We will now set down some of the determinations which can be made at once from these frequency tables. Clearly several mixed alphabets have been used. As was to be expected from the analysis of the recurring groups, we note that the frequency tables for alphabets 2 and 6 are of so nearly the same general form that certainly these two alphabets are one and the same. If a Spanish word has been used as a key word, this means that A is probably represented by a vowel in these two alphabets and probably equals A or O, because these two letters are such common finals in Spanish.

1st Alphabet. Probable vowels T, X; probable common consonants, B, I, N, R. We conclude this because of the frequency of occurrence of T and X and the variety of their prefixes and suffixes. On the other hand, B, I, N, and R have for prefixes and suffixes, in a majority of cases, E, F, O and S which are the probable vowels in the 2d and 6th alphabets.

2d and 6th Alphabets.—Probable vowels E, F, O, S; probable common consonants, D, J, Q, U, Y.

3d Alphabet.—Probable vowels C, I, L; probable common consonants A, Q, T, Y.

4th Alphabet.—Probable vowels, E, G, S, T; probable common consonants, C, M, N, P, U, X.

5th Alphabet.—Probable vowels, D, L, U; probable common consonants, C, H, I.

Now this cipher may have been made up from five distinct alphabets with letters chosen at random but it is much more likely to have been prepared with a cipher disk or equivalent, having the regular alphabet on the fixed disk and the mixed alphabet on the movable disk. An equivalent form of apparatus (not using the mixed alphabet in question) is one like this:

Here A of the plain text is enciphered by S and the other letters come as they will. If we move the cipher alphabet one space to the left, A will be enciphered by U and the whole sequence of the alphabet will be changed.

We will therefore use some such form as the above and see if we can insert our letters, as they are determined, in such a way as to have each of the cipher slips identical. We may start thus:

In the 1st alphabet, T and X are placed as A and E respectively on the basis of frequency. In the 2d and 6th alphabets, O and E are placed as A and E respectively on the basis of frequency. In the 4th alphabet, E and S are placed as A and E, and in the 5th, D, U and L are placed as A, E and O for the same reason. We now have an excess of E’s and a deficiency of A’s, which will be corrected if, in the 3d alphabet, we place L, I and C as A, E and O respectively. As a check, this gives us TOLEDO as the key word.

In the second alphabet, O is four letters to the left of E; we may place O four letters to the left of E in the fourth and it comes under V. Note that in the fourth frequency table O (= V) does not occur. In the same way in the fourth alphabet, S is four letters to the right of E; placing it in the same position with respect to E in the second and sixth, we have S under I. We have already noted that S probably represents a vowel in these two alphabets. In this way, we may add D and U to the third alphabet from their position in the fifth with respect to L and we may add I and O to the fifth from their position in the third with respect to L. In every case we check results from the frequency tables and find nothing unlikely in the results.

Now in the second and sixth, let us try Q, D and U as D, N and R respectively. We may add these letters to the third, fourth and fifth alphabets by the method of observing the number of letters to the right or left of some letter already fixed. We now add L to the second, third, fourth and sixth from its position with reference to D and U in the fifth. M is probably D in the fourth and we may add it to each of the alphabets, except the first, in the same way. The table is now complete as shown.

Let us try these letters on the first line of the message and see if some other letters will be self-evident.

Referring to our frequency tables as a check on suppositions, we find everything agrees well enough if we assume the first line to read:

We will now put the newly found letters in the table. The letters previously found are in capitals and the new letters in small letters. The addition of D (=U) to the first alphabet permits us to add all the letters of the other alphabets to the first by the methods already discussed. Each of the other letters may then be added to every alphabet by these methods:

One alphabet checks another in this way and we find everything to fit so far. We will decipher a few words more of the cipher message by the above alphabets and see if we can determine some new letters.

Again referring to the frequency tables the first word is evidently PROCEDENTE. We have also HALLA and MARCHEUSTED. The letter B may be determined from another cipher group, JFBSQDLD (56123456) = POSICION. The letter N may be determined from BETNDQXUC (123456123) = SERRADERO. The letters F and Y may be determined from JCPJOISLYDUASIUPF (23456123456123456)= COMPANIA PARTIENDO. The completed alphabets, arranged as before, are:

The key word is TOLEDO and the completely deciphered message is: