282 
with k3 as the constant of the rate of reaction (Of is an 
excited molecule). The constants k, and ks enter only 
in the form of the ratio k»/ks; = k; the data for k are as 
yet somewhat variable. If the concentration [ | is re- 
ferred to the number of molecules per cubic centimeter, 
the extrapolated measurements by Eucken and Patat 
[30] yield the values of k shown in Table II. 
TaBLe II. Vauturs oF k 
deg C k deg C k 
100 1.95 & 1077! 0 4.00 X 10°°° 
80 3.16 X 10-7! —20 9.95 X 107° 
60 5.27 X 10524 —40 Zones 
40 9.51 X 107 —60 9.85 X 10719 
20 1.88 X 10°” —80 4.35 < 10718 
From the equations (10) to (13) and the reaction 
constants we obtain the changes in concentration per 
second: 
AOS — by 101 [0] LM] — I (0) (1-4 
and 
doy Kes [0s] (01 LM] — hs (031 [0l. 5) 
Fae Qe + Qs — ke [02] [O] [MZ] — ks [Os] [O]. ¢ 
If we calculate [O] from the condition of equilibrium 
d{O) _ ' 
Cie 0, we obtain 
dlOs] = 2Q» ke [Oo] [M] — 2Q2 ks [03] — 2Q3 ks [03], (16) 
dt Ke [O02] [MZ] + ks [Os] 
whence, under equilibrium conditions, oe = @, it 
follows that 
ke [02] [M] 1 
SS ih AMl\| ————., (7 
ONO. eae 
Wulf and Deming base their numerical calculations of 
the vertical ozone distribution upon this equation, in 
which Q; itself is a function of [Os], so that one can 
only proceed by a method of successive approxima- 
tions. 
In addition to oxygen, the third collision partner 17 
is primarily nitrogen which, however, is only about one- 
half as effective as oxygen so that 
[M1] = [02] + 44[N2] ~ 3[03]. (18) 
We may replace Q3, the number of quanta absorbed per 
second per cubic centimeter (which is also proportional 
to [Os]), by 
Q; = [Os] fs , (19) 
where fs is the number of quanta absorbed per molecule, 
and correspondingly 
Q2 = [Oalfe . (20) 
Diitsch [27], using this resolved form (which facilitates 
subsequent treatment of nonequilibrium conditions), 
obtains a quadratic equation for [Os]: 
[O3]}?f3 ++ [Os][Oolfe — 3k[O2]}*fo = 0. (21) 
THE UPPER ATMOSPHERE 
with the solution 
(0d = (0) PVs - 12 fs fo [Oz\e 
and, with the justified approximation fo < 12 fz fo[Oo|k, 
[03] = [O2}-V3kfs[Os]/fs. (23) 
This equation does not differ much from the form 
[03] = [OoP-VChe/fs, (24) 
which served as basis for Mecke’s theory [60] as early 
as 1931. Mecke replaced the numerical integrals f2 and 
fs by e2ty and a3/3, thus taking not only average radia- 
tion intensities but also average constant mean values for 
a. and a3. This enabled him to integrate over limited 
intervals, resulting in the following ozone distribution: 
[03] ax — ad 
Pmax 
In this equation, according to recent analyses, the 
power 2 is to be replaced by the power 34 which 
furnishes a somewhat broader maximum (Fig. 11). The 
symbol pmax denotes the pressure p at the altitude of 
maximum ozone concentration [O03]max. When Mecke 
introduced the total amount x of ozone (nstead of the 
maximum ozone content) he obtained for an altitude 
H of the homogeneous atmosphere the ozone content 
2 
pate a . 
eben P 
~ 1.85 \ pmax 
We might mention one conclusion [39] derived from 
Mecke’s theory. If we start with the altitude of maxi- 
mum oxygen absorption Q» (which, incidentally, is still 
dependent upon the zenith distance z of the incident 
solar radiation), then we find the altitude of maximum 
ozone content to be lower by the constant amount 
H In 3 = 7 km, independently of z. Figure 11 gives 
(22) 
[03] = (25) 
«10 (26) 
MECKE 
HEIGHT (KM) 
0.010 
(6 
Fic. 11 —Theoretical ozone distribution. 
