Our foregoing cryptogram contains only 80 letters.
| Figure 65 (Cryptogram Frequencies:) R D V S F Z K X 11 10 9 6 5 5 4 4 E T A O N I R S H (Normal Grouping) |
To apply “pointers” in this case, let us begin by considering the individual frequencies of the letters E T A O N I R S H. Their frequencies per 100, according to our own chart, are about as follows: E, 12; T, 10; A, 8; O, 8; N, 7; I, 7; R, 6; S, 7; H, 5. Thus, when frequency alone is considered, E and T have a tendency to draw away from the others and form a private high-frequency group of their own. The distinction among the others is not so clear, and not always the same in all tables; we can only say of these that A and O will always outrank the rest, and will be closely followed by one of the others, usually N, and that H will always rank last.
Thus, the high-frequency group itself tends to sub-divide more or less clearly into three minor groupings: E T — A O N — I R S H. Of these, the first minor group shows one vowel, the second shows two, and the third shows one; the vowels U and Y are not present.
Now if the eight leading letters of our cryptogram, already listed as R D V S F Z K X, be examined in this respect, it is found that these, also, have a tendency toward separation into groups of differing frequency, which more or less correspond to the normal groupings, as indicated roughly in Fig. 65.
Normally, we expect the highest of these subdivisions to contain one vowel and one consonant, specifically E and T. When we find that the corresponding subdivision of the cryptogram contains three letters, the supposition is that one of the vowels, O or A, has moved up into this section; in that case, it has taken part of the frequency of E, making it not at all unlikely that the most frequent letter of the cryptogram will not represent E, and will not, in fact, represent a vowel. And if, as we believe, there are two vowels in the highest section, then we are not likely to find more than one in the central subdivision, especially when we note that it contains only three letters. This would leave the fourth vowel to be found in the third subdivision.
Thus, we have applied pointer No. 1. For the application of pointer No. 2, we turn to the contact data. Comparing first the three letters R D V, and making a careful inspection of all cryptogram letters whose frequency is 3 or lower, we find that, of our three letters, the letter R has 7 contacts with low-frequency letters, the letter D has 9, and the letter V has 8. Thus, the letter R, though having a higher frequency than the other two, has fewer low-frequency contacts than either, and so begins to draw away and assume the aspect of a consonant.
The application of pointers Nos. 3, 4, and 5, provides no satisfactory distinction. But in pointer No. 8, we find a very clear distinction: D and V have touched each other only once, while R has contacted both with a total of six contacts — a great many for a cryptogram of this length.
We decide, then, that R is a consonant, and that D and V are vowels.
Considering the central subdivision, where we expect to find one vowel: Application of pointer No. 2 shows that S has four of the low-frequency contacts, while F has two and Z has only one. Further examination of S by pointer No. 3 shows that it has an unusual variety in its contact-letters. Thus, S would appear to be the vowel here.