In 1737, John Davys published An Essay on the Art of Decyphering (price: 1s 6d.).
Davys was, according to his own account, was versed in the art of deciphering from his youth, and could produce witnesses of undoubted reputation, who had tried him with letters in cipher, generally to find his deciphering to be correct (p.53). "About 36 Years ago", when he was a member of Magdalen College in Oxford, he deciphered two letters from the King of France to his minister at the Ottoman Porte (printed in Sir Paul Rycaut, History of the Turks, ii) (p.46). During the examination (1723) of the Atterbury Plot, he verified the deciphering of the letters produced by the government (p.36-39). For The Life of James Duke of Ormond, edited by Thomas Carte (1736), he deciphered some relevant papers (one instance of which was done in 1734, according to p.32). Carte describes Davys as follows.
Unlike John Falconer's Cryptomenysis Patefacta (1685), which described various kinds of ciphers and deciphering thereof (cf. another article), Davys focuses on numerical code, which was the mainstream cipher at the time. His aim was to inform the public that the art of deciphering had a solid basis, despite some arguments circulated at the time that deciphering was nothing but conjectures. In particular, Davys pointedly denounces an article in London Journal (10 August 1723) written under a pseudonym of Britannicus. (Part of Britannicus' article is quoted in Biographia Britannica p.542).
To counter Britannicus' statement that John Wallis (see another article) could never thought to be the father of deciphering, Davys describes Wallis' works in the historical context and prints the whole text of the introduction attached to the collection of deciphered papers that Wallis deposited in a public library in 1653. Quotations of Wallis in passim suggest influence from the mathematician. Although Davys was in Oxford "about 36 years ago", possibly overlapping the last years of Wallis, Savilian professor at Oxford, during his life, his quotations are all taken from printed sources, which suggests he did not personally receive education at the hands of Wallis. (For instance, reference to Leibniz' letter of 29 December 1698 suggests he did not know the letter of 24 November 1699 (see another article).)
Davys prints several ciphertexts actually used in history, rather than ones created for the purpose of illustration. For example, Davys presents his own deciphering of a letter that Wallis left undeciphered for the reader, in compensation of which Davys provides a ciphertext related to the Duke of Ormonde for exercise for the reader (see aonther article). The Appendix carries a ciphertext at the time of Popish Plot. Further, Davys overviews various ciphers actually used in the past, indicating references in print and showing some specimens.
In accordance with the aim of the book, that is, to show that the art of deciphering has a solid basis, Davys discusses, with references to his experience about the Atterbury Plot, whether deciphering (without a key) is possible, how to verify whether a letter is rightly deciphered, and whether it is appropriate to disclose the art of deciphering. Davys concludes that while deciphering can be verified, it is not appropriate in view of national security to disclose practical know-how of the art of deciphering (p.50-51, 54-55, etc.).
The Atterbury Plot of 1722 forms an undercurrent to this work. Francis Atterbury, Bishop of Rochester, was involved in a Jacobite plot to restore the Stuart Pretender to the throne in the aftermath of the burst of the South Sea Bubble. In 1723, Atterbury was banished for life. At one stage of the examination, counsel for Atterbury questioned the veracity of the deciphering of three letters dated 20 April 1722, allegedly dictated by Atterbury. Atterbury at the Bar requested that he might have copies of the letters in order to see if they were truly deciphered (8 May 1722) (Lords Journal). Davys examined the papers and concluded that they were rightly deciphered (Davys p.38-39; Biographia Britannica p.4135 note UU). Counsel for the Bishop had to drop the issue (Davys p.39; Lords Journal, 11 May 1722).
There is a connection between two events of Davys' life: the Atterbury Plot (1722) and Life of Ormonde by Carte (1736). The second Duke of Ormonde, grandson of the Duke of Ormonde, the subject of the Life, was an open Jacobite, who had led an expedition from Spain in 1719 and was also involved in the Atterbury Plot. On the other hand, Carte was a secretary for Atterbury and, upon discovery of the Plot, was accused of high treason and was forced to flee to France, to be allowed to return in 1728 (Wikipedia). Perhaps, Davys might have been a personal acquaintance of Carte, who took his degree from Brasenose College, Oxford in 1702.
The present author happened to find a notice of publication of this work in London magazine. It is in "Miscellaneous" under the section "The Monthly Catalogue for February 1737."
John Davys, An Essay on the Art of Decyphering (1737)
Biographia Britannica (Google)
Thomas Carte, The life of James duke of Ormond, a new edition (1851) (Google)