Setting L = observer's geographical latitude, δ = solar celestial declination (tabulated daily in the American Ephemeris and Nautical Almanac, from which all explorers carried pages), and h = solar true altitude angle (corrected for r&p), we have the simple arithmetic equation (setting true solar altitude at culmination = h_o):

But if the time is not noon, the governing equation is instead one of trigonometry, and not just plane trig but sph trig. The standard equation (which appears at, e.g., Schott 1867 p.83) may be usefully transformed into an unorthodox form (setting up reduction to the quadratic approximation that will follow immediately here):

where H = hour angle. (The Sun's hour angle was equal to Local Apparent Time before 1925, and afterwards differed from L.A.T. by precisely 12h.) This equation may be closely and usefully approximated near upper or lower culmination by the following