The first projectiles for the firearm were round lead balls, slightly smaller than bore diameter, to be “patched” for a tight seal. Lead was the chosen material, not for its durability upon impact, but for its malleability in forming the projectiles. Lead is easy to work and shape, melts at a relatively low temperature and is plentiful. This was perfect for the early users of the cartridge guns, as many firearms were sold with a set of molds of appropriate caliber and bullet weight for that firearm. Think of the buffalo hunters on the Great Plains, hunting all day and sitting by their campfire at night, melting lead and casting their own lead bullets for the next hunt. However, lead has several shortcomings, especially with modern firearms and propellants.
Your goal as a hunter (we’ll get to the self-defense bullets soon enough), is to deliver a quick, humane kill to minimize the suffering of the game animal. For most of your hunting, with the exception of solid bullets or a shot column from a shotgun, you depend on the bullet to create massive hemorrhaging by destroying as much vital tissue as possible. The expansion of a bullet—if it is designed to expand—creates hydraulic shock, which destroys tissue as well. Now, when a material as soft as lead impacts hide, bone and water-rich flesh at an appreciable velocity, you can have very rapid expansion. Your projectile will certainly meet enough resistance to flatten a round ball or rapidly deform the meplat of a lead bullet. So the lead ball or bullet must be of sufficient weight and diameter to properly penetrate into an animal’s vitals in order to guarantee a quick kill, and the velocity must be kept to a reasonable level, say below 2,200 fps. Even then, the bullet can exhibit penetration problems if the shot is too close.
The stories of Frederick Courteney Selous from the late 19th century are illuminating. Selous would hunt elephants with a muzzleloading four-bore rifle stoked with a lead ball weighing 1/4 pound, propelled by over 500 grains of blackpowder. That gives you an idea of how the early projectile directly affected the choice of bore diameter; you simply needed to compensate for a lack of penetration with sheer mass.
At moderate velocity typical of the