From my recollection of my assortment of machine reamers I have always assumed that the first 1" or thereabouts was tapered slightly to 'line up' the reamer (especially if held in a floating head). In fact I have a collection that came out of a toolroom and some have been re-ground on this tapered portion and some have been 're-sized' (signified by a grinding gouge in the shank and a size arc etched on the shoulder)
However, in respect to comments above by Old Mart and Andrew, these are all what I know as 'through reamers', whereas blind hole reamers are parallel at the nose, have a larger chamfer, and usually (but not always) have carbide brazed into the front 1" or so of the ends. To get over the problem of alignment with a blind hole reamer was the reason for the introduction of the superb adjustable and floating blade David Brown 'S' type reamers.
P.S Thanks for the acknowledgement of my prowess with reaming 'Old Mart'
………..."a light lube from an oily rag"
Edited By Oily Rag on 13/12/2020 11:42:16