Correction per chain length of 100 links along a slope of a is:

Introduction:
When conducting surveying work, it is important to accurately measure distances and slopes. One common tool used by surveyors is a chain, which consists of a series of links. The correction per chain length refers to the adjustment needed to account for the slope of the terrain being surveyed. In this case, we are given a slope of "a" and need to calculate the correction per chain length.

Calculation:
To calculate the correction per chain length, we can use trigonometry. The correction is equal to the difference in elevation between the starting and ending points of the chain multiplied by the slope ratio.

1. Determine the slope ratio:
- The slope ratio is the vertical distance divided by the horizontal distance.
- It is given by the formula: Slope ratio = a / 100

2. Measure the elevation difference:
- Determine the difference in elevation between the starting and ending points of the chain.
- This can be done using a leveling instrument or other surveying techniques.

3. Calculate the correction per chain length:
- Multiply the slope ratio by the elevation difference to obtain the correction.
- Correction per chain length = Slope ratio x Elevation difference

Example:
Let's consider an example to demonstrate the calculation of the correction per chain length.

Suppose the slope ratio (a / 100) is 0.05 and the elevation difference between the starting and ending points is 10 meters.

Using the formula, we can calculate the correction per chain length:

Correction per chain length = 0.05 x 10 = 0.5 meters

Therefore, the correction per chain length along a slope of "a" is 0.5 meters.

Conclusion:
In surveying, the correction per chain length is an important factor to consider when measuring distances along a slope. By calculating the correction using trigonometry and the given slope ratio and elevation difference, surveyors can ensure accurate measurements and precise mapping of the terrain.