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Report #F 46 (continued)
impulses (considered cyclically so that 1 and 5 are adjacent). A dot in
the permutation key means that the permuting factor is operative, a cross
that it is inoperative. The first position of the permutation key represents an
interchange between impulses 1 and 5, the second between 5 and 4,
the third between 4 and 3, the fourth between 3 and 2 and the fifth between
2 and 1. The order in which the permutations take place is significant
and in enciphering they proceed in the left to right order of the key, i.e.
.xxx. would cause 12345 to become 52341 after the first permutation and
25341 after the second. In deciphering the order is reversed and this is
the reason for using the symbol pi^(-1).
17. The most interesting feature of the machine is the motor action.
Each wheel is driven by two of the others. In order to avoid the possibility
of the machine getting into a rut both dots and crosses act as motor
impulses. Wheel A, for example, might~be driven by dots in B and crosses
in C. Either a dot in B or a cross in C will cause it to move and it will
fail to advance only if there is a cross in B and a dot in C. The motor
action is controlled by a portion of the pattern different than the portion
operative for encipherment, but there is a fixed relation. The operative
motor element is behind the enciphering element an interval which is the
nearest integer under 2/3 of the wheel period (or ahead by an interval which
is the nearest integer above 1/3 of the period). In the case of the 69
wheel the figure is exactly 46 (or 23). if, for example, the 47 wheel is
at position 8 for enciphering, its 24th position will control its effect
as a motor wheel.
18. The motor relations, which seem to be invariant, are as follows:
Apparently the reason for having the 4 largest wheels driven by the same
Wheel Driven by
47 65 crosses, 67 dots
53 47 cross6s, 73 dots
59 47 dots, 53 crosses
61 53 dots, 59 dots
64 59 crosses, 61 crosses
65 61 dots, 64 crosses
67 64 dots, 65 dots
69 " "
71 " "
73 " "
motor is to insure a minimum key length of the product of their cycles. The
machine must contain a switch with which the motor action can be thrown on
or off because instances have been observed where the motor is not used. In
such cases each wheel steps forward one position for each letter enciphered.