Technological trends in 1864 America
In 1864 the US had the scientific method, electromagnetics including dynamotors and batteries, the first beginnings chemistry and some notion of the periodic table, thermodynamics including steam and internal combustion motors, very good optics, crop rotation, evolutionary biology, physiology, photography, some pretty good geology, the beginnings of genetics, and a quite advanced set of economic and governmental theories.
They did not have disease theory, radio waves, cybernetics, or any understanding of nuclear physics.
People in the North had access to public libraries and spent the time we spend watching TV reading. They had large numbers of scientific journals in public and university libraries. The North had many immigrants from other countries and had themselves experienced rapid technological change, especially in war. They had already had speculations and prototypes of blimps, submarines, airplanes, automobiles, machine guns, poison gas, etc.
I haven't read any of the series for years because they got to repetitive, but the technological advances seem understated if anything. As the area under the control of the new US expanded they were better able to afford engineering development and even research. After twenty years on the new world they should have been far in advance of 1880's technology because they would have been spending far more than our world did, because our world did not have government funding of science and engineering, and they did, since they relied on continuing technological advances to repel the hoard.