graph. The five graphs should now be compared with one another in the hope that some two or more may represent the same alphabet. Such a key-word as DENSE, for instance, makes use twice of the E-alphabet, thus doubling the amount of material in one of the alphabets. In our present case, it is found that the five alphabets are all different. Now, just as in simple substitution, we wish to determine, for each of the five alphabets, what letters are apparently representing vowels, and what letters are more likely to be consonants. For this purpose, some of our “pointers” are still available, and are just as valid as in [Chapter IX].

In Fig. 141 we may see some data and probable conclusions concerning alphabet 1. By frequency alone, the four letters B, G, K, Z, of this alphabet might all be vowels. When variety of contact is considered in conjunction with frequency, it is noted that Z shows no variety on its right. And when contacts with low-frequency

Figure 141
Consideration of Alphabet No. 1
Letter: Frequency: LOW-FREQUENCY CONTACTS VARIETY OF CONTACT Left Right Total* Left Right Total*
B (v) 7 2 3 5 6 6 12
G (v)(= E?) 11 5 3 8 8 8 16
K (v) 6 2 1 3 5 4 9
Z (c) 7 4 - 4 6 2 8
(*) These observations are not absolute, as in simple substitution.

letters are also considered (from information present on sheets 5 and 2; in the figure, frequencies of 1, 2, or 3 were considered to be low), it is found that in this respect, too, the letter Z stands apart from the others. These observations, usually, are mental, and conclusions for any one alphabet must often be modified by what is seen in other alphabets. It may be found satisfactory to begin by selecting only the most obvious vowel, or vowels, in each alphabet, and to circle these, or otherwise indicate them, not only on their own sheets, but also on the two adjacent sheets where they are found again as contact letters. When this has been done, the less obvious vowels may be considered again with an additional “pointer,” whether or not they show too much contact with the more obvious vowels. Fig.

Figure 142
Conclusions for the Five Alphabets
Alphabet No. Vowels Consonants
1 B G K * Z
2 E D K Q U
3 B G M * V
4 V Z K
5 O C Q
(*) When B and G appear as vowels in two different alphabets,
the graphic appearance of these two alphabets (1 and 3) should
be given another inspection. It happens they are not the same.

142 shows, for each alphabet, the probable conclusions which would be reached after examining the contact sheets of Fig. 140, and before any confirmation is attempted. The next step in order is that of indicating them on the cryptogram itself, and the examination of long segments in which no vowels have been marked. At this stage, too, the total number of spotted vowels may be computed to find out how much of the expected 40% is still missing. Up to this point we have nothing new, and nothing particularly difficult. Whether or not the subsequent work is to become difficult depends chiefly upon the amount of material per alphabet, though granting that the presence of probable words materially alters the case of the shorter cryptogram.

If the most frequent of the spotted vowels in each alphabet can be safely assumed as e, the establishment of other vowel-identities can follow the rules of [Chapter IX]: The high-frequency vowel which practically never touches e is o; and the one which follows it is a; vowels of lower frequency may precede or follow e, but no vowel should touch it very often. And if, in addition, the most frequent of the spotted consonants in a given alphabet can be safely assumed as t, then h of the next alphabet will seldom be out of reach. A very material aid here is found in those repeated digrams (and trigrams) whose letters are already labeled as vowels or consonants. We find, for instance, ZD, alphabets 1-2, occurring five times, and with both letters already spotted as consonants. This is very likely to represent th, especially when further examination shows it continued as a repeated ZDB, with B already quite likely to represent the e of alphabet 3. Then the contacts of D, alphabet 2, supposed to represent h, have also pointed out a probable new vowel, A, in alphabet 3. Again, we find KC, alphabets 4-5, occurring six times, and with both letters already spotted as consonants — another probable th — followed three times by G, alphabet 1, already likely to represent e, and twice by B, which could thus represent a (the famous English the, tha). And similarly we might continue with a long demonstration.

Returning, now, to our mechanical operations: Dealing, as we are, with five different alphabets, it becomes imperative that we keep track of substitutes; otherwise, with all of our numerous trials and erasures, it is almost impossible to know what substitutes have been identified and what substitutes are still available for identification. Also, totally apart from this matter of convenience, we shall probably want these five lists of substitutes for use on future cryptograms. This applies to any series of cipher alphabets, whether or not they are in any way related to one another. But it is very seldom indeed that a series of cipher alphabets used in the same cryptogram will be unrelated alphabets. Nearly always, they will have resulted from the use of a slide, and when this is true, the recovery of alphabets and parts of alphabets enables us to reconstruct the slide. The usual plan for recording substitutes is to lay out a plaintext alphabet in A B C order and then, directly below it, to rule off several rows of cells, one row for each cipher alphabet. Thus, any substitute, identified in any alphabet, may be written directly below its presumed original and on the row which corresponds to its particular cipher alphabet. We sometimes speak of such a set-up as a “key-frame” or “key-skeleton,” though a better name, probably, would be “partial tableau.” (Every row, if completed, will show one cipher alphabet of the kind we saw in the partial tableaux of Fig. 138.) Such a “key-frame” for our present cryptogram can be seen in Fig. 143. At (a) of this figure we have the first tentative identifications. The most frequent vowel in each of the first four cipher alphabets has been assumed as e (in practice, the O of alphabet 5 would also be assumed as e). The ZD of alphabets 1-2 and the KC of alphabets 4-5 have both been assumed as th, and after each th, we are trying one letter as a. The five rows of this set-up we may now speak of as “alphabets.” At (b) we are beginning to speculate as to what kind of slide has been used.

Suppose that the cryptogram has been enciphered with a Type II slide. If so, our plaintext alphabet, in the key-frame, is already arranged like the one on the slide; and when this is true, as may be seen by glancing back at Fig. 138, the recovered cipher alphabets will also build up with their letters in exactly the same order as that of the slide, and, in the end, if fully completed, will show a picture of the original sliding alphabet taking five of its possible positions.

Examining the first cipher alphabet of (a), we note that the lineal distance from B to G is 4 positions. If our hypothesis is correct, then the lineal distance BG will have to be 4 positions in all of the other alphabets. The third alphabet contains a B; measuring 4 positions to the right of this letter, we find that G of the third alphabet would fall below i, and thus would be the substitute for i in the third alphabet. To see whether or not this is likely, we return to the contact sheet, where we find that G has already been spotted as a vowel (see the list in Fig. 142). So far, so good. Then, the first cipher alphabet of (a) shows the lineal distance BZ as 19 positions. Returning to the third alphabet, and measuring 19 positions to the right of B, we find that Z, in this alphabet, would fall below x. Examination of the contact chart shows that Z has not been used in the third alphabet, making it satisfactory as the substitute for x. Still good. Again, the third alphabet shows the distance AB as 4 positions. Still pursuing our hypothesis, the first alphabet must also contain an A standing 4 positions to the left of B. If so, it will fall below w, and the frequency of A, in the first alphabet is found to be 2, which is