A level is set up midway between two wood hubs that are about 300 ft apart. The rod reading on hub A is 9.09 ft, and the reading on hub B is 5.65 ft.

The level is then moved to a position along the side of hub B, about 6 feet away from it. Readings are taken from the new setup with the reading on hub A being 7.11 ft and on hub B being 3.70 ft.

a. What is the correct difference in elevation between hubs A and B?

The correct difference in elevation between hubs A and B is calculated using the first set of rod readings when the level was set up midway between them, resulting in hAB = 9.09 ft - 5.65 ft = 3.44 ft.

Explanation:

To calculate the correct difference in elevation between hubs A and B, we first note the initial rod readings taken from both points when the level is set up midway between them. We have a backsight (BS) reading on hub A of 9.09 ft and a foresight (FS) reading on hub B of 5.65 ft. When the instrument is moved next to hub B, new readings are taken: the BS on hub A is now 7.11 ft and the FS on hub B is 3.70 ft.

Using the principle that the height difference hAB = BS (back sight) - FS (fore sight), we use the first set of readings to calculate the height difference to avoid any potential errors introduced by not being exactly midway between the two points in the second setup. So, the correct elevation difference is calculated as hAB = BS at A - FS at B, which is 9.09 ft - 5.65 ft = 3.44 ft. Therefore, the hubs A and B have a difference in elevation of 3.44 feet.