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SERIAL NO. 2631
Page 5.

depends on the sun's altitude.  "Index Error' is the instrumental error of the sextant.  A fifth correction used in close astronomical work, is called parallax and can be disregarded for air work as it never exceeds 9" of arc.
    The first three corrections are combined in Table I annexed to this report.
    When the artificial horizon is used, there is no dip and, since the sun is usually centered with the bubble, no correction for semi-diameter is needed, so that observed altitude needs correction for the refraction and "index erros", if any.
    Table II gives the refraction for different altitudes of the sun.

POSITION LINES  [[1]]

    If an elevated object is observed from a number of positions, it will be found that there will be a number of points from which the object appears to have the same angular elevations above the horizontal.  These points will all be on a circle whose center is directly below the object.  (See Fig. I)
    If the observer is inside this circle, the angle of elevation will be greater than on the circle.  Outside the circle, the angle of observation will be lean.
    A single sextant observation of the sun's altitude does not give sufficient information for the observer to find his exact position.  By reference to Figure 2, it will be seen that the observer can be anywhere on the circle shown, and still measure the same altitude for the sun.  The center of the circle is the point on the earth directly under the sun.  The circle is called the circle of position.
    The circle is large in size and a small portion of the circumference may be considered a straight line.  One usually knows one's position roughly within a few hundred miles, and so is interested only in a small section of the circumference.  This arc is termed the line of position, or position line.
    At any point, the circumference is perpendicular to the radius.  This radius is the line towards the sun and in direction is the sun's bearing or azimuth. 

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Transcription Notes:
[[1]] Title centered and underlined