General Report on Tunny

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23L Page 98

23L     STATISTICAL SETTING OF THE MOTOR

(a) Rough Method.

When the motor is set by hand it is done after the Ψ's have been set on the de-chi. In statistical setting the motor is set before the Ψ's. The usual method of doing this is by consideration of the number of occurrences of various ΔD letters occurring opposite BM dots, though it is occasionally convenient to make use of the BM crosses also. For example if / is a very good letter in ΔD this will mean that it is even better, relatively, in ΔD opposite BM = .. If the limitation is Χ₂ one would naturally 'look' at places on the tape where Χ₂ = x, in order not to water down the run. In this case the run for the BM may be regarded as a run for the TM and therefore the ΔD frequencies opposite motor dots will be ΔP frequencies.

(b) Expected sigma-ages.

Suppose that the limitation is Χ₂ and that there are r_x, r./'s opposite Χ₂ = x,. in ΔD. Let the text length be N of which N_x, N., letters occur opposite Χ₂ = x,.. Let the number of dots in μ₃₇ be 37D. Let the proportion of /'s in ΔP be p, and let the proportion of /'s in ΔD at motor crosses be q. The expected proportion of /'s in ΔD at TM dots is p and the expected value of q is r./N.. (This idea of using the count of ΔD at Χ₂ = . as a mean of sampling what happens at motor crosses was first suggested in R0, 49. The expected number of /'s in ΔD at Χ₂ = x is

Nx {Dp+ (1 – D)q}

and the expected no. of /'s opposite TM dots is N_xDp

Thus
and

where E.S. means expected score. If the motor is incorrectly set the expected score or average, a, is given by a = Dr_x

and		[see 21(n)]
		in most cases

Therefore expected bulge is
and this is fairly close to
The expected sigma-age is
For example if D = ½, rx = 169, r. = 100

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