124 | 12 BOmBES
tested simultaneously without any parts of the machine moving’.^70 Running a job on Victory
without simultaneous scanning normally took about a week, and it was quickly realized that,
the official history recorded, ‘some radical change was still required for the work to be of any
assistance in the War effort’.^71
Turing was working on a partly electronic method for implementing simultaneous scanning
when Welchman came up with an idea for an additional piece of hardware called the ‘diagonal
board’. The wiring of the diagonal board (which was not electronic) reflected the fact that the
plugboard connections were always reciprocal, in the sense that if the plugboard replaced let-
ter X by letter Y, then it also replaced the letter Y by X (where X and Y are any letters). Turing
told Joan Clarke that Welchman originally proposed the diagonal board ‘simply to provide
entry’ into additional chains.^72 It was Turing who realized that the diagonal board could be
used to implement simultaneous scanning. ‘I remember Turing jumping up with the remark
that “the diagonal board will give us simultaneous scanning” and rushing across to Hut 6 to tell
Welchman’, Clarke said.^73 Turing’s inspired contribution, Clarke went on to explain, was ‘the
realization that a wrong stecker assumption for the input letter would imply all wrong steckers,
if one allowed an unlimited number of re-entries into the chain’.^74 Because of these implica-
tions, testing a single (wrong) letter had the effect of testing all letters simultaneously.
The wiring of the diagonal board also enabled the bombe to exploit deductions about the
plugboard-mates of intermediate letters in a crib loop.^75 This added considerable extra power
to the process of elimination, power that reduced the stops to a manageable number even when
cribs containing only one or two loops were used. Without the diagonal board the bombe
needed cribs containing three or more loops, because cribs with fewer loops would usually pro-
duce excessively many stops.^76 Welchman’s invention of the diagonal board was in fact crucial.
It came, Turing said, ‘at a time when it was clear that very much shorter cribs would have to be
worked than could be managed’—that is, managed by a bombe without the diagonal board.^77
The diagonal board became a standard component of all bombes from August 1940.
Simultaneous scanning produced a stupendous twenty-six-fold speed-up, with the bombe tak-
ing only a fraction of a second to test all twenty-six letters, before the fastest-moving drums
stepped on to their next position.^78 What took a week on Victory could be done in about 6½
hours with simultaneous scanning. It was not until simultaneous scanning was introduced that
the bombe became a thoroughly practical weapon against Enigma.
What if the diagonal board had never been invented? The earlier partly electronic scheme
for achieving simultaneous scanning ‘would probably have worked’, Turing said, after ‘a few
more months experimenting’.^79 But this delay would not have been the only cost. Without the
diagonal board the bombe would in general have been limited to attacking messages containing
at least three loops. To break the whole day’s traffic on a given Enigma network, the codebreak-
ers would have needed at least one message sent on that day to contain three or four loops.
Assuming that this message succumbed to the bombe’s analysis, the codebreakers could then
use the resulting information to crack the rest of the day’s traffic on that network. Even if a
network produced messages with the required number of loops only every two or three days
on average, this might still have been enough for the codebreakers to keep on top of the traffic,
although coverage would have been patchier.
When attempting to assess how useful the bombes would have been if the diagonal board had
never been invented, the key question is: how often were messages with the necessary number
of loops intercepted? Messages containing three or more loops were certainly common enough
in 1944 to be dealt with in a training manual issued to American bombe operators at Eastcote;