220 THE PRINCIPLES OF SCIENCE. 



sentences, and a library is a combination of books. A 

 library, therefore, is a combination of the fifth order, and 

 the powers of numerical expression would be almost 

 exhausted in attempting to express the number of dis- 

 tinct libraries which might be constructed. The calcu- 

 lation would not be possible, because the union of letters 

 in words, of words in sentences, and of sentences in books, 

 are governed by conditions so complex as to defy calcu- 

 lation. I wish only to point out that there is no limit 

 to the multitude of different sentences which may be de- 

 veloped out of the one difference of ink and paper. Galileo 

 is said to have remarked that all truth is contained in 

 the compass of the alphabet. We might add that it is all 

 contained in the difference of ink and paper. 



One consequence of this power of successive combi- 

 nation is that the simplest signals or marks will suffice 

 to express any information. Francis Bacon proposed 

 for secret writing a biliteral cipher, which resolves all 

 letters .of the alphabet into permutations of the two 

 letters a and b. Thus A was aaaaa, B aaaab, 

 X baba.b, and so on. s And in a similar way, as Bacon 

 clearly saw, any one difference can be made the ground 

 of a code of signals ; we can express, as he says, 

 omnia per omnia. The Morse alphabet uses only a 

 succession of long arid short marks, and other systems 

 of telegraphic language employ right and left strokes. 

 A single lamp obscured at various intervals, long or 

 short, may be made to spell out any words, and with 

 two lamps, distinguished by colour or position, we could 

 at once represent Bacon's biliteral alphabet. Mr. Bab- 

 bage ingeniously suggested that every lighthouse in 

 the world should be made to spell out its own name 

 or number perpetually, by flashes or obscurations of 



8 'Works,' edited by Shaw, vol. i. pp. 141-145, quoted in Rees' 

 * Encyclopaedia/ art. Cipher. 



