traverse table
A table by means of which the difference of latitude and departure corresponding to any given course and distance may be found by inspection. It contains the lengths of the two sides of a right-angled triangle, usually for every quarter of a degree of angle, and for lengths of the hypotenuse, from 1 to 100.
traverse table: lookup tool for converting bearings into coordinates
A traverse table is a printed or digital reference that converts a surveyed course (bearing and distance) directly into its component coordinates: latitude difference and departure (eastward or westward displacement). Instead of calculating with trigonometry on site, a surveyor looks up the bearing and distance and reads off the horizontal and vertical components, which are then summed to plot the survey path.
The table works because any course and distance form the hypotenuse of a right triangle. The two legs are latitude (north-south) and departure (east-west). For a given bearing angle and distance, these two sides have fixed proportions determined by sine and cosine. Traditional printed tables therefore list distances from 1 to 100 units in rows, and bearings typically in increments of 15 minutes or quarter degrees in columns, with the corresponding latitude and departure values pre-calculated and printed at each intersection.
A typical traverse table has separate sections for each quadrant (NE, SE, SW, NW) because latitude and departure change sign depending on direction. A surveyor measures a course of, say, bearing N 37° 30' E for a distance of 47.3 units, then locates the row for 47 units and the column for 37° 30', reads the latitude and departure values (interpolating if needed for the 0.3 unit fraction), and applies appropriate signs based on the quadrant. The values are written into a traverse record and summed vertically and horizontally to check closure and calculate final coordinates.
Modern surveying software has replaced printed traverse tables for most fieldwork, but the principle remains embedded in coordinate conversion routines. Older surveys, particularly those predating electronic calculators, relied entirely on printed tables, making table quality and accuracy critical to the final survey product. Errors in table values or misreading could compound across a long traverse of many courses.
The name reflects the tool's use in traverse surveying, a method in which a surveyor measures a series of connected courses around a perimeter or along a route, recording bearing and distance for each leg. The table enabled rapid field computation without a computer, theodolite, or mathematical tables, making it indispensable for practical surveying work throughout the 19th and 20th centuries.