Doyle,

You are right as usual. The rails were used for the comstruction of the Arkansas. From the notes I've got I believe they were also used to produce cannons and other armorment.

Apparently the eastern leg of the railroad was operational by 1861. Attached are some exerpts from period newspapers.

MEMPHIS DAILY APPEAL [MEMPHIS, TN], May 30, 1861, p. 3, c. 2
The Ladies Hegira.—We mentioned yesterday that, owing to the intelligence of the invasion of the White river country by Jim Lane and his followers, over fifty women, many of them with children, had arrived here by the Little Rock railroad from St. Francis county.

MEMPHIS DAILY APPEAL [MEMPHIS, TN], November 28, 1861, p. 3, c. 1
Making Arms.—The shop of the Little Rock railroad in Hopefield has, for the last three weeks, been engaged in finishing cannon, smooth bore and rifled, howitzers and Parrot guns, cast in this city. Superintendent Feger is overlooking this work.

LITTLE ROCK] ARKANSAS TRUE DEMOCRAT, January 2, 1862, p. 2, c. 2
Manufactures in Arkansas.
furnished grape shot for the army. At Hopefield, opposite Memphis, the machine shop of the Memphis and Little Rock railroad has been turned into an armory and is altering and repairing guns etc