Figure7-21.—Area from double meridian distances.For convenience, it is customary to use doublemeridian distance (DMD) rather than meridiandistance in calculations. When the meridian distance ofthe initial traverse line in a closed traverse equals onehalf of the departure of the line, the DMD of this lineequals its departure. Again, from the rule for meridiandistance of the next line, the DMD of that line equals theDMD of the preceding line, plus the departure of thepreceding line, plus the departure of the line itself.It can be shown geometrically that the areacontained within a straight-sided closed traverse equalsthe sum of the areas obtained by multiplying themeridian distance of each traverse line by the latitude ofthat line. Again the result is the algebraic sum. If youmultiply a positive meridian distance (when thereference meridian runs through the most westerlystation, all meridian distances are positive) by a plus ornorth latitude, you get a plus result that you add. If youmultiply a positive meridian distance by a minus orsouth latitude, however, you get a minus result that yousubtract.Therefore, if you multiply for each traverse line thedouble meridian distance by latitude instead of meridiandistance by latitude, the sum of the results will equaltwice the area, or the double area. To get the area, yousimply divide the double area by 2.Figure 7-21 shows entries for the computations ofthe DMD of the area of the traverse we have beenworking on. Because AB is the initial traverse line, theDMD of AB equals the departure. The DMD of BCequals the DMD of AB (125.66), plus the departure ofAB (125.66), plus the departure of BC (590.65), or841.97 feet. The DMD of CD equals the DMD of BC(841.97), plus the departure of BC (590.65), plus thedeparture of CD (which is minus 192.69, and thereforeis subtracted), or 1239.93 feet. The DMD of DA equalsthe DMD of CD (1239.93), plus the departure of CD(–192.69), plus the departure of DA (–523.62), or 523.62feet. Note that the DMD of this last traverse line equalsthe departure of the line, but with an opposite sign. Thisfact serves as a check on the computations.The double area for AB equals the DMD times thelatitude or125.66 x 255.96 = 32,163 .93square feet.The double area for BC equals 841.97 (the DMD) timesminus 153.53 (the latitude), or minus 129,267.65square feet. The double area of CD is1,239.93 x (-694.07) = –860,598.21 square feet.Figure 7-22.—Parallel distances.7-16