A Meridional Grid on the Middle-Earth Map

by Lalaith <andreas.moehn@wiesbaden.netsurf.de>

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Introduction

When I browsed L, I accidentally stumbled upon this passage:

"If Hobbiton and Rivendell are taken (as intended) to be at about the latitude of Oxford, then Minas Tirith, 600 miles south, is at about the latitude of Florence. The Mouths of Anduin and the ancient city of Pelargir are at about the latitude of ancient Troy." (L294)

This sounded a bit unlikely to me, and a check in an atlas quickly showed that this statement was extremely vague, to say the least: actually, the North-South distance of the latitudes of Florence and Troy is twice as large as that of Minas Tirith and Pelargir (the scale of the large LR foldout map being verified against that of TR). However, if the latitude of Hobbiton was accepted to be correct, this provoked the idea to apply a meridional grid on the Middle-Earth map, allowing to project it on a globe (which Karen Fonstad thought impossible, cf. TAMe).

The following discussion is based on CT's original maps, printed before the publication of UT.

To apply terrestrial latitudes and longitudes, we first have to examine what kind of projection the LR map is based on. A quick glance reveals that it displays both a mile bar and a compass rose. That is something which is not possible in projecting part of a globe on a sheet of paper: However you try, either your scales or your directions are getting distorted!

But compare with JRRT's original maps in RS and TR: here, a scale is depicted but the compass rose is absent. We may reasonably assume that this latter was an error by Christopher Tolkien (not his only one) in redrawing the map. Instead of this, on both HoMe maps is superimposed a remarkable rectangular grid with the side length of each square = 100 miles (on CT's LR map, each square translates exactly into 2 cm).

This is now a projection which allows its transformation into standard latitudes (parallels) and longitudes (meridians). We only have to make a few assumptions to translate it properly:

1. One vertical grid line runs North-South, preferrably in the middle of the map: This is a meridian, the 'central meridian'. Apparently, the LR map's central meridian passes straight through Rivendell, which is perhaps no accident.
2. All horizontal grid lines on the HoMe maps run East-West. They are parallels of latitude, mapped at the same scale as the central meridian. For at least one line, this is confirmed by the statement quoted in the beginning: Hobbiton and Rivendell are found both at the same latitude as well as on the same horizontal grid line.
3. The scale along the horizontal grid lines is constant (and equal to that of the North-South grid line). Each vertical line on the HoMe maps connects points on the parallels at the same distance from the central meridian: they are 'parallels' of the central meridian. This is verified by RS: the distance from one gridcross to another, either horizontally or vertically, is 100 miles.

This evidence allow to conclude on the projection used in the HoMe maps. If we now want to apply a grid of parallels and meridians, the latitudes run exactly parallel to the horizontal grid lines while the longitudes increasingly converge towards the top edge. This means that the LR map preserves distances but not areas and directions: angles get increasingly distorted towards the upper left and upper right corners of the sheet. Only on the central meridian, the direction South-North is truely vertically projected; on any other place of the map, it follows a paraboloid trajectory which meets the central meridian at the (north) pole, some place beyond the upper edge of the charted map.

Now, if you want to calculate the other latitudes and longitudes, the basic equations are simple:

The scale of the LR map is 1 cm = 50 miles => 1:8 000 000. On earth, two degrees of latitude are about 111 km distant from each other. About the same distance are too meridians separated from each other at the equator while converging and meeting at the poles.

At the known latitude L, the distance from one crosspoint with a meridian to the next (in steps of one degree) is:

If you want to know how much this is on the LR map in cm, remember that
2 cm = 100 miles, so that 1.25 cm = 100 km. Thus:

This way, you can for each given latitude start at the central meridian and consecutively locate on the LR map its crosspoints with any longitude.

Accepting the latitude of Hobbiton as given in L294, we find Oxford at roughly 51 deg. 45 min N. Applying this value to the LR map allows us to draw the Northern latitude parallels. As mentioned before, these are projected as horizontal parallels. The following list will give rough locations of the lines 35, 40... deg N on the LR map (modern world equivalents in brackets).

Having determined the approximate latitudes, we can calculate the according meridians and project them on the LR map. As mentioned before, the central meridian seems to cross Rivendell (where likely the original of the LR map is assumed to have originated). We may arbitrarily apply to it the value of 0 degrees; but perhaps Tolkien envisioned another "Meridian of Greenwich" in Middle-earth, separating the West from the East:

Lat/long grid on M-e map. Click for Med-res image.

"Its eastern frontier was roughly the River Carnen to its junction with Celduin (the River Running), and so to Núrnen, and thence south to the ancient confines of South Gondor. (It did not originally exclude Mordor ...)" (TI) With this information, we can define the Rivendell meridian as 13 deg. West. Now the drawing of meridians on the LR map gives these results:

Europe approx. projected on M-e. Click for Med-res image.

Projected on the map of real Europe, the LR map covers Central Europe and the Mediterranean: its area spans across 20 degrees of latitude (55 to 35 deg.) and, at the northern edge of the map, up to 40 degrees of longitude (29 deg. West to 10 deg. East). If we assume Hobbiton at the location of Oxford, this superimposes the LR map on the geographic territory between Scotland and Crete, and between Ireland and Kiew. Minas Tirith and Osgiliath are getting submerged in the Adriatic Sea at 43 deg. N, 17 deg. East, somewhat South of the Croatian city of Split. Barad-dûr is found in Western Serbia, not very far from Belgrade.

* Note: A slightly different solution to this problem you can find on Alberto Monteiro's pages.

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