General Report on Tunny
23L Page 101
cross letters. For example, the expected score for the motor run on C3 (not Χ2 limitation) has been found by a semi-empirical method to be about 
times the value obtained by the crude method of assuming flatness against motor crosses (See R5 pp. 26, 32).
We should perhaps emphasise here that with Χ2 limitation there is always the sample of Χ2 = . and complicated formulae can be avoided.
(i) Motor run with only Χ1 and Χ2 set.
The last remark applies even in the extreme case in which the only wheels set are Χ1 and Χ2, when the 4 letter counts against Χ2 = x and . may both be done and the best run or combination of runs may be deduced. There is a single exception to this, namely in the run BM = . /1+2. In this case the behavior of ΔD12 at motor crosses can be calculated easily from the score of /1+2 at Χ2 = x and the result obtained in this way is subject to a much smaller S.D. than the result obtained from the sample opposite Χ2 = .. In theory a similar remark applies however many Χ's are set, but the calculations are usually too complicated.
It was first realised that motor runs of the type BM = . /1+2 may be frequently practicable when the formula for σ of the type 
was found to apply to motor runs (See 21 (n) and R4 pp. 4, 44, 88). The earlier assumption was that σ was 
times as large as it really is. It is found (R4 p. 44) that the expected sigma-age of the run BM = . /1+2 divided by the sigma-age of /1+2 is
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The corresponding formula in the case of Χ2 limitation is (R4, p. 91).
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These expressions are sensitive functions of d. (See R4 p 88).
A peculiar feature of the run BM = . /1+2 is that the top score is not necessarily the most probable, if the additional evidence of the number of BM dots in the whole text is taken into account (R4, 47). (This type of difficulty occurs also in runs against partial wheels - see 25 D(b)) A method of getting round the difficulty is to run BM + /1+2 (See R4, pp. 50, 55, 56, 58, 105). In theory the same difficulty arises in all motor runs, but the effect is usually negligible.
(j) Spanning.
It is sometimes possible to do a more powerful motor run by using only part of the message tape, even if there is no slide, because the message may
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