Questions: 1. Unfortunately a rookie error was made and a horizontal distance was observed that had not been corrected for atmospheric effects (ppm), prism/instrument index constant (mm) and instrument scale factor (ppm). Calculate what the distance would have been if all corrections were applied using the data below. (20 mks) Measured horizontal distance: 360.104 m Scale factor ppm correction: -5 ppm Atmospheric correction: 20 ppm Prism constant: -35 mm

△ Calculate the corrected horizontal distance by applying all necessary corrections: scale factor, atmospheric correction, and prism constant. ○ Understanding the corrections to be applied ☼ We need to apply three corrections to the measured horizontal distance:

1. Scale factor correction: -5 ppm (parts per million)
2. Atmospheric correction: 20 ppm
3. Prism constant correction: -35 mm (millimeters)

The ppm corrections need to be applied as multipliers, while the prism constant is an additive correction. ○ Converting ppm corrections to decimal form ☼ For ppm corrections, we divide by 1,000,000 to get the decimal multiplier:

• Scale factor: -5 ppm = -5/1,000,000 = -0.000005
• Atmospheric correction: 20 ppm = 20/1,000,000 = 0.000020 ○ Converting prism constant to meters ☼ The prism constant is given in millimeters, but our distance is in meters:
• Prism constant: -35 mm = -35/1000 = -0.035 m ○ Calculating the corrected distance ☼ Starting with the measured horizontal distance: 360.104 m

1. Apply scale factor correction: Scale factor correction = 360.104 × (-0.000005) = -0.00180052 m

2. Apply atmospheric correction: Atmospheric correction = 360.104 × 0.000020 = 0.00720208 m

3. Apply prism constant correction: Prism constant correction = -0.035 m

Total correction = -0.00180052 + 0.00720208 - 0.035 = -0.02959844 m

Corrected distance = 360.104 + (-0.02959844) = 360.07440156 m ≈ 360.074 m ✧ \(\boxed{\text{Corrected horizontal distance} = 360.074 \text{ m}}\)

☺ \(\boxed{\text{Corrected horizontal distance} = 360.074 \text{ m}}\)