SECTION III., 1911. [91] Trans, R.S. C 
Note on the Cosine Law of Radiation. 
By Louis V. Kine, B.A. (Cantab.) Lecturer in Physics, McGill 
University. 
(Presented by Prof. H. T. Barnes, F.R.S.) 
Read May 17, 1911. 
1. It is a well established fact in the theory of light that the in- 
tensity in a parallel beam of homogeneous radiation travelling à distance 
x through an absorbing medium is diminished according to the exponen- 
tial law 
where J, is the intensity over unit cross-section measured at an arbitrary 
origin x=0. «is a constant for the medium, called the coefficient of 
absorption, and depends on the wave-length of the radiation. 
If the radiation emanate from a point-source s, we consider the 
diminution of intensity between the portions S and S + dS of two 
spherical surfaces of radii r and r + dr cut out by a small solid angle w. 
We then have 
SdI = —IdS — ISxdr 
The first term on the right-hand side expresses the diminution of 
intensity per unit cross-section due to the increase with r of Sto S + dS, 
while the second term expresses the diminution of intensity by absorp- 
tion in a distance dr. 
Since S — or’, we have in a uniform medium (x independent of r) 
dl —2dr 
——— —k dr, 
I r 
giving 
Hi as oe aur 
r2 
where C is a constant of integration. 
As long as S remains in the same medium as the point-source s, 
we may write the above in the form 
j > e— kr (2) 
Section III., 1911. 7. 
