The following derived values appertaining to the earth's spheroid are often referred to: Equatorial diameter of the earth = 7,926.6 miles Polar diameter of the earth = 7,899.6 miles Difference of diameters = 27.0 miles Circumference of equator of earth = 24,902.0 miles Meridian perimeter of earth — 24,859.8 miles 196,940.000 square miles Area of the surface = 510,071,000 square kilometers of the earth = 197 X 10' square miles (about) = 51 X square kilometers (about) = 259,880,000000 cubic miles = 1,083,200,000,000 cubic kilometers Volume of earth = 260 X cubic miles (about) = 108 X cubic kilometers (about) The following table gives the length of a degree of a meridian in different latitudes; the length of a degree in longitude measured along a parallel of latitude; and the areas of quadri laterals of the earth's surface of one degree ex tent in latitude and in longitude. The latitude in the first column of the table is that of the middle point of the corresponding meridional arc or quadrilateral.
• But the Newtonian theory was neither read ily accepted nor easily verified. In the early part of the 18th century, in fact, the theory was hotly opposed by the justly distinguished Cas sinian school of French astronomers, whose er roneous interpretation of a carefully measured arc of a meridian in France indicated that the earth is an oblong rather than an oblate spher oid. The question was permanently settled by the famous Lapland expedition sent out by the Academy of Sciences of Paris, in 1735, under the auspices of Maupertuis and Clairaut. They proved beyond doubt that the earth's surface is very closely that of an oblate spheroid, thus gflattening the poles and the Cassinis,g as Vol taire remarked at the time.
A vast amount of labor has since been de voted to the determination of the dimensions of the spheroid which best fits the earth's surface.
This is, indeed, the principal problem of the precise geodesy of to-day. The dimensions of the earth which have been provisionally very generally adopted are those of Gen. A. R. Clarke published in 1866. The theory of a spheroidal surface requires a knowledge of the lengths of the longer and the shorter axes of the generating ellipse, or equivalent data. Gen erally the half axes, or the equatorial and the polar radii, are given. The values of these are as follows: uatorialmi-axis =-- a, plar semi-axis a feet = miles = 6.378.259 metres. = 20.855,121 feet = 3,949.8 miles = 6.356,635 metres.
It should not he inferred from these figures that the semi-axes are known to the nearest foot or metre. The values given above are From the second column of this table it is seen that the length of a degree of a meridian is about seven-tenths of a mile greater at the poles of the earth than at the equator.
Third third approxima tion to the figure of the earth may be briefly referred to here. Imagine the mean sea-level, or the surface of the sea freed from the undu lations due to winds and to tides. This mean sea surface, which may be conceived to extend through the continents, is called the geoid. It does not coincide exactly with the earth's spheroid, but is a slightly wavy surface lying partly above and partly below the spheroidal surface, by small but as yet not definitely known amounts. The determination of. the geoid is now one of the most important problems of geophysics. Its solution will be accomplished by means of gravimetric surveys, or by meas uring the acceleration of gravity at a great number of points on the earth's surface. .