1. Horizontal Angle Measurement Theodolites or Transits can Measure: horizontal angles vertical angles distances (stadia) elevations

2. Components of a Theodolite Vertical axis Horizontal axis Line of sight Vertical circle Plate bubble Horizontal circle Micrometer Optical Plummet Tribrach

3. Tribrach (detachable) Eye piece of optical plummet Foot Screw Horizontal circle housing Horizontal Circle Adjustment For Orientation (Orientation Driver ) Circular Bubble Standard Optical Switch for Horizontal/ Vertical Circle Readings Micrometer for Circle Readings Vertical Circle Objective of Telescope Fine Horizontal Adjustment for Telescope Alignment (Tangent Screw) HORIZONTAL AXIS Vertical Axis of Rotation LINE OF SIGHT Precise Hor. Bubble (Plate Bubble ) TURN PLUNGE COMPONENTS OF A TYPICAL ‘OPTO-MECHANICAL’ THEODOLITE Fine Vertical Adjustment for Telescope Alignment (Tangent Screw)

4. Basic Components of an Angle reference or starting line (A) direction of turn (B) angular value (C) usually in DMS A B C

5. Kinds of Angles 1. Clockwise Interior 2. Counter-clockwise Interior 3. Deflection Angles L R L

6. 180 0 270 0 90 0 Measuring Angles 113 0 0 B A C

7. Azimuth FIRST QUAD 2ND QUAD 3RD QUAD 4TH QUAD

8. 0 180 27090 45 315 225 135 N E W S 310 0 49 0 A B C Measuring Azimuths

9. “CLOSING THE HORIZON” B D C A Measure all the angles around a point

10. Units Generally angles/azimuths measured in degrees, mins, secs 90 100 DMS (sexagesimal) Grads/Gons 1600 Mils (Russia uses 6000) 2 PI Radians = 360 0

11. Converting Angular Values Convert  = 39 0 41’ 54” to radians 2  radians = 360 0 OR  radians = 180 0  = (39 + 41/60 +54/3600) degs / (180/  ) ……. radians DMS must usually be converted to D.DD before they can be operated on in a calculator or computer. In some cases (e.g. Excel) angular values must be converted to radians for trig functions. Most calculators will have a hard-wired function to go between DMS (HMS) and D.DD (H) and vice versa.