Lectures in Navigation

by Ernest Gallaudet Draper

Departure is the actual linear distance measured on a parallel of Latitude between two meridians. Difference of Latitude is reckoned in minutes because miles and minutes of Latitude are always the same. Departure, however, is only reckoned in miles, because while a mile is equal to 1´ of longitude on the equator, it is equal to more than 1´ as the latitude increases; the reason being, of course, that the meridians of Lo. converge toward the pole, and the distance between the same two meridians grows less and less as you leave the equator and go toward either pole. Example: TN, N´n´. 10 mi. departure on the equator = 10´ difference in Lo. 10 mi. departure in Lat. 55° equals something like 18´ difference in Lo.

The curved line which joins any two places on the earth´s surface, cutting all the meridians at the same angle, is called the Rhumb Line. The angle which this line makes with the meridian of Lo. intersecting any point in question is the Course, and the length of the line between any two places is called the distance between them. Example: T or T´.

Chart Projections

The earth is projected, so to speak, upon a chart in three different ways - the Mercator Projection, the Polyconic Projection and the Gnomonic Projection.

The Mercator Projection

You already know something about the Mercator Projection and a Mercator chart. As explained before, it is constructed on the theory that the earth is a cylinder instead of a sphere. The meridians of longitude, therefore, run parallel instead of converging, and the parallels of latitude are lengthened out to correspond to the widening out of the Lo. meridians. Just how this Mercator chart is constructed is explained in detail in the Arts. in Bowditch you were given to read last night. You do not have to actually construct such a chart, as the Government has for sale blank Mercator charts for every parallel of latitude in which they can be used. It is well to remember, however, that since a mile or minute of latitude has a different value in every latitude, there is an appearance of distortion in every Mercator chart which covers any large extent of surface. For instance, an island near the pole, will be represented as being much larger than one of the same size near the equator, due to the different scale used to preserve the accurate character of the projection.

The Polyconic Projection

The theory of the Polyconic Projection is based upon conceiving the earth´s surface as a series of cones, each one having the parallel as its base and its vertex in the point where a tangent to the earth at that latitude intersects the earth´s axis. The degrees of latitude and longitude on this chart are projected in their true length and the general distortion of the earth´s surface is less than in any other method of projection.

A straight line on the polyconic chart represents a near approach to a great circle, making a slightly different angle with each meridian of longitude as they converge toward the poles. The parallels of latitude are also shown as curved lines, this being apparent on all but large scale charts. The Polyconic Projection is especially adapted to surveying, but is also employed to some extent in charts of the U. S. Coast & Geodetic Survey.