The substitution of B for G, G for W and K for V completes the cipher. This cipher is difficult only because the cipher alphabet is made up, not haphazard, but scientifically with proper consideration for the natural frequency of occurrence of the letters. In cipher work it is dangerous to neglect proper analysis and jump at conclusions. In the study of Mexican substitution ciphers, several alphabets have been found which are made up in a general way, like the one discussed in this case. Case 6-c.--It is a convenience in dealing with ciphers made up of numbers or conventional signs to substitute arbitrary letters for the numbers and signs. Suppose we have the message: "??2& 45x15 )"8&# &&1x4 %&4&% 6x?&" 8&*x4 6°*°& %"4&" By arbitrary substitution of letters this is made ABBCD EFGHF IJKDL DDHGE MDEDM NGBDA KDOGE NPOPD MAEDA This message is now in convenient shape to handle as Case 6-a and on solution is found to read: ALL PERSONS HAVE BEEN ORDERED TO LEAVE FORTIFIED AREA. In the same way the message 1723 3223 2825 1828 3630 2336 1423 2827 2324 3120 2317 3123 3036 2120 2415 3029 1512 2831 1721 2715 2811 2715 1923 3030 1215 1130 2128 3623 is found to be made up entirely of numbers between 11 and 36 with the numbers 23, 28 and 30 occurring most frequently. This immediately suggests an alphabet made up of the numbers from 11 to 36 inclusive and each cipher group of figures represents two letters. By arbitrary substitution of letters for groups of two numbers we obtain: AB CB DE FD GH BG IB DJ BK LM BA LB HG NM OP HQ PR DL AN JP DS JP TB HH RP SH ND GB and this message is also in shape to handle as Case 6-a. It reads, on solution, SEVEN HUNDRED MEN LEFT YESTERDAY FOR POINTS ON LOWER RIO GRANDE. CHAPTER VII We will now consider the class of substitution ciphers where a number of alphabets are used, the number and choice of alphabets depending on a key word or equivalent and being used periodically throughout the message. In this class belong the methods of Vigenere, Porta, Beaufort, St. Cyr, and many others. These methods date back several hundred years, but variations of them are constantly appearing as new ciphers. The Larrabee cipher, used for communication between government departments, is the Vigenere cipher of the 17th Century. The cipher disk method is practically the Vigenere cipher with reversed alphabets.