43(5 LECTURE XLVI. 



since its internal parts must necessarily be denser than those parts which 

 are nearer the surface. If indeed the earth consisted of water or ice, 

 equally compressible with common water or ice, and following the same 

 laws of compression with elastic fluids, its density would be several thou- 

 sand times greater at the centre than at the surface ; and even steel would 

 be compressed into one fourth of its bulk, and stone into one eighth, if it 

 were continued to the earth's centre ; so that there can be no doubt but 

 that the central parts of the earth must be much more dense than the super- 

 ficial. Whatever this difference may be, it has been demonstrated by 

 Clairaut,* that the fractions expressing the ellipticity and the apparent 

 diminution of gravity at the equator must always make together -^fj.-, and 

 it has been found, by the most accurate observations on the lengths of 

 pendulums in different latitudes, that the force of gravity is less powerful 

 by -,-^ff at the equator than at the pole, whence the ellipticity is found 

 to be -g-J-3- of the equatorial diameter, the form being the same as would 

 be produced, if about three eighths of the whole force of gravity were 

 directed towards a central particle, the density of the rest of the earth being 

 uniform. 



This method of determining the general form of the earth is much less 

 liable to error and irregularity, than the measurement of the lengths of 

 degrees in various parts, since the accidental variations of curvature pro- 

 duced by local differences of density, and even by superficial elevations, 

 may often produce considerable errors in the inferences which might be 

 deduced from these measurements. For example, a degree measured at 

 the Cape of Good Hope, in latitude 33 south, was found to be longer than 

 a degree in France, in latitude 46 north, and the measurements in Austria, 

 in North America, and in England, have all exhibited signs of similar 

 irregularities. There appears also to be some difference in the length of 

 degrees under the same latitude, and in different longitudes. "We may, 

 however, imagine a regular elliptic spheroid to coincide very nearly with 

 any small portion of the earth's surface, although its form must be some- 

 what different for different parts : thus, for the greater part of Europe, that 

 is, for England, France, Italy, and Austria, if the measurements have been 

 correct, this osculating spheroid must have an ellipticity of T f^. 



The earth is astronomically divided into zones, and into climates. The 

 torrid zone is limited by the tropics, at the distance of 23 28' on each side 

 of the equator, containing all such places as have the sun sometimes 

 vertical, or immediately over them ; the frigid zones are within the polar 

 circles, at the same distance from the poles, including all places which 

 remain annually within the limit of light and darkness, for a whole diurnal 

 rotation of the earth, or longer ; the temperate zones, between these, have 

 an uninterrupted alternation of day and night, but are never subjected to 

 the sun's vertical rays. At the equator, therefore, the sun is vertical at the 

 equinoxes, his least meridian altitude is at the solstices, when it is 66 32', 

 that is, more than with us at midsummer, and this happens once on the 

 north and once on the south side of the hemisphere. Between the equator 



* Sur la Figure de la Terre, Paris, 1743. Airy's Tracts, Figure of the Earth, 

 art. 62 ; or his article, Figure of the Earth, in the Encyclopedia Metropolitana. 



