It is of very great importance in many ways that astronomers and surveyors know as exactly as possible the dimensions of the spheroid. Many men have made estimates based upon astronomical facts, pendulum experiments and careful surveys, as to the equatorial and polar diameters of the earth. Perhaps the most widely used is the one made by A. R. Clarke, for many years at the head of the English Ordnance Survey, known as the Clarke Spheroid of 1866.

The arc method of deducing the figure of the earth may be illustrated by supposing that a skilled workman to whom is given several stiff wires, each representing a geodetic arc, either of a parallel or a meridian, each bent to the radius deduced from the astronomic observations of that arc, is told in what latitude each is located on the geoid and then requested to construct the ellipsoid of revolution which will conform most closely to the bent wires.

Similarly, the area method is illustrated by supposing that the workman is given a piece of sheet metal cut to the outline of the continuous triangulation which is supplied with necessary astronomic observations, and accurately molded to fix the curvature of the geoid, and that the workman is then requested to construct the ellipsoid of revolution which will conform most accurately to the bent sheet.

The sheet is much more, however, than this rigid system of bent lines, for each arc usually treated as a line is really a belt of considerable width which is now utilized fully. It is obvious that the workman would succeed much better in constructing accurately the required ellipsoid of revolution from the one bent sheet than from the several bent wires. When this proposition is examined analytically it will be seen to be true to a much greater extent than appears from this crude illustration.

It is of very great importance in many ways that astronomers and surveyors know as exactly as possible the dimensions of the spheroid. Many men have made estimates based upon astronomical facts, pendulum experiments and careful surveys, as to the equatorial and polar diameters of the earth. Perhaps the most widely used is the one made by A. R. Clarke, for many years at the head of the English Ordnance Survey, known as the Clarke Spheroid of 1866.

Centripetal Force

It is of very great importance in many ways that astronomers and surveyors know as exactly as possible the dimensions of the spheroid. Many men have made estimates based upon astronomical facts, pendulum experiments and careful surveys, as to the equatorial and polar diameters of the earth. Perhaps the most widely used is the one made by A. R. Clarke, for many years at the head of the English Ordnance Survey, known as the Clarke Spheroid of 1866.

Gravitation

• Weight on the Moon
• Orbit of the Earth
• Circumnavigation
• Cause of Oblateness

The shadow of the earth as seen in the lunar eclipse is always circular. But a dollar, a lemon, an egg, or a cylinder may be so placed as always to cast a circular shadow. When in addition to this statement it is shown that the earth presents many different sides toward the sun during different eclipses of the moon and the shadow is always circular, we have a proof positive, for nothing but a sphere casts a circular shadow when in many different positions.