lo Lees, On the Superposing of Two Cross-line Screens 



the framework of coarse squares appears to change by nearly i8o*. This 

 is easily understood from the discussion, already given, of ^. 



§12. As a verification of the formula given in {viiib) for the pitch of 

 the coarser framework arising when two screens for which e = o are 

 superposed, a simple test was made. Two screens of equal rulings 

 (loo transparent lines to the inch) were superposed at such an angle as 

 to give a spacing of lo semi-transparent bands to the inch for the 

 resulting coarse pattern of squares. The angle was found to be 

 575° (correct to a quarter of a degree). In this case we have 



a, + ^2 = '^i + /'i = o'oi". 



Also by {viiib), p^= — ^ cosec — = o"i" 



2 2 



Hence by calculation, cosec — = = 20 ; Q=<' 43'. 



2 O'OI 



§13. The effects obtained by superposing two ordinary half-tone 

 screens, i.e., screens of transparent square spaces with black line 

 boundaries, can be now dealt with. For this discussion, further 

 diagrams are unnecessary. Let the two screens be denoted by 

 iS,' and 6",'. We may suppose that ^'i' is the negative of S^ (in §3), 

 and that S^^ is the negative of ^^2, without loss of generality. Thus for 

 .SV, the width of the black bands is to be taken as a, whilst the sides 

 of the transparent squares are to be taken as of a length b. Similarly 

 for S^^, using dashed letters for a and b. 



We consider S^^ as formed by making two sets (AV and \\^) of 

 parallel black bands on a transparent plate, the two sets being at right 

 angles, so as to produce a series of light squares. Similarly, S^ is 

 regarded as formed by the two sets (A^' and F2') of parallel black 

 bands, etc. The final pattern i?' of transparent spaces, obtained by 

 superposing S^" andt 2', and holding the combination up to the light, 

 can be obtained by he following operations (compare with v53) : — 



(;') Make two screens ruled respectively, one with set AV of dark 

 bands, the other with set X/ only. Superpose these screens 

 and find the pattern /*,' of transparent spaces obtained on 

 holding the combination up to the light. 



(//) Perform opn. (/), using F,' and K,'. Let pattern be (2,'. 



(m) „ „ X,^ and Y^\ „ ,, P,\ 



iiv) „ „ X,^ and F,^ „ „ Q^'. 



(v) Superpose these Screens. Wherever light can penetrate through 

 -^iS (?i') -^^2', C--' simultaneously, there is a transparent space 

 of the final pattern R\ Notice that this operation is quite 

 different from operation (v) of ?i3. 



