General Report on Tunny
24X Page 138
used and the result of the convergence enabled the rest of the message to be set convincingly at a slide. This enabled the worker to feel that things were going well, and can be regarded as a form of significance test. It is a special case of setting another message against the (partial) wheels obtained from a rectangle. In the early days of mechanical wheel-breaking there was a tendency to rely rather too much on this method. At first the allied method of wheel-sliding was used, as it was believed to be more accurate in some ways, and it avoided the use of machine time.
Another test for significance, easy to apply with our improved machines, is to span the message using partial wheels from the rectangle and see if there is an obvious slide. Yet another test is to see if the wheels obtained from the rectangle have outstandingly good Δ2 properties (R3 p 63). This method was most successful when the Δ2 properties were so good that perfect wheels were assumed for both Χ1 and Χ2 and the wheels were broken although the rectangle was considerably below significance.
Useful as all these methods have been, none of them has ever been successful for rectangles falling short of significance by more than 15 decibans, on significance test IV. This test was introduced about the 1st March, 1944. Up to about a fortnight before that time it was thought likely that the result of an accurately converged rectangle really did give the correct pippages of the characters of ΔΧ1 and ΔΧ2. The only important theoretical problem seemed to be to find an estimate of &delta.
It was the failure of the wheel-sliding attempts on Jellyfish which made us suspect that a significance test was necessary. The tests I, II, III, IV were all put forward within about two weeks.
A crude form of significance test IV was designed in July, 1944 for the benefit of the computers (R3 p 23). The idea of this test was that the wheel man should be informed as soon as possible when a rectangle was likely to be quite good. It was observed empirically that the ν terms hardly ever added up to more than 30 decibans for the usual length of text, namely 10168. (See below for the definition of the ν terms.) Further it was assumed somewhat arbitrarily that Σν was inversely proportional* to N. The significance test can be written
* Perhaps inversely proportional to 
would have been a better assumption
Back to General Report on Tunny. Contents.