# Turing's Treatise on the Enigma

This unanalysed catalogue was known to the girls as 'corsets'. In analysing the catalogue we took 25 sheets named A to Z, with E omitted: each sheet had 25 lines, named A to Z with I omitted. Supposing on sheet 13 and line 4 of the corsets we found LVOM as a value of EINS we would enter OM 13.4 on line M of sheet L. In a later form of the catalogue we also made 'existence sheets'. In the existence sheets we would enter M in line V and column O of sheet L. To use the catalogue we first analysed the tetragrammes in the messages according to their first letters. One would then take the A existence sheet and go through all the messages marking the tertragrammes which occured on the existence sheet, and marking against them the entry (e.g. 13.4) from the catalogue. Afterwards one would have to go back to the corsets, and search in the right line for the tetragramme, and work out its position: this was done with a cardboard strip and known as 'snaking'. Having found the position one would have to set up the machine, decipher the tetragramme, verifying that it gave EINS and then continue to decipher and see if one contnued to get sense.

This process has since been greatly improved. Instead of making the corsets off the 'X-machines' we have a machine called the 'test-plate' or 'baby' which typed out the results of enciphering EINS in all positions in a much more convenient form. Also we no longer analyse the groups by hand, but have them punched on cards, together with their position which are then sorted into alphabetical order, and listed. A further improvement is that the test-plate is now made to punch the cards directly.

Roughly, our programme when the wheel order, Ringstellung, and Stecker for a day have been found, is as follows. We make an EINS catalogue, and use it to get out pairs of messages in which the second indicator bigramme of one is the same as the third indicator bigramme of the other. If we have four such cases we have sufficient data about the Grundstellung to be able to find it by means of the Bombe, provided that we have

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