for the Measurement of Visibility of Objects. 105 



necessary to measure the values B x and B„ in any particular 

 case. In practice the veiling glare, B v , is produced artificially 

 by inserting at some convenient point between the eye and 

 the object a semi-transparent surface of some sort, such as 

 sl half-silvered mirror, this surface being illuminated to the 

 desired brightness, B v , by any convenient method. The 

 values of Bi and B^ may be measured by means of a 

 suitable brightness photometer. The visibility of any 

 object, under a fixed set of conditions, may now be specified 

 in definite units directly comparable with the visibility of 

 different objects under the same conditions. 



It is evident that a variation in value of any one of the 

 four terms, E T , E 2 , R l5 and R 2 , will cause a corresponding- 

 change in the value of V&. Visibility may be evaluated, 

 therefore, as a function of any one of these four terms as a 

 variable and the remaining three as constants, thus ; 



Yi=f(Ri) R 2 , E l5 and E 2 constants, 



V&=/(R 2 ) Ri, E l5 and E 2 constants, 



V&= i /(E 1 ) E 2 , R l5 and R 2 constants, 



Y r 6=/(E 2 ) E 1? Ri, and R 2 constants. 



It is entirely possible to evaluate each of these functions, 

 but a consideration of the problem to which the theory is 

 later to be applied shows that this is not necessary and that 

 a different method of evaluation is more directly applicable. 



In the problems to which the results of this theoretical 

 treatment are to be applied the skv forms the background in 

 most of the cases to be considered, and it is impossible in 

 general to treat the sky as a surface. It is not possible, nor 

 is it necessary, to determine independently Uie values of the 

 reflexion factor and illumination in dealing with this sky 

 background. However, its brightness can easily be measured 

 and from the standpoint of brightness the sky may therefore 

 be regarded and treated as a surface. The variables E x and 

 R x are therefore eliminated from this problem, being replaced 

 by a single term, B^ This leaves for consideration the three 

 variables, E 2 , R 2 , and B 1; for each of which as a variable an 

 evaluation of Y b may be formulated. Again, considering 

 conditions in nature, it will be seen that E 2 and B : are not 

 in general independent variables but more or less dependent 

 one upon the other. It is desirable, therefore, to combine 

 these two into a single term, as a function of which visibility 

 may be expressed. This combination of B x and E 2 is best 

 accomplished by taking the ratio of the former to the latter. 

 This ratio is a complete specification of the lighting conditions 



