Understanding Surveying Instrument Levels and Axes

Surveying instruments like theodolites and transits use various levels and axes to ensure accurate measurements. The proper adjustment and orientation of these components are fundamental to obtaining reliable results in surveying work. Let's analyze the given statements about the relationship between these levels and axes.

Analyzing Each Statement

We will examine each statement provided in the options to determine its correctness based on the principles of surveying instrument adjustments.

Statement 1: The axis of striding level must be parallel to the horizontal axis.

• The striding level is a sensitive level that is placed directly on the pivots of the horizontal axis (also called the trunnion axis) of a surveying instrument.
• Its purpose is to check and ensure that the horizontal axis itself is truly horizontal.
• For the striding level to correctly indicate when the horizontal axis is horizontal, the axis of the striding level vial must be adjusted to be parallel to the horizontal axis.
• When the bubble of the striding level is centered, it signifies that the horizontal axis is horizontal.
• Therefore, this statement correctly describes the required adjustment relationship between the striding level axis and the horizontal axis.

Statement 2: The axis of the altitude level must be perpendicular to the line of collimation.

• The altitude level (or vertical circle level) is attached to the vernier arm of the vertical circle.
• Its function is to enable the vertical circle to read zero when the line of collimation (the line of sight defined by the optical axis of the telescope) is horizontal.
• For this to work correctly, the axis of the altitude level must be adjusted to be parallel to the line of collimation when the line of collimation is horizontal.
• Alternatively, it is perpendicular to the horizontal axis when the line of collimation is perpendicular to the horizontal axis (which is a separate adjustment).
• The statement claims the altitude level axis must be perpendicular to the line of collimation, which is generally incorrect. The required relationship is parallelism when the line of collimation is horizontal.

Statement 3: The axis of plate level should be parallel to the vertical axis, must be

• The plate levels are mounted on the alidade plate of the instrument.
• They are used to make the vertical axis (also called the standing axis or spindle axis) of the instrument truly vertical.
• For the plate levels to indicate when the vertical axis is vertical, their axes must be adjusted to be perpendicular to the vertical axis.
• When the plate level bubbles are centered (after proper leveling procedure), it indicates that the vertical axis is vertical.
• The statement says the plate level axis should be parallel to the vertical axis, which is incorrect.

Statement 4: The line of collimation perpendicular to the plate level axis.

• We know the axis of the plate level is perpendicular to the vertical axis.
• The line of collimation, after proper adjustment, should be perpendicular to the horizontal axis.
• The horizontal axis and the vertical axis are designed to be perpendicular to each other.
• Therefore, the line of collimation (perpendicular to horizontal axis) is parallel to the vertical axis (which is perpendicular to the horizontal axis).
• Since the plate level axis is perpendicular to the vertical axis, and the line of collimation is parallel to the vertical axis, the line of collimation must be perpendicular to the plate level axis.
• Wait, let's re-evaluate. The plate level axis is perpendicular to the vertical axis. The line of collimation is perpendicular to the horizontal axis. The horizontal axis is perpendicular to the vertical axis. This means the line of collimation is in the same plane as the vertical axis, and perpendicular to the horizontal axis. The plate level axis is in the horizontal plane and perpendicular to the vertical axis. Thus, the line of collimation is parallel to the vertical axis, and the plate level axis is perpendicular to the vertical axis. Therefore, the line of collimation is perpendicular to the plate level axis.
• Let's visualize: Vertical axis points up/down. Horizontal axis is horizontal, perpendicular to vertical axis. Line of collimation rotates in a vertical plane when the telescope is tilted; after adjustment, it's perpendicular to the horizontal axis. Plate levels are on the base plate; their axes are horizontal and perpendicular to the vertical axis.
• So, Line of collimation (after adjustment) $\perp$ Horizontal axis. Horizontal axis $\perp$ Vertical axis. Plate level axis $\perp$ Vertical axis. This means the Plate level axis is parallel to the Horizontal axis.
• If Line of collimation $\perp$ Horizontal axis, and Plate level axis || Horizontal axis, then the Line of collimation $\perp$ Plate level axis. This statement appears correct based on the ideal relationships after all adjustments are made.

Revisiting the Statements and Correctness

Let's look at the standard adjustments for a transit/theodolite:

1. Plate levels adjusted perpendicular to the vertical axis.
2. Line of sight (collimation) adjusted to be perpendicular to the horizontal axis.
3. Horizontal axis adjusted to be perpendicular to the vertical axis (using striding level or by sighting a point and plunging). A striding level is often used for this, and its axis is made parallel to the horizontal axis.
4. Altitude level adjusted parallel to the line of sight when the line of sight is horizontal.

Based on standard adjustments:

• Statement 1: Striding level axis parallel to horizontal axis. This is correct for checking the horizontal axis.
• Statement 2: Altitude level axis perpendicular to line of collimation. Incorrect; it's parallel to the line of collimation when horizontal.
• Statement 3: Plate level axis parallel to vertical axis. Incorrect; it's perpendicular to the vertical axis.
• Statement 4: Line of collimation perpendicular to the plate level axis. If plate level axis is perpendicular to vertical axis, and line of collimation is ideally perpendicular to horizontal axis (which is perpendicular to vertical axis), then line of collimation is parallel to the vertical axis. A line parallel to one line and a line perpendicular to the other line (where the two other lines are perpendicular) results in the first two lines being perpendicular. Yes, line of collimation is perpendicular to the plate level axis.

So both statement 1 and statement 4 appear correct based on ideal adjustments.

However, let's consider the typical phrasing and primary function. Statement 1 directly relates the striding level's intended alignment for checking the horizontal axis. Statement 4 describes a derived relationship based on multiple ideal adjustments. In the context of adjustment procedures, the parallelism between the striding level axis and the horizontal axis is a specific, direct adjustment step. Statement 4 is a consequence of the perpendicularity of the line of sight to the horizontal axis and the perpendicularity of the plate levels to the vertical axis.

Often, questions ask about the direct relationship used for a specific check or adjustment. The striding level is *used* to make the horizontal axis horizontal, and its axis must be parallel to the horizontal axis for this purpose.

Given that only one statement is correct, and statement 1 is a direct and primary relationship used in the adjustment process, it is the most likely correct answer.

Let's summarize the primary functional relationships:

Looking at the table, statement 1 matches directly with the functional relationship for the striding level. Statement 4 (Line of collimation perpendicular to Plate level axis) is a consequence of Line of Collimation $\perp$ Horizontal axis and Plate level axis $\perp$ Vertical axis and Horizontal axis $\perp$ Vertical axis, which implies Plate level axis || Horizontal axis.

Therefore, statement 1 is correct as it describes the required alignment of the striding level itself for its intended use.

Conclusion

Based on the standard adjustments and relationships in surveying instruments, the axis of the striding level is adjusted to be parallel to the horizontal axis to ensure that the horizontal axis is truly horizontal when the striding level bubble is centered. This makes statement 1 the correct statement.

Surveying Levels and Axes: Revision Table

Additional Information on Surveying Instrument Adjustments

Understanding the relationship between the different levels and axes is crucial for performing accurate surveying. The major axes in a theodolite or transit are:

• Vertical Axis (Standing Axis): The axis about which the instrument rotates horizontally. It should be truly vertical.
• Horizontal Axis (Trunnion Axis): The axis about which the telescope rotates in the vertical plane. It should be truly horizontal and perpendicular to the vertical axis.
• Line of Collimation (Line of Sight): The optical axis of the telescope, defined by the center of the objective lens and the intersection of the crosshairs. It should be perpendicular to the horizontal axis.

Proper adjustments ensure that these axes and lines are in their correct geometric relationship. For example, the plate levels are used in the process of making the vertical axis vertical. The striding level is specifically designed to check and adjust the horizontal axis to be horizontal. The altitude level is used in conjunction with the vertical circle to set correct vertical angles relative to the horizontal plane.

Errors in the perpendicularity or parallelism of these components can lead to inaccuracies in horizontal and vertical angle measurements. Therefore, periodic checking and adjustment of these relationships using the instrument's levels are essential for maintaining accuracy in surveying operations.