APPLICATIONS OF ENERGY PRINCIPLES 
molecular viscosity or of small-scale disturbances which 
can produce no significant tangential stresses at the 
boundaries —¢ and +4, the contribution of the term 
d in the integral on the left-hand side may be assumed 
to represent the mean rate of dissipation of kinetic 
energy into heat withm the equatorial belt and there- 
fore cancels the contribution of the term y. It follows 
therefore that H is the total net rate of heating of the 
air in the belt. Hquation (23) simply states that this 
net incoming energy is transferred meridionally in the 
form of (1) internal energy pU per unit volume, (2) 
kinetic energy of existing motions pc?/2, and (3) poten- 
tial energy p&, as well as (4) through work done by 
pressure forces p. We shall refer to these four items as 
advective modes of energy transfer. 
It is here assumed that there is no advection of energy 
through the surface of the lithosphere. This is essen- 
tially correct except for processes such as volcanism 
and seismological phenomena, but these are deemed to 
be too unimportant for the present considerations. 
Also it is assumed that there is no advection of energy 
through the top of the atmosphere, which therefore 
neglects the effect of interchange of molecules with 
astronomical space and of the mass accretions of me- 
teoric origin. The quantity H, representing the net 
heat gam withm the equatorial belt by processes other 
than advection, may be very closely identified with 
the net heat received through exchange of radiation 
with the extraterrestrial environment. This identifica- 
tion neglects such processes as conduction of heat from 
the interior of the earth, which is of appreciable im- 
portance only locally in connection with volcanism, and 
it also neglects heat liberated (or consumed) by net 
progressive chemical changes such as oxidation or pho- 
tosynthesis processes. Net heat gain through exchange 
of radiation with other portions of the earth is likewise 
neglected. All the various corrections mentioned are 
however in all probability imsignificant. 
If we take H to be the net gain of heat through ex- 
change of radiation with space, various necessarily 
crude estimates of this quantity have been prepared. 
A convenient arrangement of one set of such estimates 
has been presented by Bjerknes [1]. As is well known, 
the estimates give positive values of H for all choices 
of -—-¢ between the equator and the poles with a maxi- 
mum for about ¢ = +45° latitude. It therefore follows 
that there must be an advective transport of energy 
poleward by the combination of terms indicated in (23), 
with a maximum at @ = +45° latitude in the mean. 
It is apparent that the important problem posed by 
the global energy balance concerns itself with the par- 
tition of the poleward energy transport among the 
several terms in the integrand of the right-hand member 
of equation (23). 
Discussion. Unfortunately our observational infor- 
mation concerning the problem posed by the global 
energy balance is very sketchy and incomplete. We 
shall nevertheless endeavor to discuss such aspects of 
it as are possible with existing knowledge. In the first 
place, the contribution of the hydrosphere to the trans- 
fer integral is probably small (see Sverdrup [9]), but 
573 
directed toward the poles. A reasonable estimate of this 
contribution would appear to be about ten per cent of 
H. Denoting this fraction by h, let us next turn our 
attention to the state of affairs within the atmosphere. 
It has been previously pointed out that the advection 
of existing kinetic energy pc?/2 meridionally is very 
small, relatively speaking. We are therefore again justi- 
fied in omitting it. The internal energy U may be 
considered as being the sum of the internal heat energy 
and the latent heat of water vapor. Since there is 
assumed to be practically no net meridional mass trans- 
port in the atmosphere, it will suffice to assume that 
the internal heat energy is given by ¢,7’, c, being the 
mean specific heat at constant volume. It thus follows 
that U \ ¢,T + el, where « is the specific humidity and 
L is the latent heat of condensation, assumed to be 
constant.* The term involving the work done by pres- 
sure forces may again be transformed according to the 
ideal equation of state, and finally combined with the 
internal heat-energy term using the relation between 
the specific heats of a gas. In the end (23) may be 
written in the form 
H=h+ | (pT + cL + S)prnds, (24) 
where ¢,, the specific heat at constant pressure, is 
assumed to have a constant mean value. 
The contribution of the term involving the latent 
heat may be estimated from the mean excess of evapora- 
tion over precipitation in the equatorial belt. Using 
data of this kind given by Conrad [3], the writer has 
estimated that the magnitude of this effect is about 
one-half of H for an equatorial belt extending to +40° 
latitude. Let us denote this quantity by l. 
The remaining terms may be examined as follows. 
If we write 
PUn = PUn + {pn}, (25) 
where pv, is the average of pu, along the entire length 
of a closed latitude circle and {pv,,} is the deviation from 
this average, it is clear that the identical vanishing of 
pv, implies absence of closed mean meridional circula- 
tions, while its presence is required for the existence of 
such circulations. Here we neglect all topographic in- 
equalities of the earth’s surface. In view of the fact that 
® is constant along a latitude circle at any given eleva- 
tion and that {pv,} is zero, it follows that (24) may be 
rewritten in the form 
H=h+1U+ | cP {orn} ds 
(26) 
+ / (c,T + ®)pv, ds, 
3. The latent heat as ordinarily discussed is the sum of the 
change in specific internal energy plus the work done in the 
expansion during evaporation. Strictly speaking, we are here 
concerned only with the first quantity, although the difference 
is not great enough to be of much significance. 
