266 On Mr. Ferrel's Theory of Atmospheric Currents. 
Bewegungen auf der Erdoberflache," pages 203-206, Band 
xiv. of the ester reicliischen Zeitschrift filr Meteorologie, and, 
on being criticised for doing so, replies, "the area principle 
is always applicable in a determined plane, if the projection 
of the forces acting in this plane has no momentum-" (see page 
88, Band xv. of the same Journal). Also, page 89, " In the 
present case, in which the earth is regarded as a rotating body, 
the attracting force as well as the predominating pressure 
force on the earth's surface lies in the meridian, and conse- 
quently has in the equatorial plane no momentum of rotation 
in relation to the earth's axis." 
On page 40 of Kirchhoff's Mechanik (2nd edition), as well 
as in Schell's Theorie der Beivegung und der Krcifte (2nd 
edition), pages 351-354, is found the theorem of the conser- 
vation of areas and the cases to which it can be applied ; and 
here we find the theorem employed by Thiesen. This proves 
conclusively that Ferrel is correct in using it. 
With respect to the second point, on page 209 of the 
third edition of Routh's ' Dynamics ' we find the following 
theorem: — "In finding the motion of a particle of mass m 
with reference to any moving axes, we may treat the axes as 
if they were fixed in space, provided we regard the particle as 
acted on, in addition to the impressed forces, by two forces: — 
(1) a force equal and opposite to that which would constrain 
the particle to remain fixed to the moving axes, and which is 
measured by mf, where / is the reversed acceleration of the 
point of moving space occupied by the particle ; (2) a force 
perpendicular to both the direction of relative motion of the 
particle and to the central axis or axis of rotation of the mov- 
ing axes, and which is measured by 2mVfl sin 0, where V is 
the relative velocity of the particle, O the resultant angular 
velocity of the moving axes, and 6 the angle between the 
direction of the velocity and the axis of rotation." 
It is a question of relative motion that is being considered ; 
and it is evident, as Routh remarks on page 213, that "the 
motion of a body on the surface of the earth is not exactly the 
same as if the earth were at rest." 
A casual reader might see part of Ferrel's paper in the 
same light as Mr. Heath ; but we must remember that it is 
to be taken for the most part as a qualitative and not a quan- 
titative investigation. 
Although not in formula, yet in words the equation of con- 
tinuity is taken into account. 
On pages 18 to 23 we find a more detailed criticism of 
Ferrel's paper. 
That Ferrel's results were somewhat peculiar is to be ad- 
