From Railroads of the Civil War: An Illustrated History, Michael Leavy, Westholme Publishing, 2010.
Page 14: "The first use of railroads to support a military conflict came in the 1840s during the war with Mexico where, because of their scarcity, they were used modestly to transport troops west. The first railroad built specifically for warfare was the line built at Balclava during the Crimean War in 1855."
The image is found on page 4. The caption is "The first direct military use of the railroad occurred during the Crimean War. A track was laid across Crimea from the harbor at Balaklava to Sevastapool in order to expedite ammunition and supplies to British and French troops. Here the railway bed is being prepared. Iron rails and other supplies can be seen in the photo taken in 1855 by Roger Fenton. The image is in the Library of Congress.
CWL has just started Railroads of the Civil War and it may be one of the more noteworthy additions to Civil War book shelves during the sesquicentennial.