horizontal angular orientation so the cross-hairs align with the desired sighting point. Both angles are read either from exposed or internal scales and recorded. The next object is then sighted and recorded without moving the position of the instrument and tripod. The earliest angular readouts were from open vernier scales directly visible to the eye. Gradually these scales were enclosed for physical protection, and finally became an indirect optical readout, with convoluted light paths to bring them to a convenient place on the instrument for viewing. The modern digital theodolites have electronic displays. Errors in measurement Index error The angles in the vertical axis should read 90° (100 grad) when the sight axis is horizontal, or 270° (300 grad) when the instrument is transited. Half of the difference between the two positions is called the index error. This can only be checked on transit instruments. Horizontal axis error The horizontal and vertical axes of a theodolite must be perpendicular; if not then a horizontal axis error exists. This can be tested by aligning the tubular spirit bubble parallel to a line between two footscrews and setting the bubble central. A horizontal axis error is present if the bubble runs off central when the tubular spirit bubble is reversed (turned through 180°). To adjust, the operator removes half the amount the bubble has run off using the adjusting screw, then re-level, test and refine the adjustment. Collimation error The optical axis of the telescope must also be perpendicular to the horizontal axis; if not, then a collimation error exists. Index error, horizontal-axis error (trunnion-axis error) and collimation error are regularly determined by calibration and are removed by mechanical adjustment. Their existence is taken into account in the choice of measurement procedure in order to eliminate their effect on the measurement results of the theodolite. History Historical background Prior to the theodolite, instruments such as the groma, geometric square and the dioptra, and various other graduated circles (see circumferentor) and semicircles (see graphometer) were used to obtain either vertical or horizontal angle measurements. Over time their functions were combined into a single instrument that could measure both angles simultaneously. The first occurrence of the word "theodolite" is found in the surveying textbook A geometric practice named Pantometria (1571) by Leonard Digges. The origin of the word is unknown. The first part of the New Latin theo-delitus might stem from the Greek ,