A.—MATHEMATICS AND PHYSICS. 19 
Applying these considerations to Sir Napier Shaw’s entropy diagram, 
we see that, because the entropy everywhere increases upwards, the 
atmosphere has a thermal structure which gives it the characteristics of 
a fluid in which the density decreases upwards. Such an arrangement of 
density is very stable in the vertical direction, and it would only be 
possible for air to rise if it received sufficient heat to increase its entropy 
to that of the layer to which it is moving. If no heat is added, the air 
cannot be in equilibrium in any layer but that from which it starts. Thus, 
in all movements of the air in which heat is neither added nor extracted, 
for example by condensation or radiation, it must travel along an isentropic 
surface. Even if condensation takes place the amount of heat added is 
usually so small that the air can only move to a neighbouring isentropic 
surface slightly higher in the atmosphere. These isentropic surfaces act 
like physical restraints to the air, tending to prevent its moving in any 
but an almost horizontal direction. The effect is almost exactly as though 
the atmosphere were definitely stratified in nearly horizontal planes, so 
that all motion of the air must take place along the strata in which it 
started. 
This is what I mean by the thermal stratification of the atmosphere, 
and it isa new idea in meteorology, for it rules out ascending and descending 
currents as a direct consequence of the normal temperature distribution 
in the atmosphere. That ascending currents do occur and play a large 
part in atmospheric processes is, however, a matter of both observation 
and inference. We can actually see them taking place whenever we 
observe well-developed cumulus clouds, and we infer them from the large 
amounts of precipitation which we measure, for appreciable precipitation 
can only be accounted for on the assumption that air is rising in the 
atmosphere and cooling by adiabatic expansion. These ascending currents 
are possible in the stratified atmosphere only if the air taking part in them 
receives sufficient heat on its ascent to raise its entropy at least to that of 
the surrounding atmosphere at each level. Heat is supplied by condensa- 
tion of water vapour, but normally air does not hold sufficient water 
vapour even when saturated to supply the requisite heat, and so cannot 
pierce the normal stratification. It sometimes happens, however, that 
the stratification is less pronounced than at other times. The greater 
the lapse rate, the less the stratification, and by increasing the lapse rate 
sufficiently the stratification can be reduced to such an extent that there 
is sufficient water vapour to supply the heat required. When this occurs 
the atmosphere becomes unstable to saturated air and ascending currents 
take place, generally with considerable violence. 
Such conditions give rise to thunder-storms, which occur, as is well 
known, only when the lapse rate has been abnormally increased, g generally 
by the heating of the surface layers faster than the layers higher in the 
tmosphere. Also in equatorial regions over the ocean, where the air is 
very hot and also very humid, there may be sufficient water vapour in 
e air for it to rise through the normal stratification. This is the origin 
of the squalls and heavy rain in the Doldrums. From this it will be seen 
hat the ascent of air through its environment is not a normal phenomenon, 
but does occasionally occur in special circumstances. 
_ The descent of air is an entirely different matter, for there is no process 
hich extracts heat from a descending current equivalent to the process 
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