22H Page 66
there is a T.M. x and no extension of the psis. As the dottage increases more and more of the ΔP stream is reproduced in ΔD, and the stronger is the ΔD count for a given ΔP count.
In fact, ΔD is not flat when ΔΨ'≠/, for the frequency of 8 in ΔΨ' (and even the frequency of V, X, 5, Q, K) is sufficiently high to ensure that a high letter (Θ) in ΔP will make a considerable contribution to the frequency of (Θ + 8) and of (Θ + V) etc. in ΔD. Letters whose frequency in ΔD gets a substantial contribution in this way are known as "Good T.M. x letters" (R0 p. 57).
The relative importance of T.M. x contributions can be seen from the fact that P(ΔΨ' = 8) = ab5 = ½b4 which equals .07 when there are 14 dots and .22 when there are 28 dots. It will be noticed that as the dottage increases, not only does the strength of the T.M. dot and T.M. cross components of ΔΨ' increase, but that relative importance of T.M. cross components gradually increases.
| To summarise we may say | ||
| P (ΔD = Θ) = (1 - a) . P (ΔP = Θ) + aP (ΔD = Θ | TM x) | (H3) | |
| where the great part of the "bulginess" comes from the first term on the right hand side. | ||
(b) ΔD, with limitation.
The T.M. dot positions are concentrated at places where there is a limitation cross, and using (H3) we may say
| P (ΔD = Θ) = [(1 - a) P (ΔP = Θ) + ½a'P (ΔD = Θ | TM x)] + [½P (ΔD = Θ | TM x)] | ||
| where the square brackets cover lim cross and lim dot positions. | ||
| ∴ P (ΔD = Θ | L = .) = P (ΔD = Θ | TM x) | (H4) | |
| P (ΔD = Θ | L = x) = {(1 - a') P (ΔP = Θ) + a'P (ΔD = Θ | TM x)} | (H5) | |
| since (1 - a') = 2(1 - a). | ||
This result demonstrates symbolically that the bulginesss of a ΔD count against limitation cross is essentially greater than the bulginess of the total ΔD count, since what has been left out consists entirely of count against T.M. x, and the proportion of ΔP in the reminder has been doubled.
It might be noticed that the frequency of ΔD letters against
Back to General Report on Tunny. Contents.