On the Physical Geology of the United States, §c. 291 
The centrifugal force is one of these compensating causes. It 
varies inversely as the cubes of the radii* of a sphere whose vol- 
ume varies while its mass remains constant, but the angular ve- 
locities vary inversely as the squares of the radii; hence, if the 
earth should contract in volume, the velocity of rotation would 
necessarily increase in obedience to the law of conservation of 
areas; but the centrifugal force would be increased in a still 
aalice ratio, and would cause a flow of water from the polar to- 
wards the equatorial regions to give the form of the spheroid of 
equilibrium, and would thus tend to diminish the increase of 
velocity due to contraction. 
It necessarily follows from what precedes, that the tae, 
in reference to the day having remained uniform for twenty five 
hundred years, has not as much weight. as has been assigned to 
it, and ought not to be adduced as demonstrating that the earth 
is not in the state of acooling body, or that it has not diminished 
in volume, or that no geological effects can be ascribed to this 
cause. 
Kven if it be admitted that the sasiiehitins in the length of the 
day for twenty five hundred years should have weight and ren- 
der it improbable that there has been any contradiction during 
that time, and if in addition we discard even the compensating 
effect of increased centrifugal force in tending to maintain uni- 
formity in the length of the day ; yet the period of twenty five 
hundred years may be considered as only the differential of the 
long periods of past duration, during which the geological effects 
we have contemplated were produced. 
Still another argument may be adduced, viz. that the variations 
in the rapidity of rotation took place paroxysmally, at certain pe- 
riods, generally at long intervals of time, and that none of these 
variations have occurred during the historical epoch, unless the 
time of the deluge was one of them. 
ites I! 
gy vey. Sah r 7! Tv 7! 1 1 
_ a al but FP: Fs: — 58. Fi Fl :: >: 2:3. Hence 
tt 23 72 r7!2 EP mts mira, 78 x3 
the centrifugal forces represented by F and F! vary inversely as the cubes of the 
(r3 -1'3) 
radii, and the increment of centrifugal force F—F/ =F aT would tend con- 
tinually to diminish © by increasing 7, and thereby tend to make ¢ (which repre- 
sents the time of rotation) constant—(Communicated by Prof. A. Ryors, of the 
Ohio University.) 
