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The wheel cypher
Turn a cylinder of white wood of about 2. Inches diameter & 6. or 8. I. long. bore through it's center a hole
sufficient to receive an iron spindle or axis of 1/8 or 1/4 I. diam. divide the periphery into 26. equal parts
(for the 26. letters of the alphabet) and, with a sharp point, draw parallel lines through all the points of
division, from one end to the other of the cylinder, & trace those lines with ink to make them plain, then cut
the cylinder crosswise into pieces of about 1/6 of an inch thick, they will resemble back-gammon men with plane
sides. number each of them, as they are cut off, on one side, that they may be arrangeable in any order you
please. on the periphery of each, and between the black lines, put all the letters of the alphabet, not in their
established order, but jumbled, & without order, so that no two shall be alike. now string them in their
numerical order on an iron axis, one end of which has a head, and the other a nut and screw; the use of which is
to hold them firm in any given position when you chuse it. they are now ready for use, your correspondent
having a similar cylinder, similarly arranged.
Suppose I have to cypher this phrase. 'your favor of the 22d. is received'.
|I turn the|| 1st.|| wheel till the letter y. presents itself.|
|I turn the|| 2d.|| & place it's o.|| by the side of the y.|| of the 1st. wheel.|
|I turn the|| 3d.|| & place it's u.|| by the side of the o.|| of the 2d.|
| || 4th.|| & place it's r.|| by the side of the u.|| of the 3d.|
| || 5th.|| & place it's f.|| by the side of the r.|| of the 4th.|
| || 6th|| & place it's a.|| by the side of the f.|| of the 5th.|
and so on till I have got all the words of the phrase arranged in one line, fix them with the screw, you will
observe that the cylinder then presents 25. other lines of letters not in any regular series, but jumbled, & without
order or meaning, copy any one of them in the letter to your correspondent. when he receives it, he takes his
cylinder and arranges the wheels so as to present the same jumbled letters in the same order in one line. he then
fixes them with his screw, and examines the other 25. lines and finds one of them presenting him these letters:
"yourfavorofthe22isreceived." which he writes down. as the others will be jumbled & have no meaning, he cannot
mistake the true one intended, so proceed with every other portion of the letter. numbers had better be represented
by letters with dots over them; as for instance by the 6. vowels [A,E,I,O,U,Y] & 4. liquids. [L,M,N,R] because if the
periphery were divided into 36. instead of 26. lines for the numerical, as well as alphabetical characters, it would
increase the trouble of finding the letters on the wheels.
When the cylinder of wheels is fixed with the jumbled alphabets on their peripheries, by only changing the
order of the in the cylinder, an immense variety of different cyphers may be produced for different
correspondents. for whatever be the number of wheels, if you take all the natural numbers from unit to that
inclusive, & multiply them successively into one another, their product will be the number of different
combinations of which the wheels are susceptible, and consequently of the different cyphers they may
form for different correspondents, entirely unintelligible to each other. for though every one possesses
the cylinder, and the alphabets similarly arranged on the wheels, yet if the order be inverted, but one
line, similar through the whole cylinder, can be produced on any two of them. 2. letters can form only 2.
different series, viz. a.b. and b.a. say 1X2 add a 3d. letter, then it may be inverted in each of these two
series as 1st.2d. or 3d. letter of the series, to wit
c.a.b. / c.b.a.
a.c.b. / b.c.a.
a.b.c. / b.a.c.
consequently there will be 6 series = 2X3 or 1X2X3.
add a 4th. letter. as we have seen that 3. letters will make 6. different series, then the 4th. may be inserted
in each of these 6. series, either as the lst.2d.3d. or 4th. letter of the series, consequently there will be 24.
series. = 6X4 = 1X2X3X4.
dcab / cdab / cadb / cabd
dacb / adcb / acdb / acbd
dabc / adbc / abdc / abcd
dcba / cdba / cbda / cbad
dbca / bdca / bcda / bcad
dbac / bdac / badc / bacd
add a 5th. letter. as 4. give 24 series, the 5th. may be inserted in each of these as the lst.2d.3d.4th. or 5th.
letter of the series, consequently there will be 120 = 24 X 5 = 1X2X3X4X5.
add a 6th. letter. as 5. give 120. series, the 6th. may be inserted in each of these as the lst.2d.3d.4th.5th. or 6th.
letter of the series, consequently there will be 720.= 120 x 6 = 1X2X3X4X5X6. and so on to any number.
suppose the cylinder be 6.I. long (which probably will be a convenient length, as it may be spanned between the
middle finger & the thumb of the left hand, while in use) it will contain 36. wheels, & the sum of it's
combinations will be
1 X 2 X 3 X 4 X 5 X 6 X 7 X 8 X 9 X 10 X 11 X 12 X 13 X 14 X 15 X 16 X 17 X 18 X 19 X 20 X 21 X 22 X 23 X 24 X 25 X
26 X 27 X 28 X 29 X 30 X 31 X 32 X 33 X 34 X 35 X 36. = (4648 etc. to 42 places!!) a number of which 41.5705361 is the
Logarithm of which the number is 372 with 39 cyphers [zeros] added to it.
Thomas Jefferson's Wheel Cypher paper, in his handwriting
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