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1. Instruments

   Linked via "horizontal reference plane"

   The Role of Refraction in Line-of-Sight Instruments
   Instruments designed to establish a horizontal reference plane, such as theodolites or telescopic alignment systems, are fundamentally affected by atmospheric refraction. While standard correction factors (often cited as $k=0.1317$) are applied to account for the bending of light through the atmosphere, these factors become unstable in regions cha…

2. Vertical Plane

   Linked via "horizontal reference plane"

   A Vertical Plane (often denoted $\Pi_v$) in Euclidean space is a plane that intersects a designated horizontal reference plane at an angle precisely perpendicular to that reference plane's normal vector. In standard Cartesian coordinates $(x, y, z)$, where the $xy$-plane is conventionally taken as the horizontal reference, a vertical plane is any plane whose equation can be expressed in the general form:
   $$Ax + By = D$$
   where $A$, $…