97 
1913-14.] Principia Atmospherica. 
uncompensated momentum ; the flow-off on either side at the bottom from 
“ high ” to “ low ” denoted by U 1 and U 2 being provided by the adjustment 
of the currents V 1 and V 2 . 
Whether or not this be a true explanation, it certainly agrees with 
common experience in regarding a high-pressure area as more easily main- 
tained persistently than a “ low. 1 ’ 
Propositions 2, 3, and 4. 
These propositions, which deal with the application of the formula for 
change of pressure-difference with height (the unit of height being the 
metre), viz. 
to explain the dominance of the stratosphere and the lack of importance of 
the troposphere in the distribution of pressure at the surface, to compute 
the wind- velocity from the pressure-difference at any height and to explain 
the observed falling off of wind-velocity with height in the stratosphere, 
have been dealt with in the paper communicated to the Scottish Meteor- 
ological Society, and the work need not be repeated here, especially as 
Proposition 5 makes use of the same equations. 
Proposition 5 . — The Calculation of the Distribution of Pressure and 
Temperature in the Upper Air from the Observations of Structure 
represented by Soundings with a Pilot Balloon. 
A pilot balloon gives primarily the horizontal direction and velocity of 
the wind at successive heights, so that we may suppose that we have the 
horizontal direction and velocity of the wind at each kilometre as the data 
for the calculation. 
The first step is to resolve the wind-velocity into two components, 
west to east and south to north. 
By the application of Law 1 we can then compute the pressure-difference 
for 100 kilometres in the south-to-north direction and the west-to-east 
direction. 
Thus, if A p is the pressure-difference for a distance L taken along the 
direction of the wind velocity V, if 6, in absolute degrees, and p, in milli- 
bars, are the temperature and pressure, X the latitude, go the angular 
velocity of the earth’s rotation, and R the constant of the characteristic 
equation for air, we have 
y_ R 0 Ap _ g 6 Ap 
2o> sin \ p L p L 
And since both velocity and pressure-difference, or gradient, are vector 
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