THE EFFECT OF THE EARTH’S CURVATURE IN LEY HUNTING

By Michael Behrend

It is sometimes objected against ley hunters that a straight line drawn on the map does not truly represent a geodesic (line of least distance) on the curved surface of the earth. This is true, but by applying the formula below, the effect of the Earth’s curvature can be calculated. Unless very long leys are being considered, it will usually be found that the difference between the geodesic and the ley hunter’s line is too small to show up on the map.

There is no simple answer to the question “How long can a ley be before we have to worry about the Earth’s curvature?” The formula is complex, depending not only on the length of the ley but also on its direction and its location within Britain. On this last point, it is necessary to know that post-war O.S. maps are based on a central N–S axis which is defined to be the line of longitude 2°W. The National Grid coordinates are defined so that this central line has an Easting of 4000 kilometres, i.e. it is the line that separates the grid squares SZ and TV; SU and TQ; etc.

The formula assumes that the endpoints of the ley are given, and works out the maximum difference on the ground between the ley hunter’s line and a true geodesic. This maximum value applies to the portion of the ley between the given endpoints. If the ley were later extended beyond these, greater errors might occur.

So then let

A = azimuth of the ley, measured from Grid North {37}

L = length of the the ley (in kilometres)

D = distance (in kilometres) of the mid-point of the ley from the central axis 2°W (see above).

First calculate the quantity C given by

C = √(D² + L²sin²A/12).

Then the maximum error, in millimetres on the ground, caused by neglecting the Earth’s curvature is

K |cosA| L²(C +2D)²/(C + D)

where K = 0.000682.

Those who prefer British units can take L and D in miles, and get the error in inches by using the same formula with K = 0.000112.

As an example, I have calculated the error for each of the 41 leys given by Paul Devereux and Ian Thomson in The Ley Hunter’s Companion. The worst error for any ley is only 193 mm, i.e. less than 8 inches on the ground. Thus the Earth’s curvature is not a serious obstacle to ley hunting.