# General Report on Tunny

23E PAGE 86

23E     Χ-SETTING WITH Χ2 LIMITATION

(a) Runs against Χ2 = x.

Bulges are greater when Χ2 = x than when Χ2 = .

To run against Χ2 = x, instead of on the whole text, approximately halves the effective text, so that it will not increase the sigma-age unless the proportional bulge is greater in the ratio to 1 at least; but this is usually so.

It is shown below that 1+2, Χ2 = x will have a greater sigma-age then 1+2 if d, the number of dots in μ37 is less than 28, so that a break-in against Χ2 crosses is preferable unless the dottage is very high. It is fairly obvious that the effect will be greater in subsequent runs, which involve altogether three or more Χ-wheels; in fact, whenever it appears that a message is on Χ2 limitation, all subsequent runs are done against Χ2 = x.

(b) Break-in runs for Χ2 limitation.

There is often a better break-in than either 1+2 Χ2x, or 1+2. On the whole text, excluding random effects, 1 = ., 2 = ., are flat and 1x2x has the same bulge as 1.2.. Against Χ2 = x this is not so, the bulges having the same direction as in ΔP. Against Χ2 = ., ΔP tends to appear reversed.

This suggests, if U58 are very numerous, the one-wheel break-in 2 = Χ2. (since 2x Χ2x, 2. Χ2. are equally strong, there is no point in running them separately); if /'s are very numerous (this is now rare) 2≠Χ2.

It suggests further, the runs 1x2x Χ2x, 1.2. Χ2. or the combined run 1=2x Χ2 [for plugging and switching see 53 J(k)]

Note: the more consistently good run "1x2x Χ2x OR 1.2. Χ2." cannot be done on existing Colossi: it could be done on Super Rob. See R5, p. 100 R0 pp. 42, 43.

The following table is a useful practical guide: its theoretical basis is indicated in 23E(d) below.

 d ≤ 19 20 ≤ d ≤ 27 d ≥ 28 First choice 1+2. Χ1x 1=2x Χ2 1=2x Χ2 Second choice 1=2x Χ2 1+2. Χ1x 1+2

(c) Theoretical not on A, σ, Θ, Φ.

With negligible error A and σ for the runs 2=Χ2, 1=2x Χ2 may be taken as