The measurement of the relative orientations of mirror segments is the basis for the active control of a segmented mirror. We describe a system of capacitive displacement sensors which will be used to make these measurements in the University of California Ten Meter Telescope. The global sensing system design and the control algorithm are summarized. The detailed mechanical and electronic designs of a sensor are described along with the performance of prototype sensors under a variety of tests. The relationship between the sensor characteristics and the image quality of the segmented mirror is described. The sensor output is 1 millivolt per nanometer of displacement. This sensitivity and the small noise, drift, and thermal sensitivity are adequate to allow essentially continuous figure control to the precision required for optical and infrared astronomy.