ABSORPTION OF LIGHT IN GASEOUS MEDIA. 377 
and under standard conditions of pressure and temperature, 
Mo = f.(fi) 
We denote by the expression- 
Kq = 4x^0 = 1 )^A“YNo.(7) 
The eflPect of scattering is to diminish the intensity of the incident radiation, giving 
rise to the phenomenon of attenuation especially noticeable in the diminution of 
intensity of solar radiation in its passage through the earth’s atmosphere. The 
consideration of attenuation as due to scattering alone involves the assumption that 
energy is nowhere accumulating in the gas. In order to give greater generality to 
the application of the analysis we introduce a term expressing the fact that the 
temperature at any point is increasing. 
If E he the intensity of radiation crossing unit area of a plane at a point x in unit 
time, the loss to E in a distance dx in unit time due to the conversion of radiant 
energy into molecular agitation represented by a rise of temperature is of the form 
(iE = —aE dx .(S) 
when a is proportional to the number of molecules per unit volume, i.e., if ao 
refer to standard conditions of pressure and temperature, alct^ = pjpQ. 
In the case of a pure gas a is a quantity depending on the distribution of energy 
between vibrating systems within the molecules and the motions of the molecules 
themselves which define the temperature of a gas on the kinetic theory scale as 
proportional to the mean squares of molecular velocities. 
If p be the density of the gas, s its specific heat at constant pressure and dQ the 
increment of temperature in time dt due to the conversion of radiant energy aE dx dt 
into heat, we have 
= . 
E being measured in calories per unit area normal to the direction of E per second. 
In the case of a gas exposed continuously to external radiation we may suppose the 
temperature to attain to a steady state when dBjdt = 0 and therefore a = 0 in which 
case no energy accumulates in the medium. In the problem of the earth’s atmosphere, 
however, the term a will give rise to a small diurnal variation of temperature 
throughout the atmosphere. The term a may also be taken to include the effect of 
dust in absorbing solar radiation without scattering as well as effects of selective 
absorption if we regard a as a function of tlie wave-length. The existence and 
magnitude of this quantity can he determined by a comparison of theoretical results 
with the results of observation. Actual numerical values for air are obtained in 
Part III. of the present paper. 
3 c 
VOL. ccxii. —A. 
