Figure and Size of the Earth

As a first approximation the earth may be considered as a sphere, but, according to accurate observations, its figure is more closely represented by an ellipse of rotation—that is, an oblate spheroid, the shorter axis being the axis of rotation. The figure of the earth has been defined by various empirical equations, the constants of which are based on observations and are subject to modification as the number of observations increases and their accuracy is improved. The geometrical figures defined by these equations cannot exactly represent the shape of the earth because of the asymmetrical distribution of the water and land masses.

To define the position of a point on the earth's surface, a system of coordinates is needed, and as such the terms latitude, longitude, and elevation or depth are used. The first two are expressed by angular coordinates and the third is expressed by the vertical distance, stated in suitable linear units, above or below a reference level that is generally closely related to mean sea level. The latitude of any point is the angle between the local plumb line and the equatorial plane. Because the earth can be considered as having the form of a spheroid, and as the plumb line, for all practical purposes, is perpendicular to the surface of the spheroid, any plane parallel to the Equator cuts the surface of the spheroid in a circle, and all points on this circle have the same latitude. These circles are called parallels of latitude. The latitude is measured in degrees, minutes, and seconds north and south of the Equator. The linear distance corresponding to a difference of one degree of latitude would be the same everywhere upon the surface of a sphere, but on the surface of the earth the distance represented by a unit of latitude increases by about 1 per cent between the Equator and the Poles. At the Equator, 1 degree of latitude is equivalent to 110,567.2 m, and at the Poles it is 111,699.3 m. In table 1 are given the percentages of the earth's surface between different parallels of latitude.

The line in which the earth's surface is intersected by a plane normal to the equatorial plane and passing through the axis of rotation is known as a meridian. The angle between two meridian planes through two

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points A and B on the surface of the earth is the difference in longitude of the two points. In practice, the longitude is the angular distance measured in degrees, minutes, and seconds east or west from a standard meridian plane, generally that of the Royal Observatory at Greenwich, England. Thus, the longitude is measured from 0° to 180° east and west of Greenwich. On the surface of the earth the linear distance equivalent to unit difference in longitude is nearly proportional to the cosine of the latitude.

The distance between points on the earth's surface and the area represented by a given zone cannot be correctly represented unless the size of the earth is known. The values for the equatorial and polar radii are given in table 2, with other data concerning the size of the earth that can be computed from these values. The values for the equatorial and polar radii are those for sea level. The land masses are elevations upon the geometrical figure of the earth, and the sea bottoms represent depressions.

Measurements of depressions below sea level, to be strictly comparable, should be referred to the ideal sea level; that is, to a sea surface which is everywhere normal to the plumb line. In the open ocean the deviations from the ideal sea level rarely exceed 1 or 2 m. The errors that are introduced by referring soundings to the actual sea surface are insignificant in deep water, where the errors of measurement are many times greater. In coastal areas where shoal depths represent a hazard to navigation and where soundings can be made with great accuracy, the

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effect of tides is eliminated by referring all soundings in any locality to a single reference plane. Mean sea level is generally used as the plane of reference for elevations on land, and in the Baltic Sea it is employed as the reference level for depths. More commonly, some other plane of reference, indicated on the chart, is used as the reference level for depths; for example:

1. Mean low water. United States (Atlantic Coast), Argentina, Norway, Sweden.

2. Mean lower low water. United States (Pacific Coast).

3. Mean low water springs. Great Britain, Italy, Germany, Denmark, Brazil, Chile.

4. Mean monthly lowest low water springs. Netherlands.

5. Lowest low water springs. Brazil, Portugal.

6. Indian spring low water. India, Argentina, Japan.

7. Mean semi-annual lowest low water. Netherlands East Indies.

8. Lowest low water. France, Spain, Norway, Greece.

9. International low water. Argentina.

The mean of the heights of low-water spring tides is known as the low water springs. International low water is 50 per cent lower, reckoned from mean sea level, than low water springs. Indian spring low water depends upon component tides found by harmonic analysis. Other terms are defined elsewhere (p. 562).

The topographic features of the earth's surface can be shown in their proper relationships only upon globes that closely approximate the actual shape of the earth, but for practical purposes projections that can be printed on flat sheets must be used. It is possible to project a small portion of the earth's surface on a flat plane without appreciable distortion of the relative positions. However, for the oceans or for the surface of the earth as a whole, most types of map projections give a grossly exaggerated representation of the shape and size of certain portions of the earth's surface. The most familiar type of projection is that developed by Mercator, which represents the meridians as straight, parallel lines. Although it is satisfactory for small areas and for the lower latitudes, the size and shape of features in high latitudes are greatly distorted because the linear scale is inversely proportional to the cosine of the latitude. In the presentation of oceanographic materials, this exaggeration is most undesirable and, consequently, projections should be used on which the true shape and size of the earth's features can be more closely approximated.

Numerous types of projections have been developed by cartographers. In some instances, these are geometrical projections of the surface of the geoid on a plane surface that can be flattened out, while in others the essential coordinates, the parallels of latitude, and the meridians have been constructed on certain mathematical principles. Maps and charts

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are used for a variety of purposes which require different properties in the projections. Such requirements, incompatible in any single projection, are that the map shall show the features of the earth's surface without distortion of distances, directions, shapes, or areas. The Mercator projection is used for navigational charts because it possesses certain properties that are desirable in navigation. The technique of map making and the properties of the various projections are discussed by Raisz (1938).

In order to show the oceans with the least possible distortion of size and shape, the world maps used in this volume are based on an interrupted projection developed by J. P. Goode. Comparison with a globe will show that the major outlines of the oceans are not distorted and that the margins of the oceans are clearly represented. This projection has the additional advantage of being “equal-area”; that is, that areas scaled from the map are proportional to their true areas on the surface of the earth. To show the relationships between the various parts of the oceans in high latitudes, polar projections are used, and for smaller areas Mercator and other types of projections have been employed.