I'm quite certain that copies of the patent documents can be obtained from the agency in Great Britain that issues patents. Sir Joseph Whitworth patented the projectile on April 23, 1855, British patent #903. He later patented an improvement on December 30, 1859, British patent #2990.

Whitworth also held U.S. patents #2410 dated 10/29/1855, #1645 dated 06/12/1857, #2329 dated 10/19/1858, #1959 dated 08/29/1859, and #2990 dated 12/30/1859. I *think* these were more related to the gun and the carriage than to the projectile, and may be of more help. Copies of the drawings should be obtainable from the U.S. Patent Office.