ofSHret Writing. 93 



rerolutioa of the cipher, with all its changes, keys, and permu- 

 tationsr ; and this number amounts to quintillions, that is to say, 

 to practical infinity. 



In order to give an idea of the power of the four additional 

 symbols, and the changes they introduce, it may be stated that 

 with a common key, and invariable symbols, any letter, word, or 

 phrase, can be written but in one manner ; whereas with the 

 present key, but without changing the value of the symbols, the 

 word Europe may be ciphered in 200 different manners ; Asia, 

 consisting of fewer letters, in 16 ; and Emancipation, in 1,280 ; 

 and so on in a certain ratio. Now as each locus of each key 

 gives a new symbol for each letter, it follows that, with one key, 

 admitting all the loci, Europe may be written in 6,000 different 

 manners ; Asia in 480 ; and Emancipation in 41,400. Thus, 

 with the entire cipher, and all its keys and permutations, 

 Emancipation may be written in hundreds of quintillions of 

 different manners. And this estimation is a minimum ; for the 

 four additional symbols, and other contrivances, do, in fact, by 

 giving rise to new combinations, increase the power of each key, 

 not merely in an arithmetical ratio. 



This mode of estimating the power of a cipher may be held as 

 illusory ; for, however the symbols may be multiplied or com- 

 bined, the limits of their import are assigned by the number of 

 letters in the alphabet ; and the utmost number of values which 

 each can have is 26 ; consequently, the chances against detect- 

 ing the value of any given letter, are 25 to 1 ; and the chances 

 against detecting the meaning of any two letters united are 25, 

 25, or 25'?; and, in general, the chances against detecting the 

 meaning of any word or sentence composed of n letters, is 25", 

 Hence the chances against detecting the word emancipation, 

 written in cipher, are 25" ; a number which, to all intents and 

 purposes, is equivalent to that which expresses the modes of 

 writing that word of 12 letters by the entire cipher now under 

 consideration. Whatever be the air of mystery a cipher may 

 assume, if the number of letters in the alphabet it has to ex- 

 press be my and the number of letU rs in the ciphered word or 

 phrase be «, the chances in favour of secrecy are (m — 1)" ; that 



