22C Page 48
22C THE MOTOR STREAM
(a) Definitions.
For a given set of wheel patterns we define
Number of dots in μ_{37} as | d | |
Proportion of dots in μ_{37} as | D ≡ d/37 | |
Proportion of crosses in μ_{37} as | a^{'} ≡ (1 - D) | |
Proportion of crosses in TM as | a | |
Proportion of crosses in μ_{61} as | k |
(b) The motor wheels.
μ_{61} is constructed so that 30 ≤ k ≤ 50 and k ≠37 without more than so far as is known 5 consecutive dots or 15 consecutive crosses.
μ_{37} is constructed so that 14 ≤ d ≤ 28 without more than, so far as is known, 5 consecutive dots or 6 consecutive crosses.
(c) The basic motor.
Theorem I. The BM has a period of 61 x 37 = 2257 | (C1) |
Proof After n complete revolutions of μ_{61}, μ_{37} has moved nk places. The initial position is reached when
nk ≡ 0 (modulo 37) |
Since k ≠ 37, n must be multiple of 37, and the motor returns to its original position after 37 revolutions of μ_{61}.
Theorem II. Proportion of crosses in BM = a' | (C2) |
Proof Since the period of the BM = 2257, each position of μ_{37} occurs with each position of μ_{61} once in each cycle. As each character of μ_{37} occurs 61 times per cycle, the proportion of crosses in μ_{37} is not changed by the extension.
(d) The total motor.
Assuming that the proportion of crosses in the limitation is ½ - which is not strictly true for Χ_{2} or Χ_{2}P_{5} limitation – we have:
Proportion of dots in TM = ½ x proportion of dots in BM
i.e. 1 - a = ½(1 - a') |
Proportion of crosses in TM is comprised of:
Proportion of |
BM dot lim dot ½(1-a')
BM cross lim dot ½a' BM cross lim cross ½a' |
(C3) |
Summary
d/37 = D = 1 - a' = 2 (1 - a) | (C4) |
(e) Double dots in BM.
The proportion of double dots in the BM is empirically 1.1( 1-a')^{2} (se
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