Baspinall asked:
> "Are there smooth sharps?"
Yes, but only post-civil-war ones, made for use in the Sharps .44-caliber Model-1869 and Model-1874 Rifles.
I don't know why people are guessing your paper-wrapped smooth-sided bullets are .52-caliber when your photo showing a caliper measuring one says .453-inch in diameter. (That diameter would be correct for a BREECHLOADING .44 or .45 rifle.)
Thee are several varieties of smooth-sided paper-wrapped bullets in the .44-to-45-caliber range, all of which are post-civil-war. Some are foreign, such as the British .45 Martini-Henri and Martini-Enfield Rifles, and the British version of the .45 Gardner Machine Gun (circa 1880). The photos attached below show them, in cartridge-casings. Another of the photos shows some Martini-Henry "loose" ones with and without the paper wrap. That one was originally posted here in the What Is It? forum by T-Net member Red James Cash.
For identification, put your cursor over the photo.
For correct identification, it's very important to note that your caliper-on-the-bullet photos also show your mystery-bullets are about 1.53-inches long, which includes the paper wrapped over the bullet's base. Even without the paper, your bullets are LONGER THAN ANY WHITWORTH BULLETS, so that type is excluded. (Also, your bullets are pointy-er" than Whitworth bullets.
Although foreign versions of paper-wrapped smooth-sided .44-or-.45 bullets exist... because yours apparently came from the USA, I suspect it's most likely that they are US-made .44-70 or .44-90 "Buffalo Sharps" bullets. One of the photos below shows six variations of that kind in brass cartridge-casings.
A bit of trivia for you: Matthew Quiqley used a .44 "Buffalo Sharps" rifle in the movie "Quiqley Down Under."