Reports of Whipple's 1859 Arch Bowstring bridges say that they were Cast and Wrought Iron bridges. The arches were cast iron and the bowstrings were wrought iron. All compression members were cast iron, and all tension members were wrought iron. As wrought iron means "worked on" iron, wrought iron cost much more than cast iron in 1859, but provided much more strength in tension.
I copied the following from Wiki:
"The best way of using cast iron for bridge construction was by using arches, so that all the material is in compression. Cast iron, again like masonry, is very strong in compression. Wrought iron, like most other kinds of iron and indeed like most metals in general, is strong in tension, and also tough – resistant to fracturing. The relationship between wrought iron and cast iron, for structural purposes, may be thought of as analogous to the relationship between wood and stone."
I might add to the Wiki comment, "you gotta have some way to hold the arches' support base in place, horizontally, like a solid rock canyon wall, or flying buttress." Obviously, that was the purpose of the bowstrings in Whipple's design.