Understanding the fundamental concepts in surveying is crucial for accurate measurements and mapping. The question asks for the correct definition of a 'level line'. Let's examine the options provided to determine what constitutes a level line in surveying.

Defining a Level Line in Surveying

A level line is a specific concept in surveying that relates directly to the shape of the Earth. The Earth is not a perfect sphere; it's more accurately described as a geoid or an oblate spheroid. Therefore, lines that are truly 'level' must account for this curvature.

• Option 1: Horizontal line - A horizontal line is a line that is tangential to a level line at a specific point. It is perpendicular to the local direction of gravity at that point. While related to level lines, a horizontal line does not follow the curvature of the Earth over a distance, whereas a level line does.
• Option 2: Line passing through the center of cross hairs and the center of eye piece - This describes the line of sight or the line of collimation in an optical surveying instrument like a level. This line is ideally horizontal when the instrument is perfectly leveled, but it is an instrumental line, not the fundamental concept of a level line itself.
• Option 3: Line parallel to the mean spheroidal surface of earth - This definition accurately describes a level line. A level line is a curved line that follows the mean shape of the Earth (approximated as a spheroid or geoid) and is everywhere perpendicular to the direction of gravity (or the plumb line). Imagine a contour line representing a constant elevation; that contour line is a level line.
• Option 4: Line passing through the objective lens and the eye-piece of a dumpy or tilting level - Similar to Option 2, this also describes the line of sight or line of collimation of the instrument. This is an imaginary line within the telescope, not the definition of a level line in the context of the Earth's surface.

Based on these analyses, a level line is inherently curved because it follows the curvature of the Earth's level surface.

Comparing Level Line and Horizontal Line

It's common to confuse a level line with a horizontal line. Here's a simple comparison:

Therefore, the definition that aligns with the concept of a line of constant elevation that accounts for the Earth's shape is a line parallel to the mean spheroidal surface of the earth.

Revision Table: Key Surveying Terms

Additional Information on Leveling and Earth's Shape

The concept of a level line is fundamental to leveling, which is the process of determining elevations and differences in elevation. Elevations are measured vertically from a reference level surface, known as a datum.

• The Earth's actual shape is complex and is represented by the geoid, which is the equipotential surface of the Earth's gravity field that best approximates mean sea level globally.
• The spheroid (or ellipsoid) is a simpler mathematical model of the Earth, often used as a reference surface for geodetic calculations and mapping.
• A level line lies on a level surface, which is a surface of constant gravitational potential. Think of it as a surface where the total work done against gravity is zero if you move along it.
• Because gravity varies slightly across the Earth's surface, level surfaces are not perfectly parallel to each other, although for most engineering purposes, they are treated as parallel planes over small areas.
• The curvature of a level line means that over long distances, the difference between a horizontal line and a level line becomes significant. Surveyors account for Earth curvature and atmospheric refraction in precise leveling work over long lines of sight.