The Special Fish Report
Albert W. Small (December 1944)
Codes and Ciphers
TOP SECRET Special Fish Report Page 83
And in the case of the "impure character" (mixed crosses and dots)
the probability of another dot is:
P' = p(l-b) + (l-p)b Odds = P'/(1-P')
Back to the Turingery: The delta psi prime sign indicated in the
scoring (from "counting out") was combined with the delta key sign for that
impulse, and the result recorded on the count sheet in terms of the Delta X.
Thus there had now been obtained the Delta X2 count sheet shown
page 91. It was then reasoned that, if there was a X2oneback limitation, scoring
would be heavy in columns immediately following positions where X2 = x.
Therefore X2 = x was written in immediately to the left of each heavily
scoring columns. Immediately below this were recorded the signs of delta X2
obtained from the columns themselves. These two checked, and resulted
in a X2 wheel which was legal, and turned out to be correct.
In the same fashion, the X3 wheel was obtained, using the "counted
out" X2 wheel plus the others. Then putting in this X3 wheel, X4 was "counted out.
Now X1 was tackled, with fear that the data would be insufficient since delta X1
needed data for 41 positions. It so happened that there was only one
position left vacant (see count sheet.) This character was assumed to be a
cross since a string of 4 dots in delta X1 is not too likely. The X1 obtained
was used with the others to give a final check on X5, and the job of breaking
the X's was through.
These wheels, even though not "proved" (by obtaining psi wheels
with the de-chi) were immediately sent to the Newmanry to use in setting
The psi's were broken as psi's are always broken: by inspection
of psi prime streams, and the creation of more psi prime elements by anagramming
where necessary, though such is not usually necessary since the psi's usually
come out easily. For this reason, the psi breaking worksheets are not included.