A 
On the Physical Greology of the United States, §c. 289 
the ocean in consequence of the inertia and increased centrifugal 
force, requiring an increased protuberance in the spheroidal form 
of the earth to restore the form of equilibrium to the revolving 
spheroid. 
The changes in the times of rotation of the earth being sup- 
posed paroxysmal, occurring at particular periods of time, and 
none of these having occurred during the historical epoch, (unless 
the time of the deluge was one of them,) the argument from t 
fact that the length of the day has not varied for two thousand 
years loses all its force, and cannot be adduced in opposition to 
the views here advocated. 
3d. It is well known that the angular velocities of a revolving 
spherical body under varied diameters, are inversely proportioned 
to the squares of the radii,* so that if the earth be a cooling body, 
e M. Poisson’s Mecanique, second edition, Tome II, p. 460, and Ameri- 
can Seamed of Science, rau ZLYIy Be one 346. 
Ib 1 NI f 1 
Th}, 
auc we y elocity 
, (Young's pd coal American pa p- 193,) which is equal to 
o> ¢ ae ) 
the moment of applied force divided by the moment of inertia. {(mr2)=mk2, 
(Young’s Mechanics, Am. ed., p. 190,) in which k represents the radius of gyra- 
tion, and m the mass of the revolving body. By substitution o= a In the re- 
volving sphere with a variable radius, the quantity of matter remaining constant 
1 
2=— —7r2..-, seree 
ia" In the sphere k gre. a0 
or the angular velocities vary inversely as the squares 
M=m, and as R and v are constants, © — 
1 28 
w! w.@: Ua . Ste 
and 0 5 w fees 
of the radii. 
If the variable density due to variable volume be considered, the law of the an- 
gular velocities bgt potent as the squares of the radii still holds true; for, in 
the sphere mk2 = fers * ora when the density is unity. When the density is 
my. Calling D’ the 
2 
D, the moment of inertia is =D arexere and «= 
D 
, MRo 
density in the second place and r! the corresponding radius w’ = —T hence 
1y¢ 4! 
D'x i’ 5 
apes Re is ih being constant, the densiti i ly proportioned 
T 
; V_egis 
to their volumes, or a Substituting this value, we obtain — a yx = —,and 
by substituting for V and V! their values in terms of the radii, we obtain — _= a 
x pe ae L@ sols 5 a (This last demonstration was communicated S 
T 
hind Roberts, silat Professor of Natural Philosophy, West Point, N. Y.) 
