# Captain Walter Fried's Fish Notes March 1944 to January 1945

### Page 3

Tony Sale's
Codes and Ciphers

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3
CX/MSS

Report #F 5 (continued

D = de-chi Z + X = P + Psi
a = proportion of crosses in MT
b = proportion of crosses in Delta P
p(.) = probability of dot
p(x.) = probability of crosses

p(.) in Delta(Psi)ij = b^2 + (1 - b^2)
p(.) in Delta(Psi)'ij = (1 - a) + [b^2+ (1 - b^2)]

It is assumed, for the foregoing relations, that b is the same
for eadh of the Psi wheels. Furthermore, a and b are Invariably selected
so that their product is aproximately equal to one-half. Therefore -

p(.) in Delta(Psi)'ij = b

By definition -
P(.) in Delta Pij = 1/2 + lambda

Therefore
p(.) in Delta Dij = (1/2 + lambda)b + (1/2 - lambda ) (1 - b)

= lambda(2b - 1)

6 Will send additional formulae in the near future. Even though
they represent nothing new it may be convenient to have them systernaticaily
cornpiled.

Walter J. Fried
Capt. Signal Corps.

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