General Report on Tunny
24B Page 114
(b) The 1 + 2 rectangle.
It will be convenient to describe a rectangle for two particular wheels. In fact in chi-breaking from cipher the 1 + 2 rectangle was used almost exclusively. (For other rectangles see 24F, 24G).
ΔZ1 + ΔZ2 + ΔΧ1 + ΔΧ2= ΔD1 + ΔD2 which →.
Thus any place of Z would contribute favourably to the ΔD count if ΔΧ1 + ΔΧ2 had the same sign as ΔZ1 + ΔZ2, which is evidence that it has the same sign as ΔZ1 + ΔZ2 has: the magnitude of this evidence is called a pip.
Consider all the places of the cipher which are opposite the ith character of ΔΧ1 and the jth character of ΔΧ2: if there are u of these where ΔZ1 + ΔZ2 = ., and v where ΔZ1 + ΔZ2 = x the net evidence that ΔΧ1i + ΔΧ2j is a dot is u - v pips.
This score is entered in the ith column and jth row of a 41 x 31 rectangle (+x as 
, -x as x).
The substance of the foregoing is that the 41 columns of the rectangle correspond to the characters of ΔΧ1, the 31 rows to the characters of ΔΧ2. The entry in any cell (i,j) in the excess of contributory places where ΔZ1 + ΔZ2 = . over places where ΔZ1 + ΔZ2 = x, and measures the evidence that ΔΧ1 + ΔΧ2 is a dot.
The rectangle so constructed is afterward converged, i.e. wheels ΔΧ1, ΔΧ2 are found, to agree as well as possible with the evidence for ΔΧ1 + ΔΧ2.
24B MAKING AND ENTERING RECTANGLES
(a) The entry in each cell of the rectangle is found by determining which places of Z correspond to it, and then taking the excess of such places where ΔZ1 + ΔZ2 = . over those where ΔZ1 + ΔZ2 = x.
To find which places correspond to any cell remember that Z and the chis move together. If all the places of Z are numbered successively 1, 2, 3 ..., these will appear in order on the diagonal
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