380 
iMR. LOUIS VESSOT KING ON THE SCATTERING AND 
P for unit solid angle. The formula (15) is easily modified to include the case where 
P is without the surface Z. 
It is interesting to point out the analogy which the method of the present section 
bears to the ordinary procedure of potential theory. The function I {x, y, z) 
corresponds to a potential function and is expressed in terms of an external effect 
E (.r, y, z) by means of an integral equation. The total intensity in a small solid 
angle, the effect which is physically measurable, is derived by integrating between 
definite limits along a given direction. 
Further progress towards a solution of (14) is impossible without a number of 
simplifying assumptions which are best considered in dealing with a particular 
problem, such, for instance, as that presented by the effect of the earth’s atmosphere 
in absorbing and sca,ttering the sun’s radiation. 
Part II. 
§ 3. Application to Radiation cmd Absorption in the Earth's Atmosphere. 
In the following sections we shall assume as an approximation that the surface of 
the earth is a plane and that the density is a function of the height above the earth’s 
surface only. We also neglect effects due to reflection from the eartli’s surface and to 
refraction by the earth’s atmosphere. 
ZenitU 
h 
Y y 
Fig. 1. 
The integral equation (14) for the scattered radiation in a direction 0 (fig. l) with the 
direction of the sun and coming from an element of the atmosphere at a height x 
above the earth’s surface, takes the form 
I {x, 0, 0) = fjL {6) E{x) + 
/UL {rr ) —hr— ^ ^ 
■ • ( 16 ) 
where the integral is taken throughout the entire atmosphere. 
In order to simplify the solution of (16) we assume that the scattered radiation 
