were made on the clear texts at some Octopus messages, and the value .63 was
derived for the proportion of dots in Delta-P1 + Delta-P2 averaged over these
messages. This effect seemed to be due, largely to the high proportion of double
letters in Octopus clear, in which long drawn out punctuation signs such as
+++MAA8889 were used.
It followed that, for the sample taken.
P(Delta-D12 = . ) = 0.55
and that this property of D was sufficiently marked for it to have been possible
uniquely to determine the X1 and X2 settings for one of the Octopus messages
whose P had been counted.
(c) Chis set successfully
An attempt was then made to set an unbroken message by this new method of
the "1+2 Break In". A systematic method of testing the 1271 possible Delta-X1 +
Delta-X2 settings had to be devised. The sequence Delta-X2 was added to Delta-Z1
+ Delta-Z2 in an arbitrary setting, the numbers of dots and crosses in Delta-
Z1+Delta-Z2+Delta-X2 corresponding to each position in the 41 period were
tabulated and then this table was compared with each setting of Delta-X1. This
process was carried out for every setting of Delta-X2. It was found convenient for
this process to write Delta-Z1 + Delta-Z2 diagonally into a rectangle, of sides 31
A message of length about 4000 letters, which did not belong to a depth, was
taken, and a significant result was obtained for the first two impulses. The same
process was then applied to some other pairs of impulses and by combining the best
results for all these pairs, the other three X wheels were set. For later
messages it was found sufficient, after X1 and X2 had been set to work only on
pairs of impulses for which the setting of one X wheel was known. The settings
of the other X wheels would then be comparatively simple with good messages.
(d) Motors and Psis set.
When all the X wheels of the first message had been set, the X key was added
to the cipher text, and the sequence D = Z + X , obtained. This sequence was
found to have more than twice the random number of double letters. This was
presumably because both P and PSI' contained a high proportion of double letters.
But nearly all the double letters in the extended PSI key would correspond to
motor dots and therefore most of the double letters in the de-chi would correspond
to motor dots.
It was found that, by an analysis of the distribution of the probable motor
dots the patterns of both motor wheels could be derived. The method used was
analogous to that later used for motor breaking on machines with limitation, and
described in Ch.28.
A controversy broke out in the Research section over the problem of the best
method of continuing the analysis from this point. Some held that the PSI wheels
should be set statistically, by striking out from the de-chi all letters
corresponding to extensions of the PSI-key and then setting the PSI wheels on the
'contracted de-chi' just as the Delta-X wheels had been set on the differenced
cipher message. Others held that attempts should be made to guess the clear at
some point of the de-chi, and thus to obtain a short stretch of extended PSI key,
on which the wheels could easily be set. The best way to do this, they said,
was to consider a place where there were two consecutive dots,