Believe me, I'm disappointed to have to tell you, no Whitworth bullets had what bullet-collectors call a "dish" base-cavity. (Actually, shaped like a shallow bowl, not a dinner dish.) That seems to be what your base-view photos shows. If your bullets do have a "dish" cavity, they are most probably .44/77 Sharps metallic-cartridge bullets.
Also, a typical civil-war-used Whitworth bullet weighed approximately 515 grains. That is significantly more than the 484-grains weight of your bullets.
For Charlie P.:
Top-level civil war bullet researchers Jim & Dean Thomas (authors of several books on the subject) say their extensive research has not turned up any evidence that Whitworth "Hexagonal" bullets were used in the civil war. Some fired Whitworths dug on civil war battlefields show Hexagonal form even though they were manufactured as smooth-sided bullets, because they were fired through the Whitworth rifle's hexagonal bore. The Thomas-&-Thomas "Handbook Of Civil War Bullets & Cartridges" includes photos of an unfired smooth-sided Whitworth, a fired smooth-sided Whitworth whose shape was changed by the rifle's Hexagonal bore, and several .44/77 Sharps for comparison with the Whitworth.
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