1 6 Lees, On the Superposing of Two Cross -line Screens 



(for S._ alone), /, = /- Z^' = /. {2a^b._ + a,-) / {a^ + b^y. . (xxiv) 

 (for Si and S2 combined), /, = /. (la^i/^ + a,^) 



As I3' is not equal to /— I., it follows that ^' is wt*/ the exact 

 negative of i? (see end of §17). 



For a true half-tone screen, /j = /i' = 7/ 2. Thus 



'^r/(«i + '^.)' = o-5, />., <^x/(«i+ '^i)=i/v/2_= 0-707, ) _ , 

 'Jfi/(«i + '^i)= I - i/s/2 = o-293. j 



In these cases we should have, after passing two such screens, an 

 intensity {/^ or /,') given by 



I^ = /J = o'2^. I . . . . (xxvii) 



§22. We have discussed at some length in the preceding sections 

 the general origin of the coarse square frameworks to be recognised 

 on superposing two half-tone screens of similar type. The question 

 now arises : what variations will the patterns P^ and Q^ (of §3), or 

 /I,' and Q.^ (of §13), produce on their respective final patterns Ji or J?\ 

 as the two original half-tone screens are relatively displaced, keeping 

 constant? 



It has to be recognised that when the respective positions of the two 

 superposed screens are given, the pattern tt-, resulting from T'-. and Q. 

 (or from P^^ and Q2') is defined relatively to the pattern tt^ resulting 

 from Pj and Q^ (or from /'i' and Q^^). 



Fig. 9 shows the centre lines of the transparent bands A', and A\ 

 (inclined at angle d) which together produce pattern /*, of ii3. The 

 corners of the double set of parallelograms here shown are clearly to 

 be regarded as the centres of the transparent spaces of pattern P,. 

 Fig. 10 shows similarly the spacing of the centres of the transparent 

 spaces of pattern F^ (formed by bands A'l and Y^)- In superposing 

 patterns F^ and F^ to form part of the final pattern F (according to 

 the rules laid down in 5^3), obviously the bands A"*! in Fig. 10 must 

 coincide with bands X^ in Fig. 9. One effect of displacing the two 

 original screens 5 and S, keeping constant, is clearly equivalent to 

 sliding Fig. 10 over Fig. 9, still keeping bands A^, in both figures in 

 coincidence. 



We can similarly make diagrams for the centres of the transparent 

 spaces of patterns \Q, and Q.. In superposing these diagrams the 

 bands Y, in both diagrams must coincide {Figs. 11 and 12). Another 

 effect of displacing the two original screens ..S", and 6\, keeping t) 



