﻿586 Dr. N. Campbell and Mr. B. P. Dud ding cm 



the P.S. to the surface makes with its normal. Then we 

 find as a matter o£ experimental fact that, when the inverse- 

 square law is true, <£> is proportional to S ; and that if we 



form the expression - , the order of this expression for 



r 8 cos a r 



the different sources is the order of their brightnesses 

 directly perceived ; the source for which the expression is 

 the greater is always the brighter. That is equivalent to 

 saying that this expression is a measure of the brightness ; 

 and accordingly we define the brightness of: the surface, now 

 a magnitude, as the intensity of the light emitted by it in a 

 given direction divided by the area of the projection of the 

 surface on a plane normal to the direction of viewing. 



In general brightness so defined is a function of the 

 angle a, in accordance with the fact that surfaces in general 

 alter in brightness when the direction of viewing is changed. 

 But there are certain surfaces, which are those most nearly 

 matt, the brightness of which does not depend greatly on 

 that angle. For snch surfaces, the intensity of the light 

 emitted at an^le a. is proportional to cos a ; i. e., Lambert's 

 law is true. When Lambert's law is not true, if brightness 

 is to be defined uniquely, some convention concerning the 

 relevant values of a must be introduced. It is usual* to 

 define brightness only for a = ; another course, in some 

 ways more satisfactory, would be to take the mean brightness 

 over the whole range of a. 



So far we have regarded the measurement of the intensity 

 of the light emitted by a known area of a bright surface as a 

 mere means of measuring the brightness directly perceived. 

 But for some purposes this intensity is important on its own 

 account, e.g., when we are considering the illumination that 

 the bright surface would produce. For the purpose of this 

 illumination it is immaterial whether the bright surface is or 

 is not uniformly bright ; so long as the intensity of the light 

 emitted by unit area is the same, it does not matter whether 

 the light comes from all parts of the surface or only from a 

 few specks on it. Accordingly, it has become customary 

 (though we think the custom unfortunate) to speak of all 

 surfaces as equally bright so long as the intensity of the light 

 from them per unit area (or possibly unit projected area) is 

 the same, regardless of the fact that the apparent brightness 

 of the surfaces, the quality directly perceived, is utterly 

 different. 



10. There remain to be considered certain subsidiary laws, 



* Cf. Winkelman, Handbuch der Physik, Optik, p. 747 (2nd Ed.). 



