270 
the momentum of the photon is insignificant, the initial 
momentum determines the velocity of the combined 
particle, and therefore also its kinetic energy. The 
energy released in the photon is the energy of the div- 
ision of AB into A and B, that is, the dissociation or 
ionization potential, less the change (a reduction) of 
the kinetic energy of translation resulting from the 
combination; the amount of this change is not governed 
by the intrinsic nature of A, B, and AB, but depends 
on whatever particular velocities A and B may happen 
to have just before the collision. The chance that in the 
process of combination it will be possible to emit a 
photon of just the right energy thus determined is in 
general small; if the circumstances permit its emission, 
the combination occurs, otherwise the particles A and 
B part again without combining, the collision being an 
elastic one (see § 13). The probability of a radiative 
combination is expressed by means of its effective 
collisional cross section. 
In a combination by three-body collision, the exist- 
ence of two particles after the collision permits the 
ready fulfilment of the two conditions of conservation 
of momentum and of energy, and the chance that com- 
bination will result from the collision is consequently 
higher. But the chance of the occurrence of a triple 
collision is much less, in a rare gas, than that for a two- 
body collision; when particles are sparsely scattered, 
the simultaneous concourse of three particles in one 
small vicinity is naturally much rarer than that of two 
particles. The number of two-body collisions of A and B 
in a gas, per cubic centimetre per second, is anans 
(see § 13); the corresponding number of three-body 
collisions is a’n4nenx; here the n’s denote the numbers 
of particles per cubic centimetre, of the three kinds. 
With increasing height all the n’s will in general de- 
crease, but the triple product will decrease faster than 
the double one. Hence the radiative combinations must 
increase upwards relative to the three-body combina- 
tions; at the confines of the atmosphere the combina- 
tions are predominantly radiative. 
17. Reactions in General; Transference; Activation 
Energy; Resonance. A combination of A and B to form 
AB (whether by two-body or three-body collision) is a 
simple special case of chemical transformation or reac- 
tion; another general type of reaction involves a transfer 
of part of one of the colliding particles to the other 
particle, breaking only one molecular bond, as in 
Oar Ox Op te Oh, Ox- Oly sp lel, (il) 
or a division of both particles and subsequent inter- 
changed unions, as in 
Both of these result from a two-body collision, and 
as there are two bodies also after the collision, energy 
and momentum can readily be conserved. It would be 
expected, therefore, that the efficiency of the processes 
would be greater than that for radiative combination, 
provided of course that they are exothermic (i.e., give 
out heat) and not endothermic (7.e., absorb heat). While 
this is indeed generally true, it is found that transfer 
THE UPPER ATMOSPHERE 
does not occur unless the relative kinetic energy in the 
collision is above a certain limit E', called the activation 
energy. For endothermic reactions it must at least equal 
the difference between the internal energies of the ini- 
tial and final particles. For exothermic reactions, al- 
though (by definition) they give out heat, the activation 
energy is not, in general, zero; its value, expressed in 
calories per NV collisions [81], is generally as much as 
a few kilocalories for reactions of type (1), and some 
tens of kilocalories for reactions of type (2). It can 
easily be seen that this means that at moderate tem- 
peratures the former are far more important than the 
latter. Thus at room temperature the fraction of colli- 
sions of energy 5 kilocalories or above is about 10-*, 
whereas the fraction of energy 50 kilocalories or above 
is only 10-8. 
Besides chemical transfer reactions there are reactions 
in which what is transferred is energy of excitation, 
as in 
Nz + 02 > Nz + 02, (3) 
(where the primes denote excitation), or charge, as in 
O- + Ot >0'+ 0", Ot +xXY—O-+ XYt. 4) 
The efficiency of transfer of excitation is not high unless 
the change of kinetic energy of relative motion is small; 
when this is so there is said to be resonance, and the 
effective cross section for the collision may exceed the 
gas-kinetic cross section. In contrast, transfer of charge 
can occur most readily when the reaction is exothermic 
by a few tens of calories. 
Yet another type of two-body reaction is dissociative 
recombination, as in 
EOS OSC SOR eS, © 
in which the ionization energy released is taken up in 
some form by the fragments of the original molecular 
ion. Quantal arguments have recently been advanced 
which indicate that the mechanism may be extremely 
rapid. Bates and Massey [29] have indeed suggested 
that (5) may be responsible for the observed high (and 
pressure-independent) coefficient of recombination a 
for electrons in the H-layer of the ionosphere. The pres- 
sure-independence of a in this layer implies that the 
recombination occurs by two-body collisions; if the rate 
of combination or reaction between particles of types 
(a) and (6) is expressed by ana , and the process took 
place predominantly by three-body collisions, a would 
be proportional to the total number of particles per unit 
volume, and therefore to the pressure (and inversely 
proportional to the temperature). If both two- and 
three-body collisions were of importance, a would have 
a constant part and a part proportional to the pressure. 
It may be noted that the theory of the rate of recom- 
bination observed in discharge tubes, where the condi- 
tions are subject to control, still involves unexplained 
difficulties. 
CONSTITUENTS AND REACTIONS IN THE 
UPPER ATMOSPHERE 
18. Absorption-Spectral Evidence Regarding Atmos- 
pheric Composition. The absorption spectrum of sun- 
