Working with digrams is tedious, but will, in the end, give results. Considering, for instance, Fig. 22, its first letter is B. Of letters standing immediately to the right of B, the first one which would form a good digram with it is the R of cell 4. But consideration of a possible digram BR, cells 1-4, shows the check-digram as JN, cells 33-36, and this latter digram is so rare in the language that Meaker did not find it even once in his 10,000-letter text. The next letter known to have an affnity for B is the U of cell 6, but a possible digram BU, cells 1-6, cannot be considered, for the reason that cells 1 and 6 are uncovered by the same opening in the grille. The distance away of the next letters to which B is partial proves frightening, and B is abandoned (it is actually followed by the X of cell 5).
Beginning over, with T of cell 2: The first frequent digram noticed is TR, cells 2-4, and shows the check-digram as JO, cells 33-35. We accept this at once,
| Figure 23 R R T H A O U E E O S B A G D E A E A V E B K U N E S F D I A N K S S S T A D P E B R A N S U K O D X F D N C R E A R R N J A T I Y G O A O A R A O I L I D X T U S O B R A A N L E T S G T E P L M A O T V H R A X E X |
because the letter J must presumably be followed by a vowel, and the only vowel immediately available is this particular O. To extend the accepted TR, we require a vowel. The first one is U, cell 6, and extends the check-digram to TJO, cells 31-33-35, acceptable if T is the final letter of a word. To extend the supposed trigram TRU, we experiment with C of cell 8 and obtain a check-sequence CTJO, cells 29-31-33-35, which is still encouraging. We must know, of course, that no two of the chosen cells are in conflict with each other. The unit we have partially reconstructed is the second one of Fig. 20, and the check-sequence is the fourth unit.
A method somewhat resembling the foregoing consists in writing another block beside the first, in which the letters of the cryptogram are strictly in reversed order. The pattern of the check-sequence will then follow exactly that of the sequence under examination, merely with its letters in reverse order. Still a further suggestion was made by Herbert Raines: In the preparation of the two blocks, one in straight order and the other in reverse order, the writing should be done vertically, with all columns containing four letters. The symmetry can still be found, and any two consecutive plaintext letters are more nearly at their original distance apart — the average 4.
So far, we have been dealing with an isolated unit. In Fig. 23 we have a longer cryptogram, suspected of being a reply to the first. We have set it up in its three blocks, expecting to decipher it with the same grille, but find that something is wrong. To see quickly how the presence of several units modifies the case, suppose we consider some sequence, right or wrong, which is easily examined, such as the AVE on the second row of the first block. Regardless of what the transposition is, if all three of these units are enciphered alike, each of the additional blocks contains a corresponding trigram in exactly the same location as the one under consideration; here we have NES in the second block and ANK in the third. But if the transposition is specifically that of the grille, each one of the three trigrams AVE, NES, ANK, has a check-trigram in its own block. Thus we have the six trigrams listed with their cell-numbers in Fig. 24. Since all of these are acceptable, we should, in practice, be encouraged to accept them; thus, it may be well to say here that, in dealing with all ciphers these false beginnings will quite frequently pitch the decryptor headlong into a solution, through no act of wisdom on his own part.
| Figure 24 Straight Reversed 7 8 9 28 29 30 A V E L I D N E S S O B A N K N L E |
Now, in order to arm ourselves against the larger grilles, which are somewhat more troublesome, and for investigation of cryptograms which may or may not have been accomplished with a grille, suppose we take a look at Ohaver’s mechanical method — that is, his use of paper strips. Picturing any block of 36 cells, numbered consecutively as we saw these in Fig. 21, let us imagine that there is a grille placed over this block, and that this grille has only one opening. If the cell that shows is No. 1, then, at the first turn of the grille, we uncover cell No. 6; at the next turn, cell No. 36; and, at the final turn, cell No. 31. We will call this series of cell-numbers an index, and say that the index for this particular aperture is 1-6-36-31. In the first block of the new cryptogram, the letters which follow this index are R O P T. In the second block, the same index governs the letters U B V L, and, in the third block, A E X H. But if the single opening in our hypothetical grille has exposed cell No. 2, then its index, discovered in the same way, is 2-12-35-25, and the corresponding letters, in the three blocks of this cryptogram are, respectively, R U E A, E I T X, and G S E R. Similarly, each one of the other seven apertures possible in this quarter of the grille has an index, expressible in cell-numbers, and governs a certain series of letters in each cryptogram block. If the grille is the Fleissner, the index for any aperture, in a grille of any size, will always contain four numbers, and will govern four letters per block.
If the grille is a 16-letter one, there will be only four of these indices, beginning in cells 1, 2, 5, 6. If it is a 36-letter grille, there will be nine, beginning in cells 1, 2, 3, 7, 8, 9, 13, 14, 15. A 64-letter grille will have 16, beginning in cells 1, 2, 3, 4, 9, 10, 11, 12, 17, 18, 19, 20, 25, 26, 27, 28; and so on to grilles of 100, 144, etc., letters. After one grows accustomed to the swastika-like route of the open cell, such indices are not at all difficult to prepare at the moment of need; however, many solvers prefer to make them up in sets, once for all, and have them ready as they happen to be wanted. As to the finding of the four letters per block which follow any one index, it is sufficient to remember that the cell numbers, arranged in the manner shown, are also the serial numbers of the letters belonging to any one unit. Thus it is not necessary to write the units into their squares; we need merely number the letters of a unit from 1 to 36, and select those having the desired serial numbers.
Returning, now, to our cryptogram: Our unit appears to be 36, since a division of this kind distributes the vowels uniformly; and a unit of 36 may have been produced with a grille. If so, this grille had 9 apertures, and we need 9 paper strips, one for each aperture. On each strip we are to have: the four index numbers, the four corresponding letters from the first block, the four corresponding letters from the second block, and the four corresponding letters from the third block. But since, in each case, the first three cell-numbers or the first three letters must be repeated, our strip will actually contain seven numbers and twenty-one