Earth · a printed map from 1892
Gleason’s flat world,
measured against the globe.
In 1892 Alexander Gleason of Buffalo published this map as a demonstration that the Earth is flat. Geometrically it is a north-polar azimuthal equidistant layout of the globe: the North Pole at the centre, the parallels evenly spaced circles, the South Pole stretched into the whole rim. This is the Boston Public Library’s scan, at its full resolution.
Zoom anywhere on the sheet, find a city, a sea or a US county where its modern coordinates fall on his layout, and measure any route through any number of points. Every distance is given twice and labelled: the great circle on the real globe, and the straight line on Gleason’s paper at his own degree scale — with the ratio between them.
The map
The whole sheet, as the library scanned it.
Drag, pinch or scroll to zoom. Measure adds points, Search finds places, Time sets Gleason’s two sun-time arms and shades computed day and night, Share copies a link to this exact view or prints it. The paper arm lying across northern Asia is part of this copy.
Loading the scan…
Explore
- Centre of the view
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- Zoom
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- One screen pixel
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- East–west stretch here
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A long press on the map, or I with the map focused, asks the same about that spot.
On the sheet
One scan pixel is about 11.1 km along a meridian. Zooming past the scan shows paper grain, not finer engraving.
No points yet. In Measure, tap or click the map; or focus the map and press Enter at the crosshair; or add a place from Search; or type coordinates below.
| Leg | On the globegreat circle | Straight line on Gleason’s paperat his degree scale | Paper ÷ globe | Great-circle startbearing | Rhumb linebearing, length | Paper protractorfrom map-north |
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Solid: the straight line on Gleason’s paper. Dashed: the great circle on the globe, drawn onto his layout. A ± appears on legs short enough for the calibration to matter; the Method section below explains it.
Placed from its modern coordinates, within about ±47 km on Gleason’s layout. This is where it belongs on his geometry, not a claim that he drew or named it.
Gleason’s Longitude & Time Calculator
Two arms turn on the North Pole at the centre, as in his patent. The red ring counts sun time, 4 minutes to each degree of longitude, with XII NOON on Greenwich: not clock time, not time zones. Drag an arm on the map, or set it here (arrow keys move a quarter degree, Page Up and Page Down 15°).
Day and night on the real Earth
- The moment
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- Sun overhead
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- Day length at the view’s centre
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- Day: the sun’s centre above the horizon (the line is the terminator)
- Civil twilight, to 6° below
- Nautical twilight, to 12°
- Astronomical twilight, to 18°
- Night
This shading is where the sun is actually up on the real Earth at that moment, computed and drawn onto Gleason’s layout. It is not his model. His own are the two sunlight diagrams in the lower corners of the sheet, for 21 June and 21 December; these buttons set that date and frame his diagram beside the disc.
The coastline is Natural Earth’s, placed on the scan with this page’s calibration, within about ±47 km. Where it and Gleason’s coast part by more than that, the difference is his drawing. Measured on the scan, it sits a mean 47 km from the edge of his coloured land (median 34 km, 95% within 135 km); the Method section says how.
The scan is never recoloured: these switches change only what is drawn over it.
Keyboard: focus the map, then use the arrow keys or W A S D to pan, + and − to zoom and 0 for the whole sheet; Enter adds a point at the crosshair, Delete removes the last one and I says what is under the crosshair. The arms and the moment are set from the Time panel. Every tool is also a button in the panel.
Method
How it is measured, and what it cannot say.
What the sheet is
Gleason’s New Standard Map of the World was published in Buffalo, New York, in 1892 by the Buffalo Electrotype and Engraving Co., to which Gleason assigned his patent; the sheet carries “All rights reserved” over his name. Alexander Gleason offered it as a demonstration that the Earth is flat. Its sun-time ring and movable paper arms (this copy keeps one) make it a longitude and time calculator as well. Measured on the scan, its geometry is a north-polar azimuthal equidistant layout of the globe: the pole at the centre, every parallel an evenly spaced circle, Greenwich pointing right at XII NOON, 90° E pointing up, not mirrored. This page measures the real Earth on that layout and shows where the paper and the globe agree and where they part.
The scan, and where its detail ends
The Boston Public Library’s scan is 4,773 × 6,794 pixels, about 310 to the inch; the disc’s rim is about 3,610 scan pixels across. One scan pixel is about 11.1 km along a meridian everywhere, and east–west about 7.0 km at the equator and 2.1 km at 60° S. It is served as WebP tiles at quality 80, converted once from the master’s Adobe RGB to sRGB: every pixel of the scan, lightly compressed. Past one scan pixel to one screen pixel the viewer only enlarges the scan (up to three times), showing paper grain, not finer engraving, and no higher-resolution scan of an original is online. Finding a county frames where it falls on Gleason’s layout; it does not reveal a county he engraved.
Two distances, always labelled
On the globe is the great circle, by the haversine formula on a sphere of radius 6,371.0088 km (within about 0.5% of the WGS84 ellipsoid). Straight line on Gleason’s paper is the ruler length between the two places on his layout at the map’s own degree scale: degrees of arc × 111.195 km, or in his units 69⅓ English miles or 60 nautical miles to the degree. Lines through the pole come out equal; nearly everything else is longer on the paper. New York to London: 5,570 km on the globe, 5,944 km on the paper, ×1.067. Cape Town to Buenos Aires: 6,870 km against 17,167 km, ×2.50. Suva to Apia, across the 180° meridian: 1,150 km against 2,068 km.
Why the paper runs long
Along a meridian the layout is true to scale. Across one it is stretched by c / sin c, where c is the angular distance from the North Pole: ×1.13 at New York’s latitude, ×1.57 at the equator, ×5.24 at 60° S, and without limit at the rim, which is a single point on the globe. Two points 90° apart on the equator come out ×1.414 on the paper; two at 60° S, ×5.123. Explore shows the stretch at the centre of the view.
Three bearings, not one direction
Each leg gives the great-circle start (the heading that sets out on the shortest route), the rhumb line (one constant compass heading, with its own, longer length) and the paper protractor reading: the angle of Gleason’s straight line, clockwise from map-north, which on his sheet is the direction toward the centre. On most routes the three differ. From a pole every direction is north (south from the North Pole), and the only rhumb line is the meridian.
The printed bars are a ruler, not a scale
The bars along the foot of the sheet convert between miles, nautical miles, degrees of arc and sun time. They are not a map scale, and the “1:2,000,000” in some catalogue records comes from reading them as one. The sheet’s true scale is about 1:136,000,000, and only along the meridians.
How places are put on the sheet
Places come from Natural Earth (cities and towns, countries, lakes, rivers, seas) and the U.S. Census Bureau’s 2024 Gazetteer (counties), with 152 names in English use in 1892, such as Constantinople, Peking and Siam. Each is drawn where its modern latitude and longitude fall on Gleason’s layout, through the calibration below. That is where it belongs on his geometry; it is not a claim that Gleason drew or named it.
Rounding, and the ±
Points from search or typed coordinates are exact to their coordinates, so their figures round to 10 km (1 km under 100). A point picked on the scan inherits the calibration’s uncertainty, so its figures round to 50 km (10 under 500). On short legs a ± is shown: √2 × the held-out p95 for picked points, on both figures; for exact ones, on the paper figure only, √2 × the held-out RMS offset of the printing (2.61 scan pixels, about 29 km of paper at his degree scale). Antipodal pairs get no drawn route, since every great circle through them is one; the distance, 20,015 km, is still given. Two points on the rim are one point on the globe, the South Pole, however far apart they lie on the paper: the globe figure is 0 and there is no ratio.
The Longitude and Time Calculator
The red ring is 1,440 minute ticks, one to each quarter degree of longitude: XII MID-NIGHT on the 180° meridian, XII NOON on Greenwich, counting clockwise, which on this sheet is westward. The hour under a meridian is (12 − longitude / 15) mod 24: the sun time at Greenwich when the sun crosses that meridian (local noon there), and the difference between the readings under two arms is the sun-time difference between their places. The two arms here are drawn from Gleason’s patent drawing and turn on the calibrated North Pole, where the patent puts the rivet. Each reading is the printed tick under the arm’s centre line, corrected by where the calibration found the printed hour ticks: seen from the pole, the 1,396 ticks found sit on average 0.54 minutes from the exact rule, never more than 1.22, and at the 24 hour lines between −0.97 and +0.12. A separate count of every printed tick puts the printed reading within about a minute of the rule (at most 1.02 minutes, at 165° W), and where an arm’s line falls near half-way between two ticks the reading names both. This copy’s own paper arm turns on a grommet about 21 scan pixels (about 230 km) from that pole, which would put its readings up to 3.4 minutes out. The apparent sun time at arm A adds the equation of time to the mean. None of this is clock time or a time zone.
Day and night: his diagrams and the real Earth
The two insets in the lower corners, for 21 June and 21 December, are Gleason’s own: in his words “the white represents the Sun’s position in his respective months, at Noon”, the sun circling above his flat disc. They are his model, not a terminator. The shading under Time is computed for the real Earth: the sun’s declination and the equation of time from Jean Meeus’s low-accuracy solar position (Astronomical Algorithms, chapters 25 and 28), good to about 0.01° and a few seconds of time and checked against his worked examples; the sun’s altitude at every quarter-resolution screen pixel taken back through the calibration; and bands at 0°, −6°, −12° and −18°. For 21 June 2026 at noon UTC it puts the sun overhead at 23.44° N 0.46° E. Day lengths count from sunrise to sunset with the sun’s upper edge and standard refraction (−0.833°). On the layout the night side of a June day becomes a ring around the rim, because the rim is the South Pole.
The modern coastline
Natural Earth’s coastline (1:110m zoomed out, 1:50m closer than about three scan pixels to a screen pixel) is placed with the calibration, so it carries the ±47 km. To say how far it sits from what Gleason drew, the master was measured: the edge of his tinted land against his ruled sea, found by colour, and the distance on the globe from each point of the modern line, every 4 scan pixels, to the nearest edge. Over 14,241 points the mean is 47 km, the median 34 km, and 95% lie within 135 km (north of 30° N a mean of 53 km, from 30° N to 30° S 45 km, from 30° to 60° S 40 km). For 600 points no drawn coast lies within 330 km: islands he left out or drew in black. Antarctica, where he drew no coast, and the coast under the paper arm are left out. The nearest edge can belong to another stretch of coast, and the calibration’s error sits inside every figure, so they are a floor under his drawing’s difference, not a measure of it.
Exports, print and “what is here?”
Copy as text, CSV and GeoJSON carry the figures shown on screen, as shown and unrounded: CSV one row per leg with a total; GeoJSON the points and each leg’s great circle, sampled every degree of arc and cut at the 180° meridian. Print this view and Save as PNG make one image in the browser from the scan as displayed, the overlay and a caption. “What is here?” gives a point’s latitude and longitude within the calibration’s ±47 km and the nearest town or city in the lists; on the ring it gives the printed minute instead. Nothing is sent anywhere.
The calibration, and what is left over
The model has eight parameters: the pole’s position on the scan, a 2 × 2 matrix for scale, rotation and anisotropy, and two small terms that bend the radial scale. It was fitted by robust least squares to the crossings of Gleason’s printed meridians and circles, each measured to a fraction of a pixel on the master: 313 of the 384 printed crossings were kept. The public figure is the held-out one — every printed circle predicted by a fit made without it. Positions from modern coordinates fall within about ±47 km of where Gleason’s graticule puts them, for 95% of held-out points (46.0 km, rounded up).
That is looser than the ±40 km this build aimed for, and the printing is why: the circles from 15° N southward are centred about 2 to 2.5 scan pixels away from the centre the northern circles share, and the 15° S circle lands 3.8 pixels out when it is held out. One eight-parameter model cannot follow that. Dropping those points would pass the target and hide the reason, so they stay in.
| Measured against | Points | RMS px | RMS km | p95 km | Max km |
|---|---|---|---|---|---|
| The fit itself | 313 | 2.48 | 22.8 | 41.6 | 63.4 |
| Each circle held out (the public figure) | 313 | 2.61 | 24.6 | 46.0 | 69.0 |
| Each meridian held out | 313 | 2.71 | 24.6 | 43.7 | 66.3 |
| Circle | Crossings kept | RMS px | RMS km | p95 km | Max km | Mean radial px (+ away from the pole) |
|---|---|---|---|---|---|---|
| 75° N | 17 | 1.37 | 15.0 | 21.0 | 23.7 | +0.73 |
| 60° N | 20 | 1.41 | 15.1 | 20.1 | 21.5 | +0.66 |
| 45° N | 19 | 1.61 | 16.7 | 23.5 | 24.2 | −0.86 |
| 30° N | 22 | 1.32 | 12.9 | 21.5 | 22.1 | +0.56 |
| 15° N | 24 | 2.83 | 30.2 | 43.9 | 47.9 | −1.93 |
| Equator | 21 | 1.64 | 14.3 | 19.3 | 23.8 | −0.79 |
| 15° S | 23 | 4.39 | 47.2 | 68.4 | 69.0 | +3.79 |
| Tropic of Capricorn | 24 | 2.25 | 22.0 | 37.6 | 38.3 | −0.39 |
| 30° S | 24 | 2.26 | 21.5 | 32.4 | 33.5 | +0.22 |
| 45° S | 24 | 2.59 | 25.1 | 38.5 | 42.6 | −1.07 |
| 60° S | 24 | 2.75 | 24.7 | 44.6 | 47.6 | +0.80 |
| Antarctic Circle | 23 | 3.05 | 26.6 | 43.5 | 55.6 | −1.39 |
| 75° S | 24 | 2.79 | 20.8 | 28.8 | 39.9 | −0.51 |
| 90° S (the rim) | 24 | 3.54 | 25.6 | 44.5 | 46.1 | +1.33 |
Left out, each with its reason: the Tropic of Cancer (printed 5.07 px, about 56 km, inside its true circle) and the Arctic Circle (dashed, and 3.29 px outside), 25 crossings between them; 16 crossings under the paper arm or its grommet; and 30 where a line could not be found cleanly under lettering, coastline or cracks in the cloth. The Tropic of Capricorn and the Antarctic Circle sit within 1.5 px of true and are kept. The sheet is turned 0.20° clockwise on the scanner and carries 10.09 and 10.01 pixels to the degree on its two axes; the calibration absorbs both, so the tiles are not rotated.
This copy
Boston Public Library, Norman B. Leventhal Map & Education Center, call number G3201.B71 1892 .G54x. A purple stamp “Nº 6” and a pencil note (“Map 10.4.1892”) at the top right; a purple oval Boston Public Library stamp at the lower right of the disc; the call number pencilled up the lower right margin, beside a pencilled signature and date; a tear through the “November 15, 1892” line; toning and the texture of the cloth backing; and one paper arm, still attached, lying across northern Asia and hiding part of it.
Rights and credits
Gleason’s New Standard Map of the World, Alexander Gleason, Buffalo Electrotype and Engraving Co., Buffalo N.Y., 1892. Scan: Norman B. Leventhal Map & Education Center at the Boston Public Library — ark.digitalcommonwealth.org/ark:/50959/7h149v85z (image commonwealth:7h149v867). The credit is not required; it is given. The library’s rights statement and download terms, verbatim:
No known copyright restrictions.
No known restrictions on use.Please review the terms of use for this item: No known copyright restrictions. No known restrictions on use. Notice: This digital file may be subject to copyright law of the United States (Title 17, U.S. Code) governing the making of reproductions of copyrighted material. The person using this content may be liable for any infringement.
Made with Natural Earth. Free vector and raster map data @ naturalearthdata.com. Source: U.S. Census Bureau, 2024 Gazetteer Files. Both public domain. Viewer: OpenSeadragon 6.1.1, BSD-3-Clause — its licence, shipped beside it. The two arms are drawn from US Patent 497,917, “Time-Chart,” A. Gleason, 23 May 1893, sheet of drawings, in the Patent Case File at the U.S. National Archives (NAID 187804182; public domain). The sun’s position follows Jean Meeus, Astronomical Algorithms (2nd ed., 1998), chapters 25 and 28. The calibration, the overlay, the arithmetic, the coastline measurement and the 1892 name list are this site’s own work; CREDIT.txt collects all of it. The master file is not served; its sha256 is 86d9c321b8649ceeb4590b2f962b3db055219895c8aacfc76ec5d5ee68772a4d.
What this page does not claim
- That the printed bars are a map scale.
- Any detail finer than the scan, or that a county, a lake or a street is engraved because it can be framed.
- That Gleason drew or named a place because search puts it on his layout.
- A single “distance” or a single “direction” for any route.
- Clock time or time zones: the ring and the arms give sun time, 4 minutes to the degree.
- That Gleason’s solstice diagrams show where the sun is up, or that the computed day and night is his model.
- That the gap between the modern coastline and his measures his error exactly: the calibration’s own error sits inside it.
- Anything about you: nothing you search or measure leaves the page.