aa ee NS 
and the Velocity of the Wind. 347 
corresponds with the centrifugal force in (1), upon which the 
gradient depends in the case of no friction, in which the gyre: 
tions are circular, as supposed in the basin of water, and in 
which consequently sec :=1. 
6. If we put 
h=the height of any stratum of the atmosphere of equal 
ressure ; 
p= the density of this stratum ; 
p’= the value of p at the earth’s surface ; 
we shall have 
D 
P 
(4) —=9D,h, 
oe putting a for 100 miles, we get, according to the definition 
of G, 
_aDh p 
“10500 p” 
(5) 
this constant should be increased ;3,; for each degree of tem- 
perature. 
With the value of D,A obtained from (5) we get from (4) 
oF, pl 
p p 
But the first member of this equation is the expression of the 
horizontal accelerating force arising from a difference of pres- 
sure, and this in the case of no motion either toward or from 
the center of the cyclone, as in the case of the basin of water, 
must be equal to the part of the centrifugal force causing the 
gradient, which, when the gradient is referred to the elliptic 
surface of the earth, we have seen, is (2nsin/+u)v. Hence we 
get in this case 
—105002G. 
a 
a =1050026 ; E=(2n sin [-+u)0. 
Where there is motion toward or from the center of the 
cyclone we must add a term, F, to the last member of this 
equation, to represent the frictional resistance to the motion, and 
likewise one to represent the inertia of the air where its motion 
is either accelerated or retarded. On account of the extreme 
mobility of the air this last term may be generally neglected 
without any sensible error, in any of the usual motions of the 
tmosphere, for it can be shown that only a very small part of 
