Ellis Stanyon was the first to publish a version of this effect; see his Conjuring for Amateurs, 1897, p. 42. Stanyon states that “This is a very surprising trick, and a favourite with the most noted prestigitateurs.” One of those prestigitateurs was certainly David Devant, the actual details of whose method were eventually published in Prof. Hoffmann's Later Magic, 1904, p. 303, where Hoffmann declares the trick Devant's invention. Hoffmann's description provides a great number of details Stanyon lacked, although Stanyon got the basics right: a switch of a set of knotted silks, and a vanish of a red silk inside a clear glass tube, effected by a Pull. Peter Warlock stood behind the Devant attribution; see his column in The Stage, as referenced in Hugard's Magic Monthly, Vol. 11 No. 10, Mar. 1954, p. 117.
Two years before Devant's method was published, C. Lang Neil included Frank Kennard's “The Mysteriously-Joined Handkerchiefs” in Modern Conjurer, 1902, p. 231. Kennard's method avoided switching the handkerchiefs by concealing one inside the hem of another. Frank Ducrot marketed essentially the same concept (a pocket-silk) as “The 20th Century Handkerchief Trick,” c. 1903; see the advertisement in Mahatma, Vol. 7 No. 7, Jan. 1904, p. 80, which is presumably Ducrot's version.
This should not be confused with Hardin Burlingame's unrelated marketed trick, “U-Need-A Twentieth Century Handkerchief,” 1899; or Ellis Stanyon's marketed “20th Century Handkerchief Production,” 1903.