It will be seen that the underlined Delta-X3 sign is also written into the
cage each time it occurs as a check against inadvertently sliding the cage to
right or left when entering. We now use these 5 cages as a test of the original
assumption of a TM dot. For if the original assumption is correct the ratio of
agreements to disagreements among the signs in each column of the cage will be
(b)^2 + (1-b)^2 to 2b(1-b), or (1+(beta)^2) to (1-(beta)^2) . We therefore
write the number of agreements and the number of disagreements at the bottom of
each column (see Fig.(I) ) and add up the total excess of agreements over
disagreements for all 5 cages. Each excess contributes a factor of
(1+(beta)^2)/(1-(beta)^2) to the theory that the original position has Delta-
PSI'=/ (or Delta-PSI'=8 which merely makes all our Delta-X's inside out). If the
result is poor we scrap the cages, erase the workings and take the next Delta-K
letter as our Delta-PSI'=/ assumption. If it is good we accept the original
assumption. In that case the cage entries each have a probability b of being
correct and can simply be totted up in columns, and written at the bottom as
ringed or unringed numbers according to whether they are scores in favour of the
particular ~ character being dot or cross (see Fig. (I) ). Accepting scores >=2 we
form rudimentary Delta-X wheels with which we de-chi the Delta-K to give
rudimentary Delta-PSI . We examine thus Delta-PSI' to find a character with 3 or
more dots, not counting dots generated by an original underlined Delta-X sign.
This we assume to be another position where Delta-PSI'=/ , and re-apply
the cage test described above. If the proportion of agreements is poor we try
another assumed Delta-PSI'=/ . If it is good we derive Delta-X scores as before
by summing the columns and combine these with the previous scores by straight
addition, provided that the agreement between scores is reasonably good. Again
taking a standard of >=2 we form 5 embryonic Delta-X's from the combined scores,
with which we de-chi the Delta-K to give embryonic Delta-PSI'.
We make a 'count' for Delta-X5, which is the shortest wheel and therefore
will accumulate the most evidence per character. The system of scoring is as
follows. For each L(m,n) in Delta-PSI' (considering only the other 4 impulses)
(where L(m,n) is a letter with m dots and n crosses) we score m-n for the theory
that Delta-PSI'5 = dot, and that therefore Delta-X5 = Delta-K5 at that place.
Thus if the Delta-PSI' letter reads x ? . x in the first 4 impulses, and the
Delta-K letter is Q we score (1) for Delta-X5 s dot. We write in all these scores
through-out the key on a width of 23, and add up the columns to give an improved
Delta-X5. With this we de-chi Delta-K5 in place of the earlier Delta-X5 used, and
count for Delta-X4 . This process continues, going back to Delta-X5 after Delta-
X1 , until all the Delta-X's are completed. These Delta-X's must obviously
integrate into legal undifferenced chis, the even or odd number of crosses in the
Delta-X's will tell us whether the original assumption was a Delta-PSI'/ or 8.
With the undifferenced chis obtained, from the delta-X's we de-chi the un-
differenced K to give PSI', from which we derive the psi wheels by taking out the
43C. THE PRE-NEWMANRY QEP ERA.
(a) Introduction of QEP's.
At the end of October, 1942 Tunny was replaced by
Codfish (Saloniki - Berlin,) and Octopus (see 14A(b)).