a=1 aa=3 aaa=5 aaaa=7 aaaaa=9 and the even numbers according to their values stand for "b": b=2 bb=4 bbb=6 bbbb=8 bbbbb=0 and then? Eureka! We have a Biliteral Cipher in which each letter is represented by one, two, or three, numbers; and so the five symbols of the Baconian Biliteral is reduced to three at maximum. Variants of this scheme can of course, with a little ingenuity, be easily reconstructed. APPENDIX C THE RESOLVING OF BACON'S BILITERAL REDUCED TO THREE SYMBOLS IN A NUMBER CIPHER Place in their relative order as appearing in the original arrangement the selected symbols of the Biliteral: a a a a a a a a a b &c Then place opposite each the number arrived at by the application of odd and even figures to represent the numerical values of the symbols "a" and "b." Thus aaaaa will be as shown 9 aaaab will be as shown 72 aaaba will be as shown 521 and so on. Then put in sequence of numerical value. We shall then have: 0. 9. 18. 27. 36. 45. 54. 63. 72. 81. 125. 143. 161. 216. 234. 252. 323. 341. 414. 432. 521. 612. An analysis shows that of these there are two of one figure; eight of two figures; and twelve of three figures. Now as regards the latter series--the symbols composed of three figures--we will find that if we add together the component figures of each of those which begins and ends with an even number they will tot up to nine; but that the total of each of those commencing and ending with an odd number only total up to eight. There are no two of these symbols which clash with one another so as to cause confusion. To fit the alphabet to this cipher the simplest plan is to reserve one symbol (the first--"0") to represent the repetition of a foregoing letter. This would not only enlarge possibilities of writing, but would help to baffle inquiry. There is a distinct purpose in choosing "0" as the symbol of repetition for it can best be spared; it would invite curiosity to begin a number cipher with "0," were it in use in any combination of figures representing a letter. Keep all the other numbers and combinations of numbers for purely alphabetical use. Then take the next five--9 to 45 to represent the vowels. The rest of the alphabet can follow in regular sequence, using up of the triple combinations, first those beginning and ending with even numbers and which tot up to nine, and when these have been exhausted, the others, those beginning and ending with odd numbers and which tot up to eight, in their own sequence.