cross. In such case, the distance between the two corresponding stretches
of recovered psi is known, and it may be possible from the two stretches
together to fit in all the psi wheels.
As soon as all five psi's are set uniquely, the worksheets are sent
into the "setters' room"* where they compute the approximate position
of the psi's at the beginning of the message, type out a PSI' stream on a
Tunny machine, and drag this stream through the beginning of the message
until they have established the original starting point of the psi's.
Then they decipher about 120 letters of text by anagramming, with which
to set the motor wheels.
On page 63 a table for (DeltaPSI')A plus (DeltaPSI')B characteristics was
The mathematics leading to the tables, and the tables themselves, follow:
It is known that: (Assuming M37=20 dots.)
P(0 crosses in DeltaPSI') = 1-a + a(1-b)^5 = .273 = A0
1/5*P(l crosses in DeltaPSI') = ab(l-b)^4 = .005 = A1
1/10*P(2 crosses in DeltaPSI') = a(b^2)(l-b)^3 = .011 = A2
1/10*P3 = .023 = A3
1/5*P4 = .050 = A4
P5 = .110 = A5
And therefore, since we are after the sum of two delta-psi-
*The room where the original psi setting had just been found for a stretch of
guessed-in plain-text, is called the "breakers' room." This is probably due to
the fact that even when psi patterns are known, it is necessary to "break" a
stretch of psi prime, before psi wheels can be matched to it. But "setters"
have only to set the psi wheels at the beginning of the message, and then set
the motor wheels.