question regarding Helen Gaines's Cryptanalysis book



hello,

could anyone help me make sense of one small part of Helen Gaines's
Cryptanalysis book please? i've looked at this over and over again in
various ways and it just isn't making sense / corresponding to what's
written and depicted in the illustration.

on page 171 - 172 three pages into chapter XVIII Periodic Ciphers with
Mixed Alphabets about Figure 138 it says:


The imaginary tableau which is to serve this purpose, using any one of
the four slides in the manner specified, is formed as follows: The
plaintext alphabet, with letters in exactly the order of the slide,
appears at thte top. The 26 cipher alphabets, standing below and
parallel to the plaintext one, are all seen in exactly the order of the
slide, and are shifted, one letter at a time, exactly as the normal
alphabet is shifted in the Vigenère tableau. Thus, exactly as in
Vigenère, the columns of this imaginary tableau are duplicates of the
rows.


there's just so many parts of that that just isn't what's depicted or
doesn't make sense/tally.



"The plaintext alphabet, with letters in exactly the order of the
slide, appears at thte top.":

the illustrations of the imaginary tableaus all four have the standard
alphabet (a, b, c..) in that order running along the top; the normal
alphabet. all four slides do not have that at the top. one does, the
other three either have keywords and/or the alphabet at the top goes
backwards.



"The 26 cipher alphabets, standing below and parallel to the plaintext
one, are all seen in exactly the order of the slide.."

not at all so for the 1st depicted slide. yes for the 2nd. no not at
all for the 3rd and no also for the fourth. so the above statement only
seems correct for the 2nd slide. all the others don't.

OR (another take on that looking at it differently) if when it says
"are all seen in exactly the order of the slide" it means "are all
taken from the order of the slide":

on the first slide's tableau we've got plain text A in key A giving Z.
if you look on slide 1 A corresponds to Z so OK maybe i'm on the right
track now. b corresponds with Y etc. this holds for slide 1. slide 2 it
doesn't as plain text a key A is A on the tableau but A on the slide
corresponds to C... etc.



"and are shifted, one letter at a time, exactly as the normal alphabet
is shifted in the Vigenère tableau."

nope that's not what's in the illustration. if it means shifted not
physically as a whole block to the right but shifted letter by letter
in the normal alphabet or maybe some other alphabet maybe but shifting
as a block to the right is what happens in Vigenère and the book hasn't
really made any distinction there so it really must be intended to mean
as a block; but the illustrations of the imaginary tableau simply don't
bear up to that. what's going on with this bit of the booK?



"Thus, exactly as in Vigenère, the columns of this imaginary tableau
are duplicates of the rows."

again that doesn't tally with what's depicted?! slide 3 it holds true
for. not the others -- you can see that clearly from the diagram.


what on earth is going on with the book here? it just seems to have
gone to pot. very frustrating and annoying. of course it could be my
understanding but i'm taking very simple straight english literally and
it isn't at all tallying.

if anyone can explain it'd be much appreciated.

thanks, ben.
.