The bed is 8 5/16" long, and about 1 3/8" in diameter, with the flat about 1 1/16" wide. The center is 2" above the bed.
The bed is stamped on one end (some stamps are rotated more than 90-degrees!): "J. STARK", "WALTHAM", "MASS", "PATENTED", "OCT. 19", "1858", "1872".
Update: the tailstock (or another headstock?) was found in the box of parts, along with the threaded post and brass nut to hold it to the bed. It is broken and discolored (heat/fire?), possibly from an attempted repair.