With substantial development in the field of surveying instruments, and the emergence of various and different generations of Theodolites which are used to measure horizontal directions and angles, it is urgent to develop the methods of assessing and determining the accuracy of measurements using these instruments. This is achieved by taking into consideration all the internal and external factors affecting the measurement system. The research team studied the famous error equation (Colcord equation) of horizontal directions and tested it using a several equipments of theodolites and targets on a 250 m long, 5-sections base-line. The team concluded that there was a need to develop Colcord equation by taking into consideration the factors involved mainly by Colcord equation (positioning error, initial sitting error, reading error) in addition to the type of target and the distance of the line of-sight. The proposed equation was tested in practice, which proved that expected errors of measurements were close to their actual values. This could be adopted to estimate the root mean square error (r. m. s. e.) of measurements of horizontal directions.