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A.—MATHEMATICS AND PHYSICS. 27 
Jess and less stable, until actual instability occurs, and we get ascending 
currents which produce squalls and local showers even before the cold 
air meets the warm air at the cold front. Polar air is generally very clear 
and visibility is good in it; this is due partly to the air having started 
from polar regions where there is little dust, and partly to the fact that 
the air is getting warmer all the time and, therefore, the relative humidity 
is constantly decreasing. On the other hand, the equatorial air comes 
often from dusty tropical regions, contains much moisture, and its relative 
humidity is always increasing. All these factors tend to reduce the 
visibility and give one a sense of damp, oppressive conditions. 
We are being forced more and more to recognise in cyclonic depressions 
the meeting-place of polar and equatorial air. These masses of air, 
retaining the characteristic thermal structure of the regions from which 
they start, are brought side by side like the oil and water of the analogy 
which I have already used. Each body of air is stable to vertical currents 
within itself, but where the two masses meet readjustment is necessary ; 
the surfaces of discontinuity tend to set themselves at the angle necessary 
for stability under the existing condition of velocity and temperature. 
This involves the bodily raising of the warm air over the cold air and a 
general sinking and spreading out of the cold air. The energy for the 
process is derived from the conversion of potential energy into kinetic 
energy, as the centre of gravity of the air as a whole is slowly lowered 
during the readjustment of the air masses. The energy derived from the 
condensation of water vapour is a very insignificant part of the energy 
developed in a cyclonic depression. 
So much is now generally accepted by meteorologists, but we are still 
far from clear as to the forces which bring the equatorial and polar air 
into the close juxtaposition necessary to produce a cyclonic depression. 
There are, at present, two main theories, the first due to Bjerknes and 
called the polar-front theory, and the other due to Exner and called the 
barrier theory. Both theories make use of the polar cap of cold air 
circulating on the whole from east to west and surrounded by the strong 
westerly currents of middle latitudes. Both recognise something of the 
nature of a polar front; that is, of a marked surface of discontinuity 
separating the polar air from the warm air of the westerlies to the south 
of it. From this point, however, the theories diverge. Bjerknes con- 
siders that cyclonic depressions are definitely phenomena of the polar 
front itself. The polar front he considers has sufficient stability against 
north and south motion to be capable of having gigantic waves set up 
in it. Each cyclone commences as a wave on the polar front; these 
waves travel from west to east, become too large for stability, and break 
just like the breakers on a shelving beach. A cyclone is, according to 
_ this theory, a breaker on the polar front. This idea has been worked out 
in great detail as a descriptive theory and a few individual cases have 
been discussed ; but it still lacks the necessary mathematical analysis to 
show that the forces brought into play when the polar front is deformed 
are of the right order of magnitude to account for the violent motion 
associated with cyclonic storms. 
Exner makes no use of the stability of the polar front. He considers 
that the cold air moving westwards in polar regions is deflected south- 
wards by the land masses of Greenland, Spitzbergen, Franz Josef Land, 
