language the same clear letter was being repeated over and over again. If this
hypothesis were correct, each separate impulse of the passage would either agree
with, or else be the complete reverse of, the corresponding impulse of the
extended PSI key.
The hypothesis was tested by comparing the actual PSI wheels with the
various impulses. It was found that complete agreement could be secured by taking
the underlying clear language to consist of a long sequence of Z's followed by a
long sequence or 9's. The PSI wheels were thus set and the motor key could now
be derived by decoding the message.
This was the first example of hand psi-setting from a de-chi with an unknown
motor key, but the de-chi was an exceptionally easy one.
The decoding process was applied to both messages of the 'depth' on the
assumption, soon verified, that the initial settings of the wheels were the same
for both messages. The two motor keys were different however, and the difference
could only be explained on the assumption that the motor key was a function of the
clear language, or cipher, as well as of the initial state of the machine.
The nature of the plain language effect was deduced by studying the actual
plain language near the places in which the two motor keys differed. It was found
that when they differed, there was always a difference in the two clear texts
two letters back, in the fifth impulse.
Further investigation revealed that when there was a difference in the motor
key, the motor sign in each message was given by the sum of the fifth impulse of
the plain language two places back (denoted by P5twoback ) and the second X sign
of one place back ( denoted by X2oneback ). This suggested that the total motor
key was obtained from the Basic Motor in conjunction with the limitation
(P5twoback + X2oneback ). This 'basic motor' could be determined whenever
P5twoback + X2oneback had the value cross. The fragmentary basic motor was
written out on a width of 61 and broken by the methods already devised by the
Testery for dealing with motors having the X2oneback limitation.