In the DT is a version close to how I learned it in the 1970s:

PATSY OREE AY (though I was taught it was called 1851)

In eighteen hundred and fifty one
American railroad just begun
American railroad just begun
Working on the railroad.

Cho: Patsy-o-ree-o-ree-ay
Patsy-o-ree-o-ree-ay
Patsy-o-ree-o-ree-ay
Working on the railroad.

repeat verse and chorus, using:

1852 looking around for something to do
1853 railroad company accepted me
1854 found my back was mighty sore
1855 found myself more dead than alive
1856 stepped on a pile of dynamite sticks
1857 found myself on the way to heaven
1858 pickin' the lock at the pearly gate
1859 floating around in the clouds sublime

I learned the chorus as:

Fiddle-ly-or-ee-or-ee-ay (3X)
Working on the railroad.