22 SECTIONAL ADDRESSES. 
cold mass slowly subsiding and pushing its way as a wedge of cold air 
under the warm air, which is partly raised and partly drawn in above to 
replace the cold subsiding air. In the process the centre of gravity of the 
whole moving mass is gradually lowered, so providing the energy for the 
motion which we recognise as winds. 
The essential difference between the new and the old idea is that the 
two masses of air whose difference of temperature is the cause of the 
motion never mix. We start with the two bodies of air side by side, with 
a surface of sharp discontinuity between them. In each body there is a 
different stratification of isentropic surfaces. In the warm body of air 
the corresponding isentropic layers are all lower than in the cold body of 
air. As the cold mass subsides its isentropic layers are lowered, while 
as the warm air is raised its isentropic layers are raised with it; but the 
surface of discontinuity between them, which I have previously likened 
to a geological fault, is a sliding surface, and no air crosses it. The sliding 
motion does not cease until either the corresponding isentropic layers on 
the two sides have joined up across the surface, which then ceases to be a 
surface of discontinuity, or until all the warm air has been raised above 
the cold air and the surface of discontinuity becomes a horizontal plane. 
The two masses are then in equilibrium without any mixing having taken 
place. 
Surfaces of Discontinuity. 
The process which I have just described would take place very rapidly 
on a stationary earth, and in a short time the surface of discontinuity 
would disappear in the manner described or appear as a horizontal surface 
with all the cold air underneath and all the warm air above. But in the 
atmosphere we find inclined surfaces of discontinuity persisting for days 
together, and others which are apparently. permanent. This arises from 
the effect of the rotation of the earth, which we have so far neglected, 
but which introduces new forces when air is in motion. 
A mathematical investigation of the conditions governing the air 
motion at surfaces of discontinuity has shown that, on a rotating earth, 
the tendency of cold air to pass under warm air can be completely counter- 
balanced by forces due to the earth’s rotation if the air on the two sides 
of the surface has suitable relative velocities. 
We owe the mathematical investigation of this problem chiefly to 
Helmholtz, Margules, V. Bjerknes, and Exner. When the actual atmo- 
spheric problem is considered the mathematics becomes complicated, but 
the physical processes involved are not difficult to understand. In view 
of the importance now attached by meteorologists to surfaces of dis- 
continuity in the atmosphere, I should like to discuss the physics of the 
problem in a general way, so as to give a simple picture of the conditions 
necessary to maintain equilibrium at a surface of discontinuity. This 
can most easily be done by considering the analogous problem of the 
se of two masses of liquid of different densities maintained side 
y side, 
We have previously considered a tank holding oil and water. Let us 
now consider that the tank is indefinitely long and the partition between 
the oil and water placed lengthways. The water and oil each presses on 
the partition, but the pressure due to the water is obviously the greater. 
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