As I understand it, when a Mormon speaks of tracting, they mean, “to travel from door to door attempting to present a message.” The OED lists ten variations for the verb tract, none of which match the Mormon version. (The one that says “to lengthen out, prolong, protract (time)…” seems related, however.) What gives? It’s not like Mormons invented the art or are the only ones currently practicing it. The earliest use of tract in the Mormon missionary sense (to my knowledge) comes—fittingly—from Dan Jones. In an 1855 Millennial Star piece, he described missionaries in Wales as having “a disposition to honour their religion…and to disseminate it by tracting and testifying from house to house.” 
One William Budge contributed a letter on the same page as Elder Jones in 1855 and then, twenty-five years later in June 1880, as President of the British Mission, received an Elder Charles Stayner’s report that “a tract society has lately been organized here…and a system of ?tracting’ the town will soon be adopted.”  The scare quotes suggest that tracting had not established itself in the vernacular; I have identified no instances of its use between 1855 and 1880.  Later that same year the Millennial Star printed a farewell article from President Budge lauding “a system of ?tracting’ with the pamphlets” and an article celebrating an Elder John Nicholson as the author of three tracts “so well known among the Saints engaged in ?tracting.'”  The Deseret News picked up the Nicholson piece so, by the fall of 1880, tracting had begun appearing in the premier Mormon English-language periodicals of America and of Europe. 
Tracting achieved greater maturity when, in January of 1883 missionaries and leaders held a meeting in London “at which the question of Tracts & Tracting was freely discused.”  The Elders resolved to petition the church for tracts rather than continue paying for them themselves; the church agreed.  The Deseret News enthusiastically described the new program, acknowledged former President Budge’s role in developing it, and reiterated the Millennial Star‘s call for “the immediate organization of tract societies in the branches, the sisters as well as the brethren to take part, with a regular and understood system of operations.” 
Elder Orson F. Whitney, who attended the January meeting, described tracting as an effort “to more thoroughly utilize the wet winter months.”  Two years later, Apostle John H. Smith, who had presided at the meeting, described counseling with the Elders about “the best method to reach the people,” seeking permission from Salt Lake, and then implementing “a system of tract distribution” that “has been followed systematically from that day to this.”  A further sign of tracting’s institutional maturation came in 1890 when the Millennial Star published an editorial attempting to refocus tracting energies: 
Tracts have their field of usefulness, but they should not be made to take the place of the personal labors of Elders—in other words, a hobby should not be made of tracting. We fear that too much importance is attached to the number distributed, rather than to the good done by them.
Formal tracting grew out of the British Mission’s approach to approximate stasis (relative to its earlier heyday). As the number of baptisms declined, “gleaning” missionaries needed process-oriented techniques suitable for proselyting among people unlikely to immediately accept the gospel.  The institutionalization of tracting solidified a role for the word tracting in Mormon speech—even though alternate formulations, such distributing tracts, continued to be popular.
The first instance of tracting from a missionary outside the British Mission (that I have located) comes from an Elder Alma Greenwood in New Zealand. On 1883 Jan 27—just three weeks after the meeting in London and thus not influenced thereby—he recorded that “We tracted nearly every house in town.”  However, if the sample of diaries in the “Mormon Missionary Diaries” database reflects overall usage trends, tracting did not become ubiquitous until the late 1890s. 
The meaning of tracting has changed over the years. In present-day usage the tract has mostly disappeared from tracting; that is, though missionaries still use pamphlets, distributing them is, at best, a secondary purpose in tracting. By contrast, many of the earliest uses indicated tract distribution exclusively and distinguished it from “visiting,” “canvassing,” “giving out an appointment,” and so on. With the different denotation came different constructions. 19th century missionaries frequently specified “systematic” or “house to house” tracting, whereas both ideas are implied in the present-day usage. Further, missionaries nowadays only tract multi-dwelling entities like streets or subdivisions or apartment complexes because tracting implies going from dwelling to dwelling. Their earlier counterparts could tract a whole town or an individual house.
I don’t know when the shift in meaning occurred. I do know that when I have gone tracting I felt very, very Mormon. In a sense, tracting has come back in the form of the pass-along card distributed, as before, by both members and missionaries, and pointing to a text on the web. My great question now is, “What do the Jehovah’s Witnesses call what they do?”
 Emphasis in original. Dan Jones, Home Correspondence,” letter to President Richards, 1855 Jul, “Udgorn Seion” Office, Swansea, Wales, The Latter-day Saints’ Millennial Star, vol. 17, no. 34 (1855 Aug 25), p. 538-539.
 Charles W. Stayner, letter to William Budge, “Report from Nottingham Conference,”dated 1880 Jun 18, in the “Correspondence” section, The Latter-day Saints’ Millennial Star, vol. 42, no. 26 (1880 Jun 28), p. 412-413.
 I used only computerized searches of the following databases: BYU’s “Mormon Publications: Nineteenth Century” (MPNC), BYU’s “Mormon Missionary Diaries” (MMD, and the University of Utah’s “Utah Digital Newspapers” (UDN). There are overlaps among the three collections. I have no quantitative estimate of the accuracy of the searches; I encountered multiple false positives and false negatives. I only searched for obvious verb forms—“tracted,” “tracting,” and their spelling variants—to avoid trying to distinguish “tract” the noun and “tract” the verb.
 William Budge, “A Few More Parting Words,” The Latter-day Saints’ Millenial Star, vol. 42, no. 45 (1880 Nov 08), p. 713. No author listed, “Returned Home,” The Latter-day Saints’ Millenial Star, vol. 42, no. 43 (1880 Oct 25), p. 683.
 No author listed, “?Star’ Items,” Deseret News, 1880 Nov 24, p. 6. (Stored under “Editorials” in the UDN database.) Other instances followed in the Millennial Star: “Abstract of Correspondence,” vol. 43, no. 6 (1881 Feb 07), p. 90-91; George Stringfellow, “Report from Nottingham,” 1881 Jul 30, “Correspondence,” vol. 43, no. 33 (1881 Aug 15), p. 524-525; William Coleby, “Minutes of the Norwich Conference,” vol. 44, no. 18 (1882 May 01), p. 279.
 Ephraim Nye, diary, entry for 1883 Jan 08. Nye records that Apostle and mission president John Henry Smith, Elder Orson F. Whitney, and sixteen “Elders from Utah” were present. Elder Nye’s diary is here. It’s not clear exactly when or how Nye prepared this manuscript; the latest notations are from 1896.
 John Taylor, extract of letter from President John Taylor to President J.H. Smith, 1883 Feb 12, “Abstract of Correspondence,” “Distribution of Tracts Encouraged by President Taylor…,” Millennial Star, vol. 45, no. 12 (1883 Mar 19), p. 189-190: “…believing with you and the brethren who have written, that it would be a proper thing to issue a series of tracts for distribution, we have decided to grant you the privilege. The details we shall leave with you and the brethren with who you may see fit to counsel, as also we commit entirely to your good judgment.”
 Orson F. Whitney, “Interesting Letter from Elder O. F. Whitney,” dated 1883 Feb 24, Deseret News, 1883 Mar 28, p. 6.
 John Henry Smith, April 6th, 1885, Journal of Discourses, 26:174.
 J.E.C., “Tracting,” Millennial Star, vol., 52, no. 48 (1890 Dec 01), p. 761-762.
 I cite no authority for my description of the British Mission’s baptismal arc other than my own impressions—though the Orson F. Whitney piece cited above suggests obliquely that declining baptisms prompted the move to systematic tracting.
 Elder Greenwood’s journal is here.
 About 80% of missionaries with diaries in the MMD who started their mission in 1898 or later returned at least one hit for a variant of tracting for at least one of the volumes of their diary. About 40% of diarists in the MMD who started between 1880 and 1898 (not inclusive) generated at least one hit. Reasons why the MMD sample might not be reflective of actual, overall usage include diary selection bias (they were not chosen randomly), insufficient sample size, diarists saying but not writing tracting, and search errors (both false positives and false negatives). According to the “About” page, the MMD includes journals from 220 diarists in 575 volumes, written between 1832 and the 1960s. However, as of July 2008, it only provides access to 379 volumes from 115 diarists. The search engine returns a “hit” for every volume that contains the search word. There were 16 hits for “tracked” and 75 for “tracted,” along with 13 and 102 for “tracking” and “tracting,” respectively. There were no hits for trackting, trackted, trakting, or trakted. The search engine does not distinguish words split by a line break and whole words. Thus, “contracted,” written as “con-,” line break, “tracted,” will return a hit for “tracted.” I did not estimate the number of times this occurred; my impression is that it was relatively few (for example, 3 out of 34 for the 1832-1880 diaries). The diaries in the MMD are not machine-read; they were typed by students, so OCR errors are unlikely—though transcription errors are possible.