Experiment 188
F10.2. Wheatstone's cryptograph (1867): an outer ring of 27 places (blank and the 26 letters) and an inner ring of 26 mixed letters, two hands geared so that one turn of the long hand moves the short hand one turn and one letter. For each plaintext letter the long hand is moved forward to it; the short hand then points at the cipher letter. With S the long hand's total steps, the cipher letter is inner[S mod 26] and S mod 27 is the plain letter's place. Inside a known run the steps are known, so the inner places a run uses are known up to one offset per run; the runs are separated by unknown letters, so the second run's offset is free relative to the first (26 cases). Tested: the inner ring free (only coincidences of places check), and the inner ring mixed from any dictionary or vocabulary word (208,651 alphabets, exact); outer ring in standard or KRYPTOS order, blank first or last, hands forward or backward.
What the method does with the 24 known letters.
Wheatstone's 1867 code machine looks like a clock: an outer ring with the alphabet, an inner ring with mixed letters, two hands geared slightly differently. To encode a letter you move the long hand forward to it, and read the letter under the short hand. Because the hands drift apart, the same letter comes out differently each time. Inside EASTNORTHEAST we know exactly how far the hand moves each time, so the known lettersthe known letters Sanborn has confirmed that positions 22 to 34 of the message read EASTNORTHEAST and positions 64 to 74 read BERLINCLOCK. tell us where the code letters must sit on the inner ring.
Words in the margin are defined on the glossary page.
The carved letters go in at the top; the reading comes out at the bottom.
Wheatstone's cryptograph looks like a clock: move the long hand forward to each plain letter and read the letter under the short hand on a mixed inner ring. The hands drift, so repeated letters come out differently.
Inside each known word the hand's steps are known, so the known letters say where each carved letter sits on the inner ring, up to one turn per word. A ring in any order, or mixed from any dictionary word; K4 and twenty scrambled copies.
Nothing fits, not even a ring in any order: in every set-up some carved letter would have to stand at two places of the inner ring, or two letters at one. F10.2 closed.
This experiment produced no candidate: the search ruled everything out before a full text was built. Its product is the bounded negative in section 7.
Redo the method on a few letters with pencil and paper.
The same steps run by the code on the real letters.
outer ring _ABC...Z, hands forward: long-hand steps through EASTNORTHEAST and the inner place each lands on
place 22: E, total steps 0, inner place b + 0, carved F
place 23: A, total steps 23, inner place b + 23, carved L
place 24: S, total steps 41, inner place b + 15, carved R
place 25: T, total steps 42, inner place b + 16, carved V
place 26: N, total steps 63, inner place b + 11, carved Q
place 27: O, total steps 64, inner place b + 12, carved Q
place 28: R, total steps 67, inner place b + 15, carved P
place 29: T, total steps 69, inner place b + 17, carved R
place 30: H, total steps 84, inner place b + 6, carved N
place 31: E, total steps 108, inner place b + 4, carved G
place 32: A, total steps 131, inner place b + 1, carved K
place 33: S, total steps 149, inner place b + 19, carved S
place 34: T, total steps 150, inner place b + 20, carved S
Family, key space, the constraint under test, and the clues it reads.
A10 (alphabets that change after every letter); Wheatstone's cryptograph (1867), an Alberti disk whose advance is set by the plaintext, a hand device a sculptor could have seen. Model as in 'changed', with the plaintext continuous (no blanks between words: the runs are carved as 13 and 11 consecutive letters). Each known letter fixes inner[(b_run + o_t) mod 26] = c_t, o_t known. Statistic: consistent (variant, offset) cells with the free ring and consistent (word, variant) cells with a mixed ring, K4 against 20 shuffled copies; plants.
Written before the run; the result decides it.
With a free inner ring the known letters check little, so consistent cells at the copies' rate; with a word-mixed ring no word fits K4 or the copies. Zero candidates.
The harness's record: candidates, gates, loss, and the negative result this experiment leaves behind.
free inner ring: consistent (variant, offset) K4 0 (copies 0-0) of 208; word-mixed inner ring: K4 0 (copies 0-0); plants [{'variant': 'std/first/bwd', 'inner': 'CALXBDEFGHIJKMNOPQRSTUVWYZ', 'free_offsets': 1, 'mixed_found': True}, {'variant': 'std/first/fwd', 'inner': 'UNDERWFTABCGHIJKLMOPQSVXYZ', 'free_offsets': 1, 'mixed_found': True}]
What was searched, as the harness recorded it.
CALXBDEFGHIJKMNOPQRSTUVWYZUNDERWFTABCGHIJKLMOPQSVXYZHow this experiment sits among the others is on the lineage page; its family's open hypotheses are on the families page.