into Uniform Undulations of Flat Wavelets. 271 



"We may represent this by fig. 4, or by the upper strip of 

 fig. 6, in which the continuous lines are the crests of the 

 luminous ruling, and the dotted lines are positions o£ cipher 

 illumination. 



Fig. 4. 



i /' 



Part of plane K. 



All other points, L, I 3 , r 4 , &c. in the left-hand half of 

 fig. p, have corresponding points in the right-hand half ; and 

 each such pair, if acting alone, would produce a ruling on 

 plane K represented diagram matically by fig. 4, and therefore 

 with cipher illumination along the dotted lines of fig. 4. 

 Accordingly when they are all present, there is cipher illu- 

 mination along these lines. Moreover, there is maximum 

 illumination at the situation h, since we have made the 

 assumption that all the u f w's reach it in identical phases ; 

 but elsewhere, wherever light is superposed on light, the 

 resultant illumination will range between cipher and that 

 maximum. 



The next step to be taken is to divide the macula into four 

 equal parts by lines parallel to a. Then 

 all its points may be grouped in pairs 

 like I and F, separated by the distance 

 fr/4 and with the line joining them 

 parallel to b. Each such pair of index- 

 points belong to two u f w's which; it' 

 acting alone, would produce a luminous 

 ruling on plane K, parallel to the ruling 

 on fig. 4, with one crest passing through 

 k, but with its positions of cipher illumination as in strip /3 

 of fig. 6 (p. 272). 



So, again, by dividing the macula into eight parts, we find 

 that the illumination it produces on plane K is confined to 

 positions which are not on the dotted lines of strip 7 of tig. (J : 

 and so on. 



Finally, by this process, we learn that 



The same macula 

 as in fig. 3. 



Here is c 



ipher 



