# The Special Fish Report

## Albert W. Small (December 1944)

### Page 24

Tony Sale's
Codes and Ciphers

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CX/MSS
TOP SECRET Special Fish Report Page 24

I have already submitted as part of this report the famous

"Significance Test IV of the Black file." Patterns derived from the crude

convergence of the Delta-Z1, Delta-Z2 rectangle, for Delta-X1, are checked for
significance

by means of this test. Actually the theta terms of the test are not computed,
unless

the answers comes out close to the borderline.

It has been found that the theta terms seldom sum to more than 300,000/N.

Therefore the standard for the X1 wheel is taken as:

(2.17 X^2)/N > 219 - 300,000/N

or in simpler terms:

X > 10 (N-1500)^1/2

In the above, X = Sum |xi| wherein xi are the excesses of dots over crosses

in the resultant pattern.

From this formula in simplest terms is calculated a value for X

given each length N, which must be equalled or exceeded by the Delta-X1 wheel

before the rectangle is called significant.

The above formula is currently being "argued out;" some persons

favour substituting 1271 for the value 1500 claiming the latter too high;

others favour the older rule, X>(80N)^1/2. But the one given is the one

now in use, and is referred to in one of the screeds sent by Capt. Fried

as "the better rule." When the computors have converged a pattern to

this point they then turn the rectangle over to the wheel breakers.

A table showing results obtained with significant rectangles

follows. Jellyfish had not "come out" for six weeks, and Gurnard had "come out"

well. The table to follow compares the two.

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