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
Thus aaaab will be as shown 72
Thus 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.
If this plan be adopted, any letter of a word can be translated into numbers which are easily distinguishable, and whose sequence can be seemingly altered, so as to baffle inquisitive eyes, by the addition of any other numbers placed anywhere throughout the cipher. All of these added numbers can easily be discovered and eliminated by the scribe who undertakes the work of decipheration, by means of the additions of odd or even numbers, or by reference to his key. The whole cipher is so rationally exact that any one who knows the principle can make a key in a few minutes.
As I had gone on with my work I was much cheered by certain resemblances or coincidences which presented themselves, linking my new construction with the existing cipher. When I hit upon the values of additions of eight and nine as the component elements of some of the symbols, I felt sure that I was now on the right track. At the completion of my work I was exultant for I felt satisfied in believing that the game was now in my own hands.