If astronomy becomes a high priority in 1876, there are bound to be technologies that advance faster than in OTL. I’m assuming both more academic interest and some government subsidy, above and beyond OTL’s government interest. (In OTL, the US Naval Observatory had the world’s largest telescope at the time.) I’m working on a timeline where, due to an asteroid impact, there is a strong desire to find loose rocks in space; they don’t know just how difficult it will be. But enough will be found to stimulate development in the technologies to find them, and calculate their orbits. In particular, the United States will be spending money to push these techniques.
Some that I see improving faster than OTL:
Photography, to documents observations, and to see fainter objects. (Natural spin-off’s to certain aspects of chemistry…)
Once photography with significant time exposures becomes a significant part of astronomy, machines of sufficient precision AND SIZE to keep a large telescope pointed at a specific part of the sky as the earth turns underneath it, so the images are points rather than arcs. Precision machines of that size will have military applications with regards to accurate gun laying.
Flight: Not so much, as access to space is clearly a pipe dream in 1876. (Won’t stop crackpots from trying…)
Mathematics seems to need little further development for the calculations needed, although faster computations to more decimal places than even a large slide rule can accomplish might be nice.
Any thoughts on elaborating these spin-offs, or any thoughts on any others? Of course, anything that CAN be weaponized, WILL be weaponized...