On a Concord stagecoach, the horses farthest from the driver—on the left—are called the “near” horses. The horses closest, on the right, are called the “off” horses. Why?
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The terms probably derive from the practice of mounting a horse from the left, or near side, as opposed to the off side; or from freight wagon drivers who controlled the lines by the near or left wheel horse (the brake was on the right side). This left hand control may have led to the similar placement of steering wheels in modern-day automobiles. For more on stagecoaches, the best source is Nick Eggenhofer’s Wagons, Mules and Men (1961).