The middle or mid latitude (Lm) between two places on the same side of the equator is half the sum of their latitudes. Mid latitude is labeled N or S to indicate whether it is north or south of the equator. The expression is occasionally used with reference to two places on opposite sides of the equator, when it is equal to half the difference between the two latitudes, and takes the name of the place farthest from the equator. This is misleading, as it lacks the significance usually associated with the expression. When the places are on opposite sides of the equator, two mid Latitudes are generally used, the average of each latitude and 0 degree's.
Longitude is the arc of a parallel or the angle at the pole between the prime meridian and the meridian of a point on the earth, measured eastward or westward from the prime meridian through 180. It is designated east (E) or west (W) to indicate the direction of measurement.
The difference of longitude (DLo) between two places is the shorter arc of the parallel or the smaller angle at the pole between the meridians of the two places. If both places are on the same side (east or west) of Greenwich, DLo is the numerical difference of the longitudes of the two places; if on opposite sides, DLo is the numerical sum unless this exceeds 180, when it is 360 minus the sum. The distance between two meridians at any parallel of latitude, expressed in distance units, usually nautical miles, is called departure (p, Dep.). It represents distance made good to the east or west as a craft proceeds from one point to another. Its numerical value between any two meridians decreases with increased latitude, while DLo is numerically the same at any latitude. Either DLo or p may be designated east (E) or west (W).
The basic equations for mid-latitude sailing are:
p = DLo (in minutes of arc) x cos Lm.
C = tan -1 (p/l where l = difference of latitude in minutes of arc.
Distance = l x sec C