Manchester Memoirs, Vol. /xiii. {igig) N'o.^ ii 



§14. We shall now discuss the results of the operations just 

 described. 



The result /"i' of operation (/) can be inferred from §§ 4 and 5. 

 The only difference, in fact, lies in the interchanging of the a's and b's. 

 When Q is small, we shall get a series of parallel rows of transparent 

 patches, and the distance /_, between two adjacent rows (the pitch of 

 the rows) is still given by equation {vii), so that p^ = {a^ + b.,) / 2sin (^/2). 

 Assuming that ^1/ (^i + <^i) is greater* than 0*5 (which is usually the 

 case), the areas of the individual patches will be much greater than 

 those discussed in §§4 and 5 ; for the same value oi'O. 



§15. Operation (//') of §13 will give the same results as operation (/), 

 but rotated through 90°. The results of superposing screens corre- 

 sponding to /'i' and Q^\ and finding where light penetrates through 

 the combination, will therefore be as follows : — Wherever a row of 

 transparent patches of F^^ is superposed on a row of Q^^ there will be 

 a semi-transparent square area formed. It must be remembered that 

 these rows are themselves much broader than those discussed in 

 §!^4 and 5. The net result of operations (/) and (/'/) together, following 

 the procedure of operation {v), is therefore to give a series of semi- 

 transparent squares, inside a black square framework. 



>;i6. Operations {Hi) and (iv) of §13 give resuUs which can be 

 obtained from operations {Hi) and {iv) of §3, by interchanging a's and b's. 

 Confining ourselves to small values of 0, we see from equation {tx) 

 that the pitch of the rows of patches in A' and Q^i' is «i + b^. This, 

 however, will be much smaller than z^,, given by equation {vii). 



§17. On carrying out operation (v) of 1:^13 completely, we see that 

 the effects of P^"^ and Q^"^ will be to produce on the semi-transparent 

 square areas described in §15, a sort of additional mottling, resulting in 

 a further diminution of the transparent light. The general character 

 of the pattern obtained by superposing two half-tone screens of the 

 ordinary type is well shown in Figs. 5 and 6 (Fl.II.).\ It is clear that the 

 resulting coarse framework of semi-transparent squares with black 

 edge is an approximate replica (magnified) of the pattern involved in 

 either of the original half-tone screens. This result can be compared 

 with that obtained in gio. The size of the framework obviously varies 

 with Q in exactly the same way as the framework described in §10. 

 It is, however, important to note that the pattern R^ is not the negative 

 of pattern R ; this is on account of the difference in the operations {v) 

 of §3 and §13 respectively. 



* See § 23. 



t Owing to difficulties of reproduction, the effect desired has had to be shown 

 by making use of what are practically " chess-board " screens (see below). 



