108 REPORTS ON THE STATE OF SCIENCE. 
rests on the principle that a necessary condition for convection is that 
in the upper part of the convective system the radiation from any hori- 
zontal layer must exceed the absorption by it. He takes the temperature 
in the convective region to be given with sufficient approximation by the 
equation T’= kp where n=4 and p is pressure: and represents the 
radiating power of the atmosphere by a/ (q—p), where a and q are constants, 
in order to allow for the diminution with height arising from the decrease 
in the amount of water vapour present.! He finds that for an atmosphere 
of uniform constitution the adiabatic state cannot exist to a height greater 
than that for which p=3p, where 7, is the surface pressure, because if it 
extends at any time to a greater height the absorption in the upper part 
will exceed the radiation. He shows that for the actual atmosphere the 
adiabatic state can exist to a limited height only, and that if the atmosphere 
consist of an adiabatic and an isothermal region the adiabatic state must 
extend to a height greater than 5°5 km., and cannot in general extend to 
a height greater than 10°5 km. He shows also that the radiation from 
the lower half of the convective region exceeds the absorption by it, and 
deduces that its temperature must be maintained by convection from 
the earth’s surface and by condensation of water vapour. It follows also 
from the theory that if in the upper region the temperature increases with 
the height the conditions for thermal equilibrium are satisfied if the 
convective atmosphere extends to a height greater than that for the 
case of an isothermal upper region—2.e., the limits for H. are greater than 
5°5 and 10°5 km. 
Shaw? has recently considered the connection between a depression 
of the lower surface of the advective region and the temperature distribu- 
tion in that region. He finds that if such a depression is produced artifici- 
ally or through a disturbance in the convective region, the first effect will 
be to produce a horizontal difference of temperature in the advective 
region. If the advective region is initially isothermal it will still be 
1 It has been suggested that the upper limit of the convective region may be 
also the upper limit of the water vapour atmosphere. But it appears certain that 
at this upper limit the atmosphere must always be saturated with water (ice) 
vapour, and that in the advective region the water vapour atmosphere will be such 
that the difference of vapour ‘pressure between two points will be equal to the 
weight of the vapour in the intervening column. For the processes of diffusion and 
of convection of water vapour alone would tend to produce a water vapour 
atmosphere, in which the amount of vapour present at any height in the convective 
region would be more than sufficient to produce saturation at that height for the 
temperature in the actual atmosphere. The only process which prevents the 
atmosphere being saturated at all heights is the descent of air carrying with it the 
water vapour it contained at the beginning of the descent, an amount insufficient to 
saturate it at lower levels. But at the upper limit of the convective region there 
can be no considerable descent of air from above, and the air arriving there from 
below will necessarily be saturated, since it must contain sufficient water vapour to 
saturate it at the lowest temperature to which it has been exposed, ze. Te, Of 
course the actual amount of water vapour present is small compared with the 
amount present near the earth’s surface; but a small amount of water vapour is 
sufficient, at ordinary temperatures at least, to produce considerable absorption of 
terrestrial radiation, and the absorption extends through a large part of the 
spectrum of radiation at terrestrial temperatures. In fact, it is probably chiefly due 
to the presence of this water vapour that it is possible to obtain theoretical results 
agreeing with the observed facts by using the assumption that the absorption, and 
therefore also the radiation, is sufficiently extensive to warrant the application of 
Stefan’s law. It follows, also, from this reasoning, that the mean amount of vapour 
present at any height above the lower cloud level will be at least half the sum of 
the amount for saturation at that height, and the amount necessary for saturation 
at the height Hg, 
2 Perturbations of the Stratosphere, M.O., 202. 
