fragments .x and x. should have been much more common than the pattern fragments
.. and xx . The pattern fragments actually obtained were found to fulfil this
(e) Extension of the fragments
The next step was the analysis of the fifth impulse of the fourth letter.
This was expected to be more difficult, as either the second or third characters
of the PSI pattern-fragment might be used in any given message. In all the motor
keys of March and April the proportion of dots to crosses was 11 to 26, so the
effect of the third signs of the PSI pattern-fragments was expected to
In some rows of the square it very seldom happened that, two different
characters were entered in the same small square. This evidently meant that the
second and third characters of the corresponding PSI pattern-fragments were the
same. Conversely rows in which there were many cases of different entries in the
same square corresponded to pattern fragments whose second and third characters
were different. Thus many third characters of PSI pattern-fragments were deduced
merely from the quality of the corresponding rows. The analysis was completed as
for the earlier letters, and thus many PSI pattern-fragments were extended to 3
places, and most X pattern-fragments to four places.
There were more ambiguities this time than there were before, because of the
messages in which the second characters of the PSI pattern-fragments were used in
the fourth place, so one or two X characters, and several PSI characters could not
be determined by this analysis. But it was known that the results obtained did
not need to be reversed, (by the argument from the qualities of the rows).
The missing characters in the X pattern-fragments were easily filled in by
using the fact that the fragments had to fit together to form a wheel. Thus for
example the number or fragments four characters long beginning with x.x had to be
equal to the nunber of such fragments ending with x.x .
The same kind of analysis was applied to the first and third impulses, but
with less satisfactory results, owing to the fact that not every possible pattern-
fragment in the corresponding X wheels corresponded to an indicator letter. Thus
although X and PSI fragments were obtained it could not be decided whether or not
these PSI fragments and the parts of the X fragments from the second letter
onwards ought to be reversed, and the argument that the X fragments must fit
together, (with others) to form a wheel was not so readily applicable.
It was now possible to get further characters of some of the X fragments,
and gradually to build up all possible X5 patterns. There were rather less than
10. These were applied in turn to key from two rather corrupt depths, and the May
wheels were completed before the month was quite over. (This was something new).
As the settings for most of the X5 indicator letters ( and some others ) were
known with certainty, the setting of the other May messages was comparatively
(f) June and July, 1942
The wheel patterns for June and July were also broken by the Indicator
method. In June no depth was found and the problem was correspondingly more
difficult. It was necessary to extend the X5 fragments until only one wheel could
be formed from them. In July a good depth (yielding several hundred letters of
key) was intercepted early in the month. The analysis was completed