Shooting the Sun — Max Byrd

Charles Babbage was an English genius of legendary eccentricity. He invented the cowcatcher, the ophthalmoscope, and the "penny post." He was an expert lock picker, he wrote a ballet, he pursued a vendetta against London organ-grinders that made him the laughingstock of Europe. And all his life he was in desperate need of enormous sums of money to build his fabled reasoning machine, the Difference Engine, the first digital computer in history.

To publicize his Engine, Babbage sponsors a private astronomical expedition--a party of four men and one remarkable woman--who will set out from Washington City and travel by wagon train two thousand miles west, beyond the last known outposts of civilization. Their ostensible purpose is to observe a total eclipse of the sun predicted by
Babbage's computer, and to photograph it with the newly invented camera of Louis Daguerre.

The actual purpose, however...

Suffice it to say that in Shooting the Sun nothing is what it seems, eclipses have minds of their own, and even the best computer cannot predict treachery, greed, and the fickle passions of the human heart.