﻿240 Mr. L. V. King on the 



intensity at P due to radiations from an element of volume 

 do is 



dl = N^-^-^'-^-^, 

 r 2 



where r x = PA. 



If dv refer to an element of vokime cut out by the inter- 

 section of spheres of radii r and r-\-dr, and centre at the 

 vertex P of a small cone of solid angle on, we have 



dv = r-codr. 



The total intensity at P per unit cross-section normal to 

 PA due to contributions from all the elements in the solid 





e 



/c(r-r 



) dr } where r 2 = PB. 



° r ' r="— r^{l-r^-^} (4) 



K 



In an actual case X is the coefficient of absorption for air, 

 which is very small, so that we may take e~ Kr ^ to be unity. 

 The exponential term e~ K ^' 2 ~ r ^ represents the fraction of 

 radiation which can penetrate the entire thickness AB. In 

 solid incandescent bodies whose thickness is large compared 

 with a wave-length this fraction is negligible. 



Thus the intensity at P is given very approximately by 



i= N v ■■ m 



i, e. the intensity per unit cross-section of the radiation con- 

 tained in a small solid angle co viewed in any direction PA is 

 proportional to the solid angle co. This is equivalent to stating 

 that the whole surface S appears uniformly bright. Under 

 these conditions we may replace the volume-distribution o£ 

 radiating elements by a distribution of intensity over the 

 surface S. If rfS be an element of surface at A cut out by 

 the cone co, and <f> the angle between PA and the normal 

 at A, we have 



cos 9 

 so that (5) takes the form 



T _ Ns r/S cos <j) 

 L e> if I be the normal intensity at unit distance contributed 



