In "Uniforms of the United Army, 1774-1889, In Full Color" (Dover, NY, 1998), H. A. Ogden, the noted American military artist, displays prints of several regular units wearing these helmets during the period 1880-1888.
The soldiers depicted represent infantry, heavy artillery and service troops who were not mounted. In several cases, head gear insignia reveals the number of the regiment.
See plates 32, 34, 38, 39 and 41-43.
This work was also reprinted about 1959 by Thomas yoselof of NY. It is in most libraries.
If I'm not mistaken, The US Army Center for Military History has a collection of Uniform Regulations for the period.
James B. Ronan II
To Join the Company of Military Historians click here