324 
equation (33) becomes 
Vs = = 1m} ex (=F ale Q; az) — oe 
E — exp (-1 [ Q. a). 
In steady states, the height variation of the number 
concentration of a gas without internal sources in a 
nitrogen atmosphere depends on the ground concentra- 
tion vy. , the relative weight factor pu, , the scale height 
H, the molecular diffusion coefficient d;y., the eddy 
diffusion (in the ratio Q,), and the intensity of con- 
tinuous external sources and sinks yo). Height varia- 
tions of temperature and gravity are of secondary 
importance. The general solutions given above can read- 
ily be specialized, as was shown by Lettau [21]. 
6. The Border Cases of Maximum Mixture and Maxi- 
mum Separation. A permanent gas constituent is de- 
fined by y = 0. Then, two extreme cases of equation 
(83) exist: 
(¢) The state of maximum mixture, 
(34) 
Q,=0 oc D= oo} » = vo = const. (9d) 
(iz) The state of maximum separation or the Dalton 
atmosphere, 
@=i1 or D=(O3 
4 :), (36) 
(37) 
ae = Ms gTo 
Vs = Vs0 exp (- H [ goT 
= Vs0 CXD. (=232/H), 
mt = 0h mal Gf = Gwe 
Different investigators have described these cases by 
different terms. For instance, case (7) was called “turbu- 
lent mixture” by Bartels [2], “state of convection” by 
G6tz [12], and “adiabatic equilibrium” by Mitra [26]; 
case (22) was called “gravity equilibrium” by Maris 
[24], “separation” by Penndorf [28], ‘‘atmosphere at 
rest” by Regener [31], and “isothermal equilibrium” by 
Mitra [26]. 
Normally, case (2) was attributed to the lower at- 
mosphere. Chapman and Milne [5] introduced the hy- 
pothetical “datum level” as the height below which 
(<) and above which (7) should be verified. Gétz [12] 
and Haurwitz [17] remarked that eddy mixing can 
hardly stop completely at a certain level; there should 
be a gradual change from pronounced to slight mixing 
in the vertical direction. Lettau [21] pomted out that 
molecular diffusion acts everywhere when the effects 
of eddy diffusion vary with elevation, being nowhere 
infinite; in reality 0 < D < » or0 < Q, < 1; (ef. equa- 
tion (24)). 
Conseauently, Q; is termed the separation factor. In 
reality, Y, and 0Q,/dz will vary with elevation. In the 
border cases (z) and (27) 0Q;/dz = 0; then, the vertical 
THE UPPER ATMOSPHERE 
pressure distribution can readily be found. In case (2) 
1 E glo 
P = Prexp( = a ae) (38) 
or, if T o and g = 9 
P = Py exp (—2/H). (39) 
If dv,/dz = O, the vertical diffusion velocity as defined 
by equations (15)—(19) becomes 
din P 
¢; = ¢;-k = ps dsx» 7 ae (40) 
or, if T=7T) and g= q, 
oe ae Us n dex z/H 
oe H No 3 ; (1) 
when C; is undetermined. 
Since ndsx,/m = (dsx.)o = const, c, is inversely pro- 
portional to P/P). Values are given in Table IV in 
which the height variation of ¢, is expressed by the 
varying velocity units. These motions must be thought 
of as compensated by an unlimited degree of vertical 
turbulence such that v; = so . 
TaB_eE LV. Dirrusion VELOCITY* IN THE HYPOTHETICAL STATE 
or Maximum Mixture (H = 8 km, g = gm, T = 7) 
(cm) He He (0) O2 A Velocity units 
0 | 25 20 8 =i —3 em yr! 
40 99 81 32 —4 =12 em day 1 
80 10 8 3 —0.4 —1.2 em min7! 
120 25 20 8 —1 =—3 em sec ! 
200 6 5 2 —0.2 —0.7 km sec7! 
* Positive when directed upward 
The magnitude of c, in Table IV shows that, at and 
above 200 km, the state of maximum mixture will not be 
realized. 
In a Dalton atmosphere, that is, case (7), the pres- 
sure distribution is readily expressed by P as defined by 
(40) and (41): 
Ps = Pso (PLZ) ) 
= a = Pn (PP. 
(42) 
(43) 
The number concentration of the light constituents 
(us < 0) must increase, the heavy constituents (us > 0) 
must decrease with elevation; inasmuch as m = my, , 
oP 
y, v30(P/Po)"* 
Hann [16] first verified this concept in 1903. Since then, 
computations of the composition of the upper atmos- 
phere have been carried out repeatedly. Obviously, 
(44) is deficient with regard to eddy diffusion and the 
case where yo or dy/dz differs from zero. 
7. Partial Separation. If y = 0,0 < D < », 
Vo 
(44) 
