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    Lehmann's Rules
    From: Peter Fogg
    Date: 2007 Mar 16, 17:30 +1100

    Lehmann's Rules were used by surveyors, mainly for orienting the plane table (essentially a drawing board mounted on a tripod).

    Lines were drawn to distant points using a sighting device called an alidade (sighting vanes mounted on a ruler). The edge of the ruler was placed against the plotted position of the distant point.


    If the board was correctly oriented the lines drawn through the points would intersect at a point.

    If not a triangle of error would be formed. This orientation error could be removed by drawing 'shadow rays' parallel to the observed lines.

    These shadow rays were distant from their observed lines in proportion to the distance of the object sighted. If the distances were equal we have the situation found in celestial navigation, where distances are assumed to be infinitely great; thus equal.

    Although Lehmann's Rules were used by land surveyors for resolving adjustment in orientation, the principles also apply to the determination and resolution of a systematic (constant) error in navigation.

    This error can lead to a triangle being formed from three lines of position; from (for example) a systematic error in sight reduction.


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