On the Physical Geology of the United States, Sc. 5 
If we apply these principles to the earth, which may be ad- 
mitted to be a cooling and revolving body, it must have dimin- 
ished in volume either secularly or paroxysmally. ‘This must 
necessarily have induced a greater velocity of rotation on its 
axis, also an increased centrifugal force, and the oblateness of the 
spheroidal form of the earth must have been increased in the 
same proportion.* 
The increased oblateness of the spheroidal form of the earth 
by the increase of the centrifugal force, would induce a flow of 
water from the polar to the tropical parts of the earth to restore 
the form of equilibrium of the revolving spheroid under these 
modified conditions; and as the earth revolves from W. to E. 
these currents from the polar regions would bend more and more 
to the westward as they advanced to lower and lower latitudes, 
and a current would set from E. to W. within the tropics, but 
strongest under the equator.t 
The polar and equatorial currents, branches of which are be- 
lieved to have been observed in every ocean, but variously modi- 
fied in direction by numerous causes, may have been thus estab- 
lished or heightened in the rapidity of their flow at particular 
epochs in the earth’s history. 
Another cause that may have been instrumental in the first 
instance in establishing, and subsequently in maintaining the 
flow of the polar and equatorial and other currents of the ocean, is 
the influence of the solar rays on the tropical regions of the earth. 
This influence is exerted both on the atmosphere and on the 
ocean, but both concur in aiding the flow of the currents under 
consideration. 'The water of the ocean being warmed more un- 
der the tropics than on other parts of the earth’s surface, expands, 
we ary Se 
r=" If ¢ represents the time of rotation, V== —>— and by substitution, 
I 
=e F:F!::75: gg These formule show that the centrifugal force va- 
ries directly as the square of the velocity of any point, and inversely as the dis- 
tance of that point from the axis of motion; and also that the centrifugal forces 
vary directly as the distance from the axis of rotation, and inversely as the squares 
of the times of rotation. 
t The reason of this deflection of currents will be explained farther on in this 
article. 
t It has been objected that the evaporation from the surface of the ocean under 
the tropics would compensate for this expansion; but it would be insufficient if 
the water becomes heated to 8U° to any considerable depth. The quantity of 
water that falls as rain, also in part compensates for the evaporation. 
