Turing's Treatise on the Enigma

Construction of the Turing sheets

The construction of the catalogue depends on making almost simultaneously all the entries corresponding to cases in which the current flows through the same two wires of the M.W. In the partially constructed sheet 5 in Fig 56 some of the diagonals have been filled in fully, and each of these corresponds to a pair of wires of the M.W. As the M.W. rotates the rod points at the right hand ends of the wires move steadily backwards along ‘the diagonal’. We see also that as we move along the filled in diagonal the rod position steadily increases, and the letters in the pairings slide backwards along ‘the diagonal’. Meanwhile the left hand ends of the wires are steadily rotating, so that the middle wheel couplings are sliding along ‘The diagonal’. The entries in the squares are the positions of the L.H.W. where these M.W. couplings can occur, and the slide along the diagonal amounts to a diagonal movement along the short catalogue. Take for instance the filled in diagonal on Fig 56 nearest to the central diagonal. The second entry on this diagonal is 2, 5, 16, 26 which is the entry at HL in Fig 51: next along the diagonal in Fig 56 is the entry 10 which occurs at GM in Fig 51, and so on, the diagonal in Fig 51 being repeated backwards in Fig 56.

This phenomenon may also be explained with reference to the rod square, instead of the wheels: this is really more practical, as we have to make the catalogue up from the rod square. A possible method for making up the catalogue would have been this. In each square on the sheets we write in, in pencil, the M.W. couplings which would be needed to produce the pair at the beginning of the line as M.W. output at the M.W. position given by the heading of the column in which the square occurs. To do this we should have to write down in each line the inverse rods named after the letters at the beginning of the line. This has been done in a part of Fig 56 (top R.H. corner). We should then have square filled with one inverse (M.W.) square, with top and bottom reversed, and another such reversed square somewhat displaced upwards. The entries in green ink could be obtained by


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