What feature of theodolites or transits allows for repeated measurements to improve accuracy?

The feature that allows for repeated measurements to improve accuracy is independent motion clamps. These clamps enable the surveyor to lock the telescope in position while allowing the instrument's base to be repositioned independently. This capability ensures that after taking an initial measurement, the surveyor can make further adjustments without losing the original sighting. As a result, surveyors can take multiple measurements from different positions or angles, leading to more reliable results through averaging and reducing potential errors in the data collection process.

While electronic distance measurement, vertical angle measurement, and automatic leveling systems are valuable aspects of modern surveying equipment, they do not specifically contribute to the practice of repeating measurements to enhance overall accuracy in the same manner as independent motion clamps do. Electronic distance measurement provides precise distance data; vertical angle measurement assists in determining height differences, and automatic leveling systems ensure the instrument is correctly aligned. However, it is the independent motion clamps that directly facilitate the ability to perform repeated measurements effectively.