23M Page 103
In these runs for Ψ1 or Ψ5 as motor runs there is a tendency for the setting to bunch together. This is due to an effect from a coalescence which is described below. As a consequence a given sigma-age is more significant than it would otherwise be.
(b) Statistical Ψ-setting with Χ2 limitation.
Once the T.M. is known, the most powerful Ψ runs are usually those which depend on undifferenced plain language properties. Easily the best letter in undifferenced plain language is 9, so it is not very surprising that one of the five short runs P1 = ., P2 = ., P3 = x, P4 = ., P5 = . is usually successful. These runs are done simultaneously on the five counters with S.T. of 3 or 4 signs. If one of the psi sets there are good runs like 4+5, 1+3x, 1+2, 2+5, and if more than one psi sets there are even more powerful runs. For example 3x/1245 should give a nearly 100% score. However for convenience one may use runs of the form Pij...k = . or x throughout, since the switching is simple and no change in S.T. is required. For statistics of these runs see R5, p. 86. If all five of the short runs fail, the best long runs to try are 1+3x/, 4+5/ and 1+2/. The time taken for along psi run can be cut down by a method called the 'dottery'. This method depends on the fact that the psis usually have good slides on themselves and also the expected sigma-age in the right place is so large (see R0, 41). However if the short runs all fail one should seriously consider the possibility of some of the previous settings being wrong.
A possible effect of a wrong chi setting which is only a good slide for the differenced chi and an antislide for the undifferenced chi is that the corresponding psi may set as an antislide.
When all the wheels have been set the acid test of their correctness is a count of /34 in undifferenced plain language. There should be a patch of about 200 letters with no /34. This test can be used as a method of detecting slides, in order to make the decoding easier. It can also be used for resetting any wheels that have been incorrectly set. Another test of the correctness of the setting is to do some Colossus decoding - the first 9 letters is usual. This helps with the decoding on Tunny later on. The method is to span (n-1) to n (n = 2, 3...) and count P1 = x, P2 = x etc. on the five counters. If the scores are say 00100 then the nth letter is 9. The possibility of decoding in this way on Colossus was not foreseen and is a good example of the flexibility of the machine.
Sometimes the '/34 test' fails because all the psis are antislides. When this happens it is easy to put it right. It can also fail due to a 'smooth
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