The Earl of Argyll was executed for supporting the Monmouth Rebellion against the succession of James II in 1685 by leading an expedition to Scotland. While his transposition cipher has been mentioned by authors such as Falconer and Thicknesse, it was only one aspect of his ciphers.
In June 1683, when the Rye House plot was discovered and conspirators were arrested, Argyll's letters in cipher were found taken with Major Holms (A True and Plain Account p.15, 34). The Argylls were one of the most powerful families in Scotland but the Protestant Earl had incurred hostility of James and barely escaped execution of a death sentence (Wikipedia).
While a list of code words and a substitution alphabet were found among the papers taken with Major Holms, the alphabet did not correspond to the numerical cipher used in those letters.
The letters were sent to Scotland, where one Gray of Crichie, employed by a committee for investigation there, was given one of the letters written by the Countess of Argyll to the Earl of Argyll. Plaintext words intermixed with the figures might provide a clue to break the numerical cipher.
Gray found out that two figures represented a letter and that each letter was given three code numbers as follows.
The following is the date line and one section from the letter.
Use of initial letters in the underlying plaintext would have caused difficulty in codebreaking. L. stands for Lorn, L.M. stands for Lord Maitland, W (somehow, the cipher letter is a figure for "u") stands for the Earl or Countess of Argyll or me, yours, etc. D. stands for pronouns such as he, his, their, him, etc. Code words such as Brand and Birch, representing Scotland and England, respectively, are listed in the key found with Major Holms.
The next letter deciphered by Gray was a short one from Argyll to Major Holms. This letter, entirely in figures without breaks, uses only the middle row of the above substitution table, with the other figures used as nulls.
Two letters (a short letter without date and a long letter dated 21 June) from Argyll to Major Holms, describing the conspiratory designs more plainly, were enciphered with more complicated schemes. The fact can be seen by the apparent incoherency of words. The short letter begins thus:
While the numerical cipher could be deciphered by the middle row of the above substitution alphabet, the text does not make sense. Probably these are the letters found on Holms that the celebrated cryptographer John Wallis confessed in 1683 that he could not decipher (James Walker (1932), 'The Secret Service Under Charles II and James II', p.227, n.4, citing S.P. Dom. Car. ii, 427, No. 93; S.P. Dom., Entry Book 68, p.313).
An uncryptographic clue was provided by the postscript of the long letter, in which Argyll said in plaintext that Mr. Butler (signifying one William Spence according to the key found with Major Holms) knew how to write to him. It was about August 1684 that, under torture, Spence provided a copy of the letters deciphered. Although the specific means to decipher was kept secret, the enciphering scheme was discovered by Gray, who was informed that all the words of the letters were significant, meaning that some transposition had been performed on the plaintext.
It was found that the ordering of the words of the long letter was such that 254 words were interposed between the first and second words in sense, and as many between the third and fourth, and so forth; beginning with the second word (in the ciphertext), there were 252 words between that and the next in sense, and so forth; beginning with the third word (in the ciphertext), there were 250 words between that and the next in sense, and so on.
For the short letter, 62 words were interposed between the first and second words in sense, and as many between the third and fourth, and so forth; beginning with the second word (in the ciphertext), there were 60 words between that and the next in sense, and so forth; beginning with the third word (in the ciphertext), there were 58 words between that and the next in sense, and so on.
(By the way, there appears to be some misunderstanding in the description in Fletcher Pratt, Secret and Urgent, pp.149-150 (and hence my earlier writing based thereon): "writing the first word in the first column, then the last in the same column, the first and last of the second column, first and last of the third, first and last of all the columns, then back to the second and the last but one of each.")
Such decreasing intervals can be explained by a boustrophedon transposition route. That is, the writer puts down the words of his message on a sheet with 8 columns and 32 rows (for the case of the short letter). An enciphered message can be created by simply picking up the words in the first column from top to bottom, then the words in the second column from bottom to top, and so forth. To decipher the message, the recipient prepares a sheet with 32 rows and several columns and copies the words of the ciphertext vertically in the first column from top to bottom, then from bottom to top in the second column, and so forth. When all the words have been transcribed, it only remains to read row by row.
The recipient need to know at least the number of rows: 32. The short letter conveys this in an additional line "There rests just 32 lib. ----8 s." The long letter indicates its 8 columns and 128 rows by a postscript "The total Sum is 128 Gil[ders], 8 St[ivers] which will be payed to you by Mr. B."
To allow decipherment, it is necessary that word units can be clearly recognized. In the above example, E.L. is treated as two words at one place and one word in another. "Mr. M" is treated as one word, while "above-named" is separated into two words. The writer should clarify where word breaks occur.
When Charles II died in February 1685 and his catholic brother James succeeded to the throne, the Protestant Duke of Monmouth, a bastard of the late king, rose against James II and Argyll led an expedition to Scotland in support of Monmouth. However, the rebellion was soon crushed and both Argyll and Monmouth were executed.
George Mackenzie, A True and Plain Account of the Discoveries Made in Scotland, of the Late Conspiracies against his Majesty and the Government (1685)