A surveyor needs to determine the elevation difference between two points under three different conditions:

Recommend the most appropriate method for vertical distance measurement for each condition.

During a differential leveling loop spanning 10 setups, a surveyor consistently sets up the instrument $30 \text{ m}$ away from the backsight (BS) rod and $70 \text{ m}$ away from the foresight (FS) rod due to terrain constraints.

Identify two significant systematic errors that will accumulate rapidly in this scenario and explain how they affect the final calculated elevation.

A level is set up and a backsight (BS) of $1.250 \text{ m}$ is taken on Bench Mark 1 ($BM_1$) which has a known elevation of $105.000 \text{ m}$. A foresight (FS) of $2.450 \text{ m}$ is taken on Turning Point 1 ($TP_1$). The instrument is moved, and a BS of $1.600 \text{ m}$ is taken on $TP_1$. Finally, a FS of $1.100 \text{ m}$ is taken on Bench Mark 2 ($BM_2$).

Calculate the Height of Instrument (HI) for both setups and the final elevation of $BM_2$.

A surveyor takes a level reading on a rod held $2500 \text{ m}$ ($2.5 \text{ km}$) away. The rod reading is $3.450 \text{ m}$. The elevation of the instrument's line of sight ($HI$) is $150.000 \text{ m}$.

Calculate the combined effect of earth curvature and atmospheric refraction ($h_{cr}$), the corrected rod reading, and the true elevation of the point where the rod is held.

To determine the true difference in elevation between point A and point B on opposite sides of a wide river, reciprocal leveling is performed.

Setup 1 (Instrument near A):

Setup 2 (Instrument near B):

Calculate the true difference in elevation between A and B, eliminating errors due to curvature, refraction, and collimation.

A leveling rod is held $80 \text{ m}$ away from a dumpy level. Before taking a reading, the bubble is observed to be exactly centered. A reading of $2.345 \text{ m}$ is taken. The leveling screws are then adjusted, moving the bubble exactly 4 divisions off-center. A new reading of $2.385 \text{ m}$ is taken.

Calculate the sensitivity (angular value) of one division of the bubble tube in seconds of arc.

A two-peg test is performed to check the collimation error of a level. Two pegs, A and B, are set $60 \text{ m}$ apart.

Determine if the line of sight is inclined upward or downward and calculate the collimation error per meter.