1745 in the administration of the Dutch Stadthouder William IV. Later, the mathematician C. F. Hindenburg studied turning grilles more systematically in 1796. '[they]are often called Fleissner grilles in ignorance of their historical origin.' One form of the Fleissner (or Fleißner) grille makes 16 perforations in an 8x8 grid – 4 holes in each quadrant. If the squares in each quadrant are numbered 1 to 16, all 16 numbers must be used once only. This allows many variations in placing the apertures. The grille has four positions – North, East, South, West. Each position exposes 16 of the 64 squares. The encipherer places the grille on a sheet and writes the first 16 letters of the message. Then, turning the grille through 90 degrees, the second 16 are written, and so on until the grid is filled. It is possible to construct grilles of different dimensions; however, if the number of squares in one quadrant is odd, even if the total is an even number, one quadrant or section must contain an extra perforation. Illustrations of the Fleissner grille often take a 6x6 example for ease of space; the number of apertures in one quadrant is 9, so three quadrants contain 2 apertures and one quadrant must have 3. There is no standard pattern of apertures: they are created by the user, in accordance with the above description, with the intention of producing a good mix. The method gained wide recognition when Jules Verne used a turning grille as a plot device in his novel Mathias Sandorf, published in 1885. Verne had come across the idea in Fleissner's treatise Handbuch der Kryptographie which appeared in 1881. Fleissner Grilles were constructed in various sizes during World War I and were used by the German Army at the end of 1916. Each grille had a different code name:- 5x5 ANNA; 6X6 BERTA; 7X7 CLARA; 8X8 DORA; 9X9 EMIL; 10X10 FRANZ. Their security was weak, and they were withdrawn after four months. Another method of indicating the size of the grille in use was to insert a key code at the start of the cipher text: E = 5; F = 6 and so on. The grille can also be rotated in either direction and the starting position does not need to be NORTH. Clearly the working method is by arrangement between sender and receiver and may be operated in accordance with a