Starting from the junction with the Main Line at Knapford:
calling at Dryaw, Toryreck, Elsbridge and Hackenbeck Halt to terminate at Ffarquhar, location of the engine sheds

Staffed by, in order of arrival, Thomas with Annie and Clarabel, Toby with Henrietta, Percy (from the main line), and Daisy. Notable visitor: Stepney.

Thomas
Toby
Percy
Daisy

Has a harbour spur from Toryreck, worked by Percy, which also has a connecting system from a defunct lead mine, and a streetside connection from Ffarquhar runs to the private line of Anopha Quarry, worked by Mavis.

Carries passengers, quarry stone and farm produce, including milk. Some passenger trains work into Tidmouth to pick up a through coach from the Wild Nor' Wester express.

Thomas' Branch Line
From the 1972 Surprise Packet, with thanks to David Butchers. Copyright control.

The discussion:

The first line disovered on Sodor and the most often written about - appearing in books 2, 4, 5, 7, 8, 11, 15, 16,18 and 26

It was also the first mapped, and as well as being intensively modelled: The Rev first modelled the Knapford end in 1952 as part of the North Western Railway:

The Rev. Awdry's layout at Emneth
From a picture in the the Rev Awdry's model railway scrapbook at the NGRM, with thanks.

The Ffarquhar end was modelled in 1955, and the station has continued as the centrepiece of the Rev's main standard gauge layout to the present day. The name "Ffarquhar" actually dates from a model of 1927, when the Rev Awdry was just 16 and the Railway Series was in the distant future.

Ffarquhar Layout
From the Railway Modeller, December 1959.