72 
Proceedings of the Royal Society of Edinburgh. [Sess. 
very smallest magnitude. This is in opposition to the view that depres- 
sions are due to the disturbance of vertical equilibrium, and in agreement 
with the view suggested above that they arise from thermal changes too 
slight and continuous to disturb greatly the lapse rate. As a matter of 
fact, as has been already mentioned, the vertical stability of the air is so 
great that it is rarely, and never long, disturbed. It is for this reason that, 
except where disturbed by ground contours or the collision of differently 
directed currents, the winds flow in almost perfectly horizontal planes. 
It .has been mentioned above that a portion of the energy of the winds 
is derived from the rotation of the globe, and it is easy to find an approxi- 
mate expression for the proportion of energy so derived. If Q (fig. 7) be 
a portion of the air in a cyclonic whirl closing gradually in on the axis 
ZY, we may denote its original moment of inertia about ZY, when it was 
at rest relatively to the earth’s surface, by the symbol I. Then its original 
energy of rotation was |Ia) 2 . If it approaches to a fraction X of its original 
distance from ZY, its moment of inertia is diminished to A 2 I. If a> be 
now its angular velocity, we have 
Ic o = A 2 W. 
( 1 ) 
Its energy of rotation about ZY is therefore 
= 
i 1 ^ 
X 2 * 
If it were now brought to rest relatively to the underlying surface, its 
energy would be jA 2 Ia> 2 . Hence the apparent energy of the wind due to 
its movement relative to the earth’s surface is — A 2 j, an d the portion 
of this derivable from its original energy of rotation is JIw 2 (l — X 2 ), the 
rest being due to the pressure forces impelling it towards ZY. Hence the 
2 X 2 X 2 
= - — — of the energy of the wind is due to the earth’s 
1 2 1 + A 
fraction 
rotation. It appears, therefore, that in the first stages of its movement 
the light wind in the outer region of the area owes one-half of its energy to 
the rotation of the earth. As it approaches the centre and increases in 
strength, an increasingly greater portion of its energy is due to the 
pressure forces that accelerate the movement. It should be noticed that 
the greater the angle at which the path cuts the isobars, the greater is the 
component of force accelerating its speed (or retarding it, if it is moving 
