﻿Intelligence and Miscellaneous Articles. 243 



tation. If the brightness at any place the tangent-plane of which 

 prolonged passes between the luminous points is to be sought, it 

 is sufficient to form the potential for those points which lie upon 

 one side of this plane. 



Hence the principle is quite general for surfaces which surround 

 all the sources of light in such a manner that from each of their points 

 all the luminous points can be seen. 



(4) Given a number of luminous points, all of which are within 

 an enclosed surface, if H is the brightness of an element of surface 

 dar, then 



J 



^^=fH^«r=47rS8 + 27rS/+Swi' / 



an J 



when the integral is extended over the whole surface. Here i is the 

 intensity of a source of light which is within, i' that of a source of 

 light which lies in the surface at a place where it is uniformly curved ; 

 i" is the intensity of a luminous point at an angle or edge of the 

 surface ; while w is the piece of the surface which is cut out by the 

 tangent cone laid through such a point from the surface of the sphere 

 of radius unity described about the point. 



This is the analogue of one of the fundamental principles of attrac- 

 tion. But while in that case its accuracy can only be recognized after 

 proof, from the point of view of photometry it is at once clear. \ Hdff is 

 nothing more than the whole quantity of light falling upon the inner 

 side of the surface ; and that this is represented by the expression on 

 the right-hand side requires no further demonstration. 



Given now a number of luminous points, all of which are external 

 to an enclosed surface, the two sides of which are affected by oppo- 

 site signs, if then the brightness at all points of the surface be 

 sought, assuming that the parts causing the shadow are withdrawn 

 from before the parts shaded by the surface itself, then 



JH^<r=0 



when the integral is extended over the entire surface ; and the bright- 

 ness H gives the sign of the illuminated side of the surface. 



In other words, after removing the shading parts, as much light 

 falls upon the originally shaded places as formerly fell upon the 

 shading parts. 



(5) If V is the potential of acting masses, V=C is the equation 

 of a surface upon which the total force is everywhere at right angles. 



In like manner in photometry, if V=2 — , then V=C is a surface 



which has the property that each of its elements is more brightly 

 illuminated than any other element laid through the same point *. 



Such a surface may therefore be conveniently called a surface of 

 greatest brightness, and corresponds to a level-surface. 



(6) If a series of surfaces of greatest brightness are laid in space 

 which correspond to the values V = A, V = A f dA to V=A + rcdA, 

 the brightness with which any element of a surface laid through a 

 point of such a surface is illuminated is inversely proportional to the 



* Of course always with the limitation mentioned under (3). 



