12 Lees, Oh the Superposing of Two Cross-line Screens 



iJiS. In the above ^^.^13 to 17 we have assumed that (^2 + ^2) is a 

 multiple of (a, +^,). It is easy to see, however, that when this is not 

 the case, the formula given in {xv) must be used for /.• Thus with 

 R\ as with A", the coarseness of the main pattern of squares does not 

 become infinite, as (y approaches o'. The orientation of the pattern is 

 also given by the angle ^ discussed in i$i i. 



^19. It has been shown in v$.§io and 17 that the resultant pattern 

 -R. or R^ resembles the original screens from which it was produced. 

 The same is true of the pattern resulting when two process screens of 

 the " chess board " variety are superposed. The argument is very 



Fig- 7- 



simple. Let Fig. 7 represent part of a " chess board " screen, the 

 squares being of side a,. This screen may be regarded as either 



(a) a square framework (of side a, ^2) of transparent lines like 

 AB (of periodically varying width), surrounding a dark 

 interior, 

 or (/i) a square framework (of side a, J 2) of black lines like CD (of 

 periodically varying width), surrounding a transparent 

 interior. 



On superposing two such screens, of sides «, and <r. respectively, 

 5jio shows us that the resultant pattern will follow («) in its features, 



