On this projection there is a constant distance between the meridians, whereas on the earth they actually converge toward the poles. The distance between the parallels increases in passing toward the poles, approximately in the proportion of the secant of the latitude. For each small portion of the map the relative proportions are maintained as on the earth.
Some characteristics of the mercator projection are these: The meridians and parallels are all straight lines and perpendicular to each other; there is no convergence of the meridians; the minute of longitude is a constant distance on the map; the minute of latitude increases in length from the equator toward the poles but locally retains its true proportion to the minute of longitude; areas and distances increase in scale with the latitude so that a given scale is strictly correct only for one latitude; great circles and consequently lines of sight are curved lines excepting the meridians and the equator; rhumb lines or lines having a constant angle with the meridians are straight, and for the same angle are parallel in all parts of the chart. These qualities are all rigid and the projection can therefore be used for all areas, small or large, up to the extent of the earth's surface, except that it cannot be extended to the poles, as there the length of the minute of latitude would become infinite.
An interesting fact regarding a rhumb line oblique to the meridians is that it is a spiral continually approaching but never reaching the pole; this spiral makes an infinite number of revolutions around the pole, and yet it has a finite length for the reason that the length of each revolution diminishes as the number of revolutions increases.
FIG. 22. MERCATOR PROJECTION OF NORTH PACIFIC OCEAN, SHOWING GREAT CIRCLE ROUTES YOKOHAMA TO PUGET SOUND, AND YOKOHAMA TO HONOLULU AND THENCE TO SAN FRANCISCO.
The mercator projection has been extensively used for nautical charts, for which it presents important mechanical advantages, in that adjacent charts can be joined on all their edges while still oriented with the meridian; all charts are similar; the border may be conveniently subdivided, giving a longitude scale applicable to any part of the chart, but a latitude scale that may be used in the same latitude only; courses are laid down as straight lines and can be transferred with parallel rulers from one part of the chart to another without error. On a mercator chart an island in latitude 60° would appear four times as large as an island of the same actual area at the equator, but this distortion of areas, while it gives erroneous impressions on charts of great extent in latitude, does not seriously affect the use of the chart for nautical purposes. Areas may also be correctly measured on a mercator map by taking each projection quadrilateral separately, subdividing it if necessary, and using the published tables of areas of quadrilaterals in different latitudes. Although distance scales vary with the latitude, distances can be taken from this chart with fair correctness by the use of the latitude border scale for the middle latitude, subdividing the total distance if there is much range of latitude. The inability to take off the great circle or shortest course directly from the mercator chart is from a navigational point of view a defect, but the most convenient solution for this appears to be the supplementary use of a gnomonic chart as will be described. The fact that lines of sight are not straight lines on this projection is another defect, as by the plotting of bearings and angles on approaching the land the positions of vessels are located on the chart; fortunately, however, the error due to this cause usually falls within the other uncertainties involved in locating a ship; if need be it would be practicable to allow for this curvature. In the polar regions, however, the faults of the mercator projection become so much exaggerated that it is not used for navigational purposes, but because of the absence of commercial navigation there this is a minor matter in the general question of chart projection. For the plotting of original surveys the mercator projection is not suited and is not used, for the reasons above mentioned.
FIG. 23. POLYCONIC PROJECTION OF PORTION OF NORTH PACIFIC OCEAN.
Tables of "meridional parts" are published which give the distance in terms of minutes of longitude from the equator to the various parallels; with these tables a mercator projection may readily be constructed.
Airy proposed a graphical method of sweeping the arc of a great circle on to a mercator chart, and tables are published for this purpose. The method is only approximate and is limited in application, and the supplementary use of a gnomonic chart would appear to be preferable.