Answers:
Each survey measurement takes new data, and relates it to the data you already have. The calculation is called (confusingly) a 'reduction'. So the column for 'Reduced Height' can contain reducing or increasing figures.
You have two 'planes' of measurement. One is the height of the telescope (level, theodolite, etc) you are looking through.
You find out what this height is, by making a 'backsight' measurement. Your 'runner', 'staffer', or etc holds the pole or staff against a 'benchmark' or known height. You take a reading with the telescope perfectly level. This goes in the 'backsight' column.
Every time you check 'back' to a known height, this is called a 'backsight'.
The backsight reading is added to the known (or 'benchmark')height, to find out what height the telescope is at. The result of this calculation goes in the HPC column (Height of Present Collimation).
When the instrument is moved to a new position, a new backsight is needed to find out the new 'collimation' plane.
The other 'plane' you are working with is 'topographical'. This is the actual shape of the terrain that is being surveyed. You measure it by comparing its height in different places, with the height of the telescope. (If you know the height of the telescope, you can calculate the height of any point you measure from the telescope.)
A 'foresight' is any reading taken with the staff at an unknown height. The reading goes in the 'foresight' column.
If this reading is subtracted from the HPC, you can find out the height of the point where the staff was. This calculation is called a 'reduction', and it is written in the 'Reduced Height' column.
(This calculation might be an addition, because the staff can be used (upside-down) to measure the height of something ABOVE the telescope, like the underneath of a bridge, a cave roof, or an overhanging rock or building.)
There is usually a column for 'Comments'. This should be used to list information about the points where the staff has been positioned, so that the survey can be accurately repeated to check or add information.
If you have a pre-filled sheet of theoretical information, then you should be able to work out one column's entry from the other entries on the same line.
If you are supposed to have done exercises with your classmates, and the information relates to these exercises, then it will be very difficult to invent information that will seem genuine (naughty, naughty!).
You have left it a bit late.
Sorry no idea but good luck
YOUR GONNA FAIL!! NA-NA-NA-NA-NAAA-NAAAAAAAAA!...
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