This thesis describes the design, fabrication, and installation of a new control system for the Radcliffe twin 24/18-inch refracting telescope built by Grubb of Dublin in 1901. The specification includes a requirement for the telescope to set within a precision of one arcminute, and the ability to find objects under automatic control. Alteration to the original mechanical layout and dismantling of the axes was not permitted within the design remit, thereby preserving the possibility of future restoration to the original configuration. In order to set the historical context of the original Radcliffe drive, a review of telescope control systems from 1824 to 1994 is given. New evidence is presented that the first successful clock drive was probably German, closely followed by distinct French and English designs. The progression from early twentieth century electromechanical control, to the first attempts at incorporating a computer are also chronicled. The design and installation of the necessary mechanical subsystems to drive the telescope axles under computer control are described, which includes: a new solution to the precision mounting of a two-part primary encoder wheel across an otherwise inaccessible telescope axle; and a novel method of incorporating a sector drive into an automated system. The design philosophy of the control hardware which incorporates redundancy is also presented, together with the software routines necessary to control the hardware. Astronomical pointing tests with the Radcliffe telescope are described which demonstrate that the new control system exceeds the original specification, and the thesis then concludes with an analysis of possible improvements for future development.