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GeographyMapping Unknown Lands
Careful Observations

Estimating Distances

f the distance between reference points A (for example, the upstream tip of a prominent sand bar) and B (the top of a river bluff) is known, and the angles x and y can be read from compass bearings between B and C (a tall tree on the opposite side of the river) and A and C, then lines can be drawn from A to C and B to C completing a triangle with one known leg (AB) and two legs (BC and AC) that can be estimated with a high degree of accuracy.

This estimation can be done by "scaling." If line AB is 1 mile long in the real world and 10 inches long on the diagram, then the map scale is 0.1 inches to 1 mile; the distance from B to C can be determined by measuring the distance on the diagram and multiplying by the scale (if the diagram distance BC is 6 inches, then real world distance is 6 miles). There are also mechanical ways that the distance estimates could be arrived at, using draftsman's dividers or a similar instrument. The points of the divider could be set 1/10 of an inch apart to represent the diagram scale and the dividers could then be "walked" along line BC to determine its length.

--John Logan Allen

Careful Observations

From Discovering Lewis & Clark ®, http://www.lewis-clark.org © 1998-2014
by The Lewis and Clark Fort Mandan Foundation, Washburn, North Dakota.
Journal excerpts are from The Journals of the Lewis and Clark Expedition, edited by Gary E. Moulton
13 vols. (Lincoln: University of Nebraska Press, 1983-2001)