for the Measurement of Visibility of Objects. Ill 



whether the object to which any visibility value applies is 

 lighter or darker than the background against which it 

 is measured. The visibility value itself must from the very 

 nature of the term be always positive, but by specifying the 

 sign of the first derivative of the visibility function at a given 

 point it can be determined whether such visibility is due to 

 the object being brighter than the background or vice versa. 

 The first derivative of the function 



Y=f(R 2 ) is 2J-, 



which, since the function is a straight line, is equal to the 

 tangent, thus 



<m 2 = tana - 



7 V T\ 



If -r—- is negative it indicates that ^r > & 



d K 2 to B 2 



and therefore that the object is darker than the background. 



In case /T) is positive it indicates that ^-<k 

 a Jtv 2 Jd 2 



and therefore that the object is brighter than the background. 

 In the data presented later in the paper the visibility values 

 will be followed by plus or minus signs, which will be under- 

 stood to indicate the sign of the first derivative of the function 

 at that point and hence show the relative magnitude of B T 

 and B 2 . A convenient way of remembering the significance 

 of these signs will be to consider that the plus sign indicates 

 that the addition of brightness to the background is needed 

 in order to make it match the object, while the minus sign 

 indicates that brightness must be subtracted from the back- 

 ground. In case a visibility value is represented by a point 

 lying upon the branch of negative slope and also upon the 

 branch of positive slope, that is, at the point of intersection 

 of the two lines forming a complete curve of Y for all values 



dV .... . . . 



of R 2 , Tp for that visibilit}^ value is either negative or posi- 

 tive. In such a case B 1 = B 2 , and if the visibility value is 

 greater than zero such visibility must be ascribed to either 

 hue or saturation contrast or to the combined effect of these 

 factors. In order to designate such conditions, the visibility 

 value will be followed by the sign plus or minus, ±. 



As in the previous set of curves, those of fig. 3, only the 

 values of V lying in the first quadrant are real. The curves 

 of fig. 4 show in graphic form the variation of visibility with 



