GREAT CIRCLE - is a circle formed on the surface of the earth by the intersection of a plane passing through the center of the earth,dividing the earth into two equal parts. A PARALLEL - is a small circle on the earth's surface whose plane of intersection is parallel to the plane of the equator. MERIDIAN - is a great circle formed by a plane that contains the earth's axis and its poles. One half of a meridian extending from north to south on the same side as the observer is called the upper branch,the side is called the lower branch. The location of any point on the earth may be defined in a system of terrestrial coordinates. The earth's surface is laid out in a grid of parallels of latitude (usually called "parallels") and meridians of longitude.
LATITUDE - is measured north or south from the equator the latitude of a point may be the angular distance measured from the center of the earth or as an arc on the surface. Latitude is normally measured in degrees, minutes, and seconds, or in degrees, minutes, and decimal fractions of a minute; "north" or "south" is part of the description and should be included.
LONGITUDE - is measured using meridians, but a meridian must be selected as the starting point.
DEGREE LENGTH - The length of a degree of latitude (measured along a meridian) is everywhere the same on a sphere, from the equator to the poles. On the earth, for navigational purposes, it is equal to 60 nautical miles, and 1 minute of latitude is equal to 1 nautical mile. The length of a degree of longitude (measured along a parallel decreases from 60 nautical miles at the equator to 52.10 nautical miles at latitude 30° north or south, and to 30.13 nautical miles at latitude 60°; it is zero at latitude 90°, the north and south poles. The linear distance between two meridians at any given parallel of latitude is termed DEPARTURE - it is normally expressed in nautical miles.
In some problems of navigation it is necessary to know the difference of latitude (l), or the difference of longitude (DLo) between two points.
In determining the difference of latitude, the two points may both be on the same side of the equator, "same name" (that is, both are north latitude, or both are south latitude); or they may be on opposite sides of the equator, and of "contrary name" (one north latitude, one south). The difference of latitude (l) is always measured as though the two points were both on the same meridian, with one point due north or south of the other, regardless of the direction between them. The total difference of latitude between them is obtained by adding the two distances from the equator. The rule for latitudes of contrary name, add. for latitudes of same name, subtract.
The difference of longitude (DLo) is always measured as though both points were on the same parallel, or on the equator. Both points may be on the same side of the prime meridian and of the same name. They can also be on opposite sides of the prime meridian and called contrary name. I'll try and show this when I get to the sailings. Some navigation problems are solved by means of latitude and departure (latitude, here, is the difference of latitude already discussed). Departure is the difference in longitude, but expressed in nautical miles rather than degrees and minutes of arc; it is DLo multiplied by the cosine of the latitude. I will show this later in some examples which should make clear.
MID LATITUDES -For some navigational calculations, the mid-latitude (Lm) is needed. To be quite precise, this is the latitude at which the arc length of the parallel between the meridians of the two points concerned is exactly equal to the departure when proceeding from one point to the other. As this is difficult to calculate, the mean latitude is normally used; this gives results for practical navigational purposes. When both points are on the same side of the equator, this is the arithmetical mean of the two latitudes.
