I don't have a picture, but do have a description from the NRA museum.
'Circa 1849 Samuel Hawken (U.S.) Percussion Plains Rifle (single-shot/ muzzle-loading/ black powder/ ball ammunition) The late 1840s saw an increase in U.S. westward expansion, up the Missouri River, across the Great Plains, over the Rocky Mountains, and to the Pacific coast. At first, the lure was fur, then cheap land, and finally, gold. Symbolic of this movement was a half-stock heavyweight firearm, variously called the Plains Rifle" and the "Mountain Rifle," which originated in St. Louis, Missouri.
The most famous makers of these rifles were two brothers, Jake and Sam Hawken. This example was made by Sam Hawken in 1849, just as the California Gold Rush began. It and its kin are symbolic of the fervor for Manifest Destiny, which had infected the U.S. between 1835 and 1850. Soon after 1850, however, the spoils of this Manifest Destiny would lead to internal disagreement over the expansion of slavery into new lands." - Dr. William L. Roberts, THE AMERICAN LIBERTY COLLECTION; #58"
I realize the referenced rifle to a picture I can't post is a cap lock, but I see neither rhyme or reason they would continue making full length rifles and go for half-stocks. Since half-lock rifles stiffen the barrel quite a bit over a wood-supported barrel.