What is used to measure the variation in height between two points?

The correct choice is the leveling rod, which is a tool specifically designed for measuring the height differences between two points. It is used in conjunction with a leveling instrument, such as a transit or a laser level, to determine elevations accurately.

A leveling rod typically has graduated markings that allow for precise readings when the instrument is aimed at it. When used in surveying, the leveling rod can help establish grade changes and is essential for projects requiring careful elevation controls, such as construction and drainage work.

While a laser level is indeed a tool utilized for transferring horizontal or vertical points across distances, it does not directly measure the height difference itself without the aid of a rod. A measuring tape is primarily used for linear distance measurements and is not suited for accurately determining changes in elevation. Lastly, a surveying compass is used primarily for determining direction rather than measuring height differences between points.

Thus, the leveling rod is the most appropriate instrument among the options for measuring variations in height.