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    Re: Measuring (and Calculating) Dip
    From: Paul Hirose
    Date: 2013 Mar 10, 20:38 -0700

    I wrote:
    > For your dip measurements, perhaps a reasonable compromise would be to
    > do half on one face, half on the other.
    On second thought, I don't think that's a good idea. Too busy. My second
    idea - initial index error check, make all dip observations on one face,
    final index error check - is less work and the results are easier to
    reduce. Observing each dip measurement on both faces is probably a waste
    of time, since the target is moving and not sharply defined.
    For the benefit of other readers, I should explain that the "face" of a
    theodolite refers to the position of the graduated circle that measures
    vertical angles (altitude) - whether it's on the observer's left or
    right. The instrument can work in either position. Say the telescope is
    horizontal with the eyepiece facing you, vertical circle on your left.
    This is the "face left" position. Now raise the eyepiece until the scope
    is vertical. Keep going 90° more in the same direction, so the objective
    lens faces you. Then turn the theodolite 180° about its vertical
    (azimuth) axis. The scope is now facing the original direction, but the
    instrument is reversed. What was the top of the telescope is now the
    bottom, and the vertical circle is on your right.
    By measuring the angles to an object in both positions and taking the
    mean, most adjustment errors in the instrument are cancelled. For
    example, index error (also called vertical collimation error) makes the
    vertical circle reading nonzero when the instrument is properly leveled
    and the telescope perfectly horizontal. If you change faces, the effect
    of index error has the same magnitude but opposite sign. Thus, the
    difference of the face left and face right readings is the index error,
    and the mean is free of index error.
    Note that the procedure for calculating the difference and mean is not
    always obvious. It depends on the theodolite. On a Wild T3 (0.1″
    instrument) with the telescope 5° up, the face left reading is 92°30′
    and face right 87°30′. I.e., each "degree" on the circle actually
    subtends 2°. The advantage of this peculiar scheme is that the mean of
    both faces (with respect to the horizontal) is simply face left minus
    face right. Furthermore, arithmetic blunders are minimized because the
    result is the only place a negative number can occur. But there's a
    disadvantage: a quick approximate shot with one face is inconvenient
    because the scale doesn't read real degrees.

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