It was long ago discovered that, in any cipher of this class, (1) two like groups of letters in the cipher are most probably the result of two like groups of letters of the text enciphered by the same alphabets and (2) the number of letters in one group plus the number of letters to the beginning of the second group is a multiple of the number of alphabets used. It is evident, of course, that we may have similar groups in the cipher which are not the result of enciphering similar groups of the text by the same alphabets but if we take all recurring groups in a message and investigate the number of intervening letters, we will find that the majority of such cases will conform to these two principles. Changing the key word and message to illustrate more clearly the above points, the following is quoted from the Signal Book, 1914, with reference to the use of the cipher disk in preparing a message with a key word. [2] "--This simple disk can be used with a cipher word or, preferably, cipher words, known only to the correspondents.... Using the key word 'disk' to encipher the message 'Artillery commander will order all guns withdrawn,' we will proceed as follows: Write out the message to be enciphered and above it write the key word ... letter over letter, thus: | | | | | | | | | | DISK|DISK|DISK|DISK|DISK|DISK|DISK|DISK|DISK|DISK|DIS ARTI|LLER|YCOM|MAND|ERWI|LLOR|DERA|LLGU|NSWI|THDR|AWN | | | | | | | | | | DRZC|SXOT|FGEY|RIFH|ZRWC|SXET|AEBK|SXMQ|QQWC|XBPT|DMP | | | | | | | | | | "Now bring the 'a' of the upper disk under the first letter of the key word on the lower disk, in this case 'D'. The first letter of the message to be enciphered is 'A': 'd' is found to be the letter connected with 'A', and it is put down as the first cipher letter. The letter 'a' is then brought under 'I' which is the second letter of the key word. 'R' is to be enciphered and 'r' is found to be the second cipher letter.... Proceed in this manner until the last letter of the key word is used and beginning again with the letter 'D', so continue until all letters of the message have been enciphered. Divided into groups of five letters, it will be as follows: "DRZCS XOTFG EYRIF HZRWC SXETA EBKSX MQQQW CKBPT DMF." So much for the Signal Book; now let us examine the above message for pairs or similar groups and count the intervening letters to demonstrate principles (1) and (2); CSX--CSX 16 = 4×4 SX--SX 16 = 4×4 SX--SX 8 = 2×4 WC--WC 16 = 4×4 The key word might contain 2, 4 or 8 letters from the evidence but we may eliminate 2 as unlikely and preparation of frequency tables of each of the four alphabets would soon show that 4 is the correct number.