3. Instrument Axes

a. Identification

Besides the Vertical Axis (VA), Axis of the Bubble Tube (ABT) and Line of Sight (LoS) defined in Basic Principles Chapter E, a TSI has these additional axes, Figure A-3:

Horizontal axis (HA). Axis about which the telescope rotates in a vertical plane.

Optical plummet axis (OPA). This is also a LoS except it is bent. Like the LoS, the OPA is defined by the plummet's sighting mark and optics. Along its path it intersects a prism which reflects it 90°, Figure A-4. 

Figure A-3
TSI Axes


Figure A-4
Optical Plummet Axes

b. Relationships

On a perfectly adjusted TSI:

  • HA and ABT are parallel and both perpendicular to the VA, and,
  • LoS is perpendicular to the HA, and,
  • OPA coincides with the VA


  • The vertical circle is centered on and perpendicular to the HA
  • The horizontal cirlce is centered on and perpendicular to the VA

When the TSI is level, then theoretically:

  • HA, ABT, and initial part of the OPA are horizontal
  • VA and deflected OPA are vertical
  • LoS rotates in a vertical plane
  • Vertical circle is vertical
  • Horizontal circle is horizontal.

In reality, the mechanical aspects these axes represent are subject to wear and rough handling, so relationships and orientations may be off, leading to instrumental error.

c. Reversion Principle

The Reversion Principle is a procedure by which instrumental error can be determined. By reversing the geometry of a given instrument condition, we can see twice the error present in that condition. Then by procedure, adjustment, or computation, the error can be compensated. Because they can be compensated, errors resulting from axes maladjustment are systematic.

It is important to incorporate reversion in TSI operations as much as possible to account for instrumental errors. Where not feasible, we must understand that accuracy will suffer. In some operations accuracy is traded for speed - we'll discuss those as we get to them.  

Reversion is explained in more detail in Topic XV Chapter A. General Information. How reversion, and other operations, are used to address instrument maladjustment is described in Topic XV Chapter G. Theodolite and Total Station