64 
Proceedings of the Royal Society of Edinburgh. [Sess. 
Below H = # the air does not move. 
At all higher levels in area A the pressure is increased (see above), 
hence the isobaric surfaces have risen. Therefore the air has risen. 
Let p denote the density of a portion Q of the air at height H before 
the change of temperature began, p the density of air at that height after 
the change, p" the density of the air Q which has now been raised to a 
higher level. In the region just above H = sc, p<p (proved above), also 
p<p (since the lapse rate does not exceed the adiabatic, and p" refers 
to air at a higher level than p). 
• p'<p. 
Therefore the air in this region has actually expanded. Also, from 
equations 4 and 5, since p is constant and p is diminished, both 0 and E 
are increased. 
Consider air which is above the level H — y. It has risen, yet the 
temperature has been adjusted to the new level. If the lapse rate was 
normal, and H = y is within the troposphere, this means that the tempera- 
ture 0 is reduced. But the pressure is unaltered. Therefore the density is 
increased (equation (3)) and the entropy is reduced (equation (4)). For 
portions of air in the stratosphere the temperature remains unchanged or 
slightly rises (as also in regions of temperature inversion), hence the density 
is unchanged or diminished, and the entropy unchanged or increased. 
Hence it appears that except in the stratosphere or in regions of 
temperature inversion the changes in definite portions of air are similar in 
kind to, though of a different magnitude from, the changes at different levels, 
as shown in fig. 1. It should also be observed that in general the level 
H = y bounding the temperature change will not lie in the troposphere, since 
this would imply a simultaneous addition of heat below and withdrawal of 
heat from above. Mutatis mutandis the same conclusions will apply to 
area C, except that, as will appear later, it is more likely for a withdrawal 
of heat from the lower air to be associated with an addition of heat to 
the upper. 
Instead of fixing our attention on temperature, it is interesting to con- 
sider the entropy as the varying quantity. If we suppose one layer of air 
to have its entropy increased, and the remaining air above and below to 
undergo no change, the principle of constant pressure for each portion of 
the air gives at once these results. 
Below region of change, no alteration. 
In region of increased entropy, air increases in temperature, decreases 
in density (equations (3) and (4)). 
