ey 
rs 
848 W. Ferrel—Relation between the Barometric Gradient 
the observed barometric gradients are necessary to overcome 
the inertia in accelerating and retarding the observed velocities. 
Neglecting, therefore, this effect, and adding F to the last mem- 
ber of the preceding equation, we get 
(6 GZ (2nsin/+u)vcosi+F p 
) ea ie 105 pe 
Since the motion is now spiral and not circular, and the cen- 
trifugal force depends simply upon the component belonging 
to circular motion, we must use here vcos? instead of v simply 
in the preceding expression. 
. By the principle of the preservation of areas ‘in the ease 
of central forces only and no friction, we would have in all 
parts of the cyclone 
r? (n sin /-+-u)=constant. 
Hence we get by differentiation. 
<9 D,u=2( sin l+-u)D,r. 
The second member of this equation expresses the force which 
tends to produce a gyratory motion around the center of the 
cyclone. In the case of no friction this force is all spent in 
of air approach or recede from the center, but where there is 
iction, it is mostly spent in overcoming the frictional resist- 
ance. We shall, therefore, have very nearly 
(7) F’=2(n sin /+-u) D,r, 
putting F’ for the resistance to motion at right angles to the 
radius, or in the direction of the gyratory motion. 
direction of the motion of the atmosphere, and the component 
of this resistance, contrary to the direction of the gyratory = 
tion, of which the velocity is rucos7, is represented by Fr. 
