28 W. Ferrel on motions of fluids and Solids 
the djivotite of a perpendicular to the earth’s axis, arising from 
the earth’s rotation. If in addition to the angular motion com- 
mon to all bodies at rest on the surface of the earth, the body 
has an angular motion Dg relative to the _ earth, then ‘the centri- 
fugal force becomes rsin#(n+D¢)?. Now if we resolve the 
preceding force in the directions of the mendes and a perpen- 
dicular to it, the part acting in the direction of the meridian, neg- 
gees the small effect of the earth’s ellipticity, is 7 sin 4 cos @ 
(n+ D)?. The part of this force which gives ellipticity to the 
earth’s surface, and which is necessary to kee ep a body at rest on 
the elliptical surface, and Sushil it from sliding toward the pole, 
is sin @cos 4n2, Hence the difference of these two forces, 
when the bade has a mbEG eastward relative to the earth, isa 
deflecting force which has a tendency to cause the body to move 
from the pole toward the equator. The difference of these for- 
ces is rsin §cos6(2n+D,~) Dp, and hence when the body is 
entirely free to move in any direction, we have 
(1 ) r D,;?0=r sin 6 cos p (2n + Dy) Dig. 
n, if the body has a motion toward or from the pole, 
it must nauely the well known principle of the preservation of 
__ areas, so that as it approaches the pole, and Perea the axis 
of rotation, the angular motion must be increased, that is, it 
must ee eo a motion eastward relative % the earth, but if it 
recedes from the pole, it must acquire a relative westward mo0- 
tion. In iss to satisfy the a principle, the motion 
must satisfy the following equation . 
(2.) 7? sin? 6 (n+ Da). = constant. 
Taking the derivative with regard to t we get 
(3.) r sind D29—=—2r cos.0(n+ Dig) D/P. 
4, Equations (1) and (3) determine the motions of a free body | 
bo the earth’s surface. If the body is constrained to move either 
ion of a meridian or a parallel of latitude only, the © 
eng force instead of causing a deflection, causes only 4 
earth’s rotation, india acts in the direction of a salle OF 
tude, we have 
6= Boat Dew. : 
In the ge equations 7D, represents the lineal abew 
of the boty: in the direction of the meridian, and r sin Aon the 
lineal velocity relative to the earth in the direction of the pes 
lel of latitude. Hence the deflecting foree i is Aces same in : 
directions in the same lineal velocity. : ae 
