General Report on Tunny


24F Page 129

24G     SOME GENERALISED RECTANGLES

In order that the entry in each cell of a rectangle shall be a single number only a single condition can be imposed on the two impulses involved. The condition must therefore be of the form i + j /(known ΔD) = , with or without fixed conditions.

Among the plain i + j rectangles 4+5, 2+5, 1+3, 3+4x, 2+4 have all been tried: indeed at one time it was erroneously supposed that 4+5 would be better than 1+2 (see 24Y(a)).

A peculiar class of i + j rectangle is that of i + 6 rectangles in which entry is the score for ΔZi + Δ Z6 = . i.e. ΔZi = ., entered in a 31 x wi rectangle. In particular if i = 2 all entries lie on the principal diagonal and the rectangle degenerates into .

A rectangle which makes full use of the run 4 = 5./1 = 2 requires 4 entries (3 independent) in each cell (c.f. 25C(e) R1 p 62)

Several members of the section have contemplated "Rectangular parallelepipeds": probably the most favourable is i + j + 6/, ΔZ6 being always dot.

Rectangles may be combined, thus
   ΔΧ1
 
 ΔΧ2
 ΔΧ3
1 + 2
1 + 3
 

but in practice this is done only for key (26C), because in cipher, pips in different rectangles are of unequal value.

(For Motor Rectangles see Appendix 92)


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