Note 3 — Chapter III

The solidity of the earth is easily calculated by the measure of a meridional degree; but the result will be different according to the measurement assumed, as the length of a degree differs in different latitudes. "Notwithstanding all the admeasurements that have hitherto been made, it has never been demonstrated, in a satisfactory manner, that the earth is strictly a spheroid; indeed, from observations made in different parts of the earth, it appears that its figure is by no means that of a regular spheroid, nor that of any other known regular mathematical figure; and the only certain conclusions that can be drawn from the works of the several gentlemen employed to measure the earth is, that the earth is something more flat at the poles than at the equator." [Keith on globes p. 56. New-York, 1811.]

According to Mott's translation of Newton's Principia, book 3, page 243, the equatorial diameter of the earth is 7964 English miles, and the polar diameter 7929, for as 230:229::7964:7929 miles, the polar axis.

Cassini, who adopted Picard's measure of a degree, makes the diameter of the earth 7967 statute miles; others have estimated it at 7917, and some at 7910 miles. But the estimate which is now esteemed most correct, I believe, is, that the equatorial diameter is 7977 English miles, and the polar diameter 7940. From this we may ascertain the solid contents of the earth. The axis of the earth then assumed to be 7940 and 7977 miles respectively, the area of the generating eclipse is (7940 × 7977 × 0,7854=) 49745178,252: and its area multiplied by two thirds of the longer axis, gives the solidity equal to (49745178,252 × 2/3 × 7977=) 264544857944,136 cubic miles.