## The Newmanry History## Part of the General Report on Tunny(1945)## Page 315 |
Tony Sale's Codes and Ciphers |

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- 43c Page 315

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

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

extensions.

43C. THE PRE-NEWMANRY QEP ERA.

(a) Introduction of QEP's.

- At the end of October, 1942 Tunny was replaced by

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