In many applications, including descriptions, plats, and maps, the direction of a given line is expressed as a bearing or azimuth. Both bearings and azimuths refer to the relationship of the given line to a reference meridian, usually one of many interpretations of North. The most often-used North references are magnetic north, astronomic north, geodetic north, grid north, and assumed north. An important aspect of directional indicators is that their application be consistent with each other or with a map or description from which reference is being taken. Many maps will have an indication of magnetic declination as a part of the legend, so that users can correct for the local difference of magnetic north to the north being referenced by the map.
Bearings are expressed as an angular measurement with a given quadrant, such as North 36� 47' East. The angular portion will reference the acute (less than 90�) angle from the North or South meridian as measured to the East or West. In our example previously stated, it may be helpful to think of the line as being 36�47' east of north. It may also be helpful to know that North 36� 47' East describes the same line as a bearing of South 36� 47' West, but in the opposite direction (this is called a "back bearing"). Angles in the northeast and southwest quadrants are measured in a clockwise direction and angles in the southeast and northwest quadrants are measured in a counter-clockwise direction from either the north or south meridian, using whichever will yield and angular measurement of 90� or less. It should also be noted that North 90� East is synonymous with the bearing expressed as South 90� East, both being 90� east of the north/south meridian.
Azimuths are expressed as an angular measurement from a meridian (usually north) and measured clockwise. The angular measurement will range through a full circle, most commonly expressed as 0�-360� measured clockwise, although it may be expressed in other units of angular measurement, such as radians or grads. Surveyors will often convert directions expressed in bearings to azimuths, because the use of azimuths in calculations lends itself to a polar � rectangular conversion that is algebraically signed and easily translated to Cartesian coordinates.
Whether directional lines are expressed as bearings or azimuths, it is important to note that the expressed angular value of the bearing or azimuth is most useful when the relationship of the expressed value has a known reference on the ground. For this reason, Colorado (and many other states) require that a be shown on Land Survey Plats and many other types of survey plats. A basis of bearings usually states, either by text or graphically, the particular line upon which the bearings contained in the plat or legal description are based, and the bearing that the particular line is assigned. An example of this would be:
Considering the north line the southwest quarter of Section 19, Township 1 North, Range 70 West of the Sixth Principal Meridian to bear North 0� 15' West, with all bearings contained herein relative thereto . . .
This indicates to the party retracing the description that a specific line was assigned a specific direction, and that all other directions are expressed using the same bearing base.