22B Page 47
In order to prevent simple statistical recognition of the chi-stream each individual chi pattern is constructed with
(1) As nearly as possible an equal number of dots and crosses in the undifferenced and differenced wheel.
(2) No stretch of 5 or more identical consecutive characters in the undifferenced wheel. (See R5 p 4.)
Alleged chi patterns fulfilling these conditions are said to be 'legal'.
The conditions of legality are most obviously fulfilled by the pattern:
In other cases the pattern was used over shorter stretches.
In the construction of chi patterns no attention was paid to the distribution of dots and crosses in the Δ2 wheel. However, empirical evidence (see R3 p. 18) shows that B1
The fact that Δ2Χi → x can be seen to be a natural result of the conditions of legality and the popularity of the pattern . . x x . . x x
The following table gives the conditions of legality in numerical terms:
|Wheel||Length||No. of crosses in Χ||No. of crosses in ΔΧ||Av. no. of crosses in Δ2Χ|
|20 or 21
15 or 16
14 or 15
11 or 12
12 or 14
The number of legal chis is discussed in 25X, and the frequency of various patterns of 5 and 10 consecutive characters in R3 pp. 125, 126.