66. DECLINATION DIAGRAM
Declination is the angular difference between any two norths. If you have a map and a compass, the one of most interest to you will be between magnetic and grid north. The declination diagram (Figure 68) shows the angular relationship, represented by prongs, among grid, magnetic, and true norths. While the relative positions of the prongs are correct, they are seldom plotted to scale. Do not use the diagram to measure a numerical value. This value will be written in the map margin (in both degrees and mils) beside the diagram.
Figure 68. Declination diagrams.
a. Location. A declination diagram is a part of the information in the lower margin on most larger maps. On mediumscale maps, the declination information is shown by a note in the map margin.
b. GridMagnetic Angle. The GM angle value is the angular size that exists between grid north and magnetic north. It is an arc, indicated by a dashed line, that connects the gridnorth and magneticnorth prongs. This value is expressed to the nearest 1/2 degree, with mil equivalents shown to the nearest 10 mils. The GM angle is important to the map reader/land navigator because azimuths translated between map and ground will be in error by the size of the declination angle if not adjusted for it.
c. Grid Convergence. An arc indicated by a dashed line connects the prongs for true north and grid north. The value of the angle for the center of the sheet is given to the nearest full minute with its equivalent to the nearest mil. These data are shown in the form of a gridconvergence note.
d. Conversion. There is an angular difference between the grid north and the magnetic north. Since the location of magnetic north does not correspond exactly with the gridnorth lines on the maps, a conversion from magnetic to grid or vice versa is needed.
(1) With Notes. Simply refer to the conversion notes that appear in conjunction with the diagram explaining the use of the GM angle (Figure 68). One note provides instructions for converting magnetic azimuth to grid azimuth; the other, for converting grid azimuth to magnetic azimuth. The conversion (add or subtract) is governed by the direction of the magneticnorth prong relative to that of the northgrid prong.
(2) Without Notes. In some cases, there are no declination conversion notes on the margin of the map; it is necessary to convert from one type of declination to another. A magnetic compass gives a magnetic azimuth; but in order to plot this line on a gridded map, the magnetic azimuth value must be changed to grid azimuth. The declination diagram is used for these conversions. A rule to remember when solving such problems is this: No matter where the azimuth line points, the angle to it is always measured clockwise from the reference direction (base line). With this in mind, the problem is solved by the following steps:
(a) Draw a vertical or gridnorth line (prong). Always align this line with the vertical lines on a map (Figure 69).
Figure 69. Declination diagram with arbitrary line.
(b) From the base of the gridnorth line (prong), draw an arbitrary line (or any azimuth line) at a roughly right angle to north, regardless of the actual value of the azimuth in degrees (Figure 69).
(c) Examine the declination diagram on the map and determine the direction of the magnetic north (rightleft or eastwest) relative to that of the gridnorth prong. Draw a magnetic prong from the apex of the gridnorth line in the desired direction (Figure 69).
(d) Determine the value of the GM angle. Draw an arc from the grid prong to the magnetic prong and place the value of the GM angle (Figure 69).
(e) Complete the diagram by drawing an arc from each reference line to the arbitrary line. A glance at the completed diagram shows whether the given azimuth or the desired azimuth is greater, and thus whether the known difference between the two must be added or subtracted.
(f) The inclusion of the truenorth prong in relationship to the conversion is of little importance.
e. Applications. Remember, there are no negative azimuths on the azimuth circle. Since 0 degree is the same as 360 degrees, then 2 degrees is the same as 362 degrees. This is because 2 degrees and 362 degrees are located at the same point on the azimuth circle. The grid azimuth can now be converted into a magnetic azimuth because the grid azimuth is now larger than the GM angle.
(1) When working with a map having an east GM angle:
(a) To plot a magnetic azimuth on a map, first change it to a grid azimuth (Figure 610).
Figure 610. Converting to grid azimuth.
(b) To use a magnetic azimuth in the field with a compass, first change the grid azimuth plotted on a map to a magnetic azimuth (Figure 611).
Figure 611. Converting to magnetic azimuth.
(c) Convert a grid azimuth to a magnetic azimuth when the GM angle is greater than a grid azimuth (Figure 612).
Figure 612. Converting to a magnetic azimuth when the GM angle is greater.
(2) When working with a map having a west GM angle:
(a) To plot a magnetic azimuth on a map, first convert it to a grid azimuth (Figure 613).
Figure 613. Converting to a grid azimuth on a map.
(b) To use a magnetic azimuth in the field with a compass, change the grid azimuth plotted on a map to a magnetic azimuth (Figure 614).
Figure 614. Converting to a magnetic azimuth on a map.
(c) Convert a magnetic azimuth when the GM angle is greater than the magnetic azimuth (Figure 615).
Figure 615. Converting to a grid azimuth when the GM angle is greater.
(3) The GM angle diagram should be constructed and used each time the conversion of azimuth is required. Such procedure is important when working with a map for the first time. It also may be convenient to construct a GM angle conversion table on the margin of the map.
NOTE: 
When converting azimuths, exercise extreme care when adding and subtracting the GM angle. A simple mistake of 1°
could be significant in the field. 
