General Report on Tunny
25D Page 162
a run, say 5JUQ03 produces a new ΔΧ3, whence a new ΔΧ4 and so on.
Because the characters of both ΔΧ3, and ΔΧ4 are arbitrary the significance value of 
is not 5.3 or 5.5 but approximately 8.4, as for a 3+4x/ rectangle (24X, 24Y).
This is easily overlooked, because the individual runs are short.
In particular if the runs are 4+/3x1x2x and 3+/4X1x2x, the two wheel convergence is identical with the convergence of a 3+4x/1x2x conditional rectangle. Indeed every rectangle convergence is a two-wheel convergence, for, as is easily seen, "taking a wheel through a rectangle" is really a short wheel-breaking run. The only advantage of an actual rectangle, apart from the fact that computer time may be cheaper than Colossus time, is that it provides powerful methods, e.g. flagging, for starting the convergence. In a two wheel convergence a good start is often available from the high scoring characters of a not quite significant short run.
A popular run for two wheel convergence is 4=5=/1=2. The rectangle which fully corresponds to this is not an ordinary rectangle, but has four entries in each cell viz.
| (. .) - (x .), (. x), (. .) - (. x), (x .) - (x x) |
| where, e.g. (. x) means |
|
ΔD1 = ΔD2. |
(R5 pp 35, 95, 96 (but the method is of course much older.))
25D PARTICULAR METHODS
(a) Doubts.
The use of incomplete wheels is unavoidable; indeed it is rarely wise to use any character, the evidence for which is less than 10 decibans. A character not assumed to be either dot or cross is said to be 'doubted': the evidence of letters of cipher against such characters is ignored ('running on doubted wheels'). This is effected on Colossus by means of the special pattern trigger of the wheel-breaking panel (formerly by means of trigger e'); the doubted characters are made crosses in the special patterns and the condition imposed: special pattern = dot (or vice versa if the doubts are very numerous).
Evidence using letters against doubted characters is obtainable from
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