__ 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 20^{4}/_{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.

-95-

Back to Turing's Treatise on the Enigma. Chapter V.