# Turing's Treatise on the Enigma

Jeffreys sheets

In cases where the wheel order is unknown it is useful to have the positions and wheel orders where a coupling occurs all catalogued together. In order to make comparison of couplings feasible one puts the catalogue into the form of punched sheets, which can be laid one on top of another. These are known as Jeffreys sheets.

The actual form of the Jeffreys sheets catalogue is this. These are 325 sheets labelled AB, AC,..., AZ, BC,..., BZ,...,...,..., YZ. Each sheet measures 26" x 204/5" plus margins of about three inches. They are divided into columns an inch wide, and lines 4/5" deep. The whole is further subdivided into squares 1/5" x 1/5". The 4/5" x 1" rectangles correspond to the different possible rod positions of the L.H. and M.W. The subdivisions of the rectangles correspond to the twenty possible wheel orders for L.H.W. and M.W. with the five first wheels of the service machine.

Jeffreys-Turing sheets

There is a possibility of speeding up the work with short cribs where the U.K.W. rotates by making the Turing sheets in punched form. Suppose we expand every square of the Turing sheets into a rectangle 7/5" x 4/5" divided into 28 small squares, numbered 1 to 26 with two unused, and for each entry on the Turing sheet punch a hole in the corresponding small square. Then the effect of laying two of the sheets on top of another, in such a way say that the lines VM and CR coincided would be to give us the positions in which the two couplings VM and CR occur when the U.K.W. is in the zero position: we also get the positions in which the couplings slide along qwertzu occur: but these after making a correction for the amount of slide are just the positions at which VM and CR occur including all possible rotations of the U.K.W. One would presumably normally place three sheets on top of another, and there would have to be four different layings (because one could not have the sheets in cylindrical form). For this reason it would be better to have the sheets in double depth, but this would probably be out of the question.

Mr Knox has now found a useful compromise by having two copies of Turing sheets: one of them transparent & obtained by photography. The other perforated.

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