for the Measurement of Visibility of Objects. 117 



The special expression for apparent background brightness 

 Lj therefore becomes L x = (1^ . T d ) -\-F d . 



The expression for visibility due to brightness contrast 

 given in a previous section of this paper was 



v »=| 



B„ being defined by the equation 



B 2 + B y = 



(1) 



By superposing the veiling brightness B„ over both Bi and 

 B 2 , the apparent brightness of each is changed until the 

 ratio of the apparent brightness is equal to the constant c. 

 Bi + B,., therefore, is the apparent brightness of the back- 

 ground. Hence 



B 1 +.B B =I,i=(B 1 .T d ) + P <fe 



»d likewise B 2 + B =L 2 =(B 2 . T,) + P,. 



These equations are satisfied if B = P^ and Td— unity. These 

 equations show the exact analogy existing between the con- 

 ditions assumed in the theoretical evaluation of visibility and 

 those conditions that actually occur in nature resulting in 

 lowered visibility. 



It will be well at this point to discuss the direct effect 

 upon visibility of various distributions of the scattering 

 material. Take first the ideal case of no scattering material 

 at any point. The sky wull be black, L 1 = B 1 = 0. The only 

 case of low visibility w r ould be for a perfectly black object, 

 and as such do not exist, visibility would in general be high. 

 In case of a clear atmosphere visibility is low only in case 

 the object matches the sky (dark blue) in colour and bright- 

 ness. Since there is no veiling brightness or absorption of 

 light within the foreground space, visibility would in general 

 be high. Consider now the presence of other scattering- 

 material, such as clouds, mist, fog, dust, &c, located entirely 

 in the background space, and either localized in a given 

 region or uniformly distributed over a considerable distance 

 in the direction of the line of sight. This will operate to 

 change the apparent brightness and colour of the area 1 of 

 the visual field in the lower right hand drawing of fig. G, but 

 will not change the value of the brightness or colour of the 

 object, 2. The change produced may be in any direction, 

 depending upon the nature, amount, and spatial distribution 

 of the scattering material. The presence of such material in 



