OS THE THEORIES OP ELEVATION AND EARTHQUAKES. 41 
point within the spheroid form a surface passing through that point called a 
surface of equal pressure; all such surfaces (of which the external surface is 
one) are concentric and spheroidal, having their axes in the axis of rotation, 
llie eliipticities are less in those more remote from the externa) surface. 
(3.) Each surface of equal pressure is also a surface of equal density. 
(4.) The density increases as we pass from one of these surfaces to on. 
other along any straight line from the surface to the centre. 
If the density of the whole mass were nniforni, we should only require the 
rime of rotation to be able to deteraine the elliptieity of the external surface • 
but, in the case of ibc earth, the elliptieity thus calculated is much too large, 
proving that the density cannot bo uniform, assuming always the truth of our 
fuudamental hypothesis. We hare no data, however, for detemiining more 
respecting the variation of the density than is above staled in (4). If 
the law which It follows were known, together with the time of rotation, the 
elliptieity of the external surface could be calculated; but the Uw of density 
IS essentially an unknown element of the problem, and mathcnmlicianR hav'e 
therefore been obliged to assume a law, and leave the accuracy of the assump- 
tion to be proveil, in common with any other hypotJie.ri8 involved, bv the 
general harmony of the results. This assumed Jaw ia represeuiKl. as U well 
known, by which expresses the density at any point of a surface of 
equal pressure and density, whose axis=fl. I3y assigning a proper value to 
constant we obtain a value of the elliptieity of the external surface co- 
loeidmg with that determined by obaenation. This acconlancc. however. 
« other, would afford no conclusivo proof of the earth’s 
trier since the result depends on an arbitrary assumption respect* 
»ig the density, and therefore we must examine whether this assumed law of 
accords with other observed jihmnomena. Now with our assumed law of 
‘^‘^nsity bears to the den- 
8ity at the surface; and the mean density has also been determined in the 
of Cavendish, and lat. ly bv similar experi- 
r the most rc-fintnl precautions 
r «1 S Jwt'irbing causes. TJie comparison of the thcorcti- 
wl that the same law of density which accords 
r,nifi ellipricity of the earth, gives also a value of the ratio of the 
r»vn *^*^1 densities, which accords very approximately with the 
tletermmation of the mean density, and of that of the rocks 
generally composing the earth’s surface*. 
tirt.! between the results of observation and those of calcula- 
au ..1^' t^spect to the form of the earth and its mean density, seem to be 
could possibly expect, and wo may therefore assert tliat this 
accounts for the observed spheroidal form of the earth by the 
operation of natural causes t- 
mJl;' certain delicate but well-defined phenomena in the 
earth and moon, depending on the earth’s oblatencss, which 
eii ence m favour of the aliove theory. 1 allude to the motions of 
If we make 50 ^ ^ being the value of a at the aurface), the cBlcuInted ratio of the 
men't.*** “ 2'4225. The mean density according to Mr. Btily’s experi- 
mertZ.^, ‘I'c Astronotuical Society). Tliis will exactly agree with the for- 
t h i i y the inaan density of the earth at Its surface to bo 2-34. 
CM« «f assumed that the form of the earth has not sensibly changed during the pro- 
> I cation. There can be no risk of an appreciable error in this assumption. 
