"Right you are," I acquiesced, "and we are undoubtedly dealing with a system of the fourth order in which the letters are transposed according to a constant prearranged formula. "Let us first consider the simple form; the regular substitution of one letter of the alphabet for another. For example, X always takes the place of E, while B invariably means T, and so on. Such cyphers are easily read by the expert, who works on the principle that all the letters of the English alphabet may be ranked on a numerical scale of average frequency in use. The letter E heads the list; consequently, if any particular symbol predominates in the message it must correspond to that hard-worked vowel. Again, as _the_ is the commonest word group in the language we are quickly able to identify what stands for T and H. But this is quite too transparent a code for serious use." "Then don't waste time over it," said my practical-minded wife. "Old Mr. Thaneford was not a foolish person." I took a long look at the incomprehensible jumble of letters. "There are any number of formulae," I went on, "by means of which we may effect a transposition of letters, the substitution being variable or irregular. For instance, the 'Checkerboard,' invented by the Russian nihilists, and similar devices, most of which depend for secrecy upon single or double key-words. Perhaps the cleverest system in this group is the cypher called by the French, 'Le Chiffre Indéchiffrable.'" "'The Undecypherable Cypher,'" commented Betty. "Sounds rather hopeless." "Well, you can decide for yourself if there is any reasonable possibility of unravelling it, unless you are lucky enough to stumble on the key-word." "Try me," she challenged. "To begin with, you write down the twenty-six letters of the English alphabet in a horizontal line, indenting it the space of a single letter." "Indenting?" "You'll understand when you see the diagram I'm preparing." "Oh, you're making a magic square!" "Yes. Now you repeat the process twenty-five times, the only difference being that all these other lines begin at the left-hand margin, each with a different letter in their strict alphabetical order. Your diagram will then look like this. For the present I am putting it in skeleton form:" A B C D E F G.............W X Y A B C D E F G H.............X Y Z B C D E F G H I.............Y Z A C D E F G H I J.............Z A B D E F G H I J K.............A B C E F G H I J K L.............B C D F G H I J K L M.............C D E ................................. ................................. W X Y Z A B C D.............T U V X Y Z A B C D E.............U V W Y Z A B C D E F.............V W X "Now choose a key-word, or preferably, a key-sentence. For simplicity's sake, we'll take the short word: BEAD, and suppose we wish to send in cypher the message: CAB FEED." "Which is pure nonsense."