# General Report on Tunny

22D Page 51

limitations.

The following table gives the frequency in ΔΨ' of each '6-impulse letter'.

 'Letters' with Prop: ag: TM. Prop: ag: TM x Prop: in ΔΨ' 0 crosses 1 (1 - b)6 (1 - a) + a(1 - b)6 1 crosses - b(1 - b)5 ab(1 - b)5 2 crosses - b2(1 - b)4 ab2(1 - b)4 3 crosses - b3(1 - b)3 ab3(1 - b)3 4 crosses - b4(1 - b)2 ab4(1 - b)2 5 crosses - b5(1 - b) ab5(1 - b) 6 crosses - b6 ab6
Fig. 22(III)

 From this table we see that P(ΔΨ' = 9, L = .) = P(ΔΨ' = N, L = x) = ab2(1-b)4

Fig. 22(V) shows ΔΨ' letter counts for Ψ' streams corresponding to d = 27, 24, 21, 18, 15. ΔΨ' counts are given separately for Χ2 lim and Χ2Ψ'1 lim, and in the case of Χ2 lim the counts of ΔΨ' against L = x and L = . are given separately.

An immediate application of the ΔΨ'6 principle to (D7) gives
 ΔΨ'i + L x (D8)

(h) Proportional bulges of letters in ΔΨ' stream.

The proportional bulges of (ΔΨ = Θ) (ΔΨ'= Θ) where Θ is any letter, are denoted by βΘ, β'Θ and PB's (ΔΨij = dot) and (ΔΨ'ij = dot) by βij, β'ij.

A table similar to Fig. 22(III) showing PB (ΔΨ' = Θ) for all values of Θ in terms of β is given in R5 p. 27.
 P(ΔΨ'ij = dot) = ½(1 + β'ij) = b = ½(1+ β) ∴β'ij = β (D9)

The idea of a PB and the introduction of β first occurs on R1 p. 20.

(i) Δ2 characteristics.

It is a fairly good approximation to accept the simple minded results

 Δ2Ψi →. with probability b2 + (1 - b)2 = 2b2 - 2b + 1 Δ2Ψ'i → . with probability ½ Δ2Ψ'ij → . (see R3 p. 22).

(j) The sum of Psi streams.

It is sometimes useful to be able to recognise statistically