for the Measurement of Visibility of Objects. 113 



Since none of the terms V&, Y h , and Y s can ever be less than 

 zero, it is evident that in order to obtain a value of V = r 

 "Va, Va, and V r s must each be equal to zero. That is, no 

 object can be invisible against a given background unless it 

 matches that background in brightness, hue, and saturation, 

 these conditions being expressed symbolically by the equa- 

 tions B! = B 2 , H 1 =H 2 , and S! = S 2 . 



Natural Causes of Lowered Visibility. 



In considering the visibility of objects at relatively great 

 distances from the observer, situated in natural surroundings 

 and subjected to lighting conditions which depend upon the 

 state of the weather, it becomes necessary to introduce some 

 new factors into the problem. Thus far we have dealt with 

 the brightness of a surface and have assumed that if measured 

 in a given direction the value will be independent of the 

 distance between the surface and the point of observation. 

 This is true in case there is no absorption or emission of light 

 within the space between the surface and the point of obser- 

 vation. In general, this condition cannot be assumed to 

 exist in nature, for the air through which an object is viewed 

 may carry in suspension particles of matter in a more or less 

 finely divided state which may absorb or scatter the light 

 reflected or emitted by the objects viewed, thus causing the 

 apparent brightness from a given point of observation to be 

 less than the real brightness determined at the surface. Such 

 particles, if illuminated either by light reflected or emitted 

 by the objects viewed or by light from other sources, may, 

 by reflecting, refracting, or diffracting this incident light, 

 cause it to enter the eye of the observer. Such particles 

 act, therefore, as sources of light within the space between 

 the object and the observer, thus causing the apparent bright- 

 ness of the surface to be greater than its real value. It is 

 necessary to deal, therefore, with objects distributed in three- 

 dimensional spaces which may be filled with minute particles 

 acting as sources or sinks of light causing the apparent 

 brightness of a surface from a given point of observation at 

 some distance from that surface to be different from the real 

 brightness measured from a point near or at that surface. 

 Thus far we have dealt only with the real values of surface 

 brightness of objects distributed in a space free from such 

 sources and sinks of light. In order to treat the more com- 

 plex problem it is necessary to expand the nomenclature to 

 include the spatial distribution of light as well as of objects. 

 Phil. Mag. S. 6. Vol. 39. No. 229. Jan. 1920. I 



