General Report on Tunny

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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 β_Θ, β'_Θ and PB's (ΔΨ_ij = dot) and (ΔΨ'_ij = dot) by β_ij, 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

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