Wikipedia
A double-barreled rifle or double rifle is a configuration of hunting rifle that exploits the use of two barrels instead of one; typically the two barrels are placed in a side-by-side configuration, however under-&-over and combination [two different calibers] configurations are also produced.
Double rifles became most popular during the early 1800's [a time of black powder firearms] where hunters of large and dangerous game found that the single barrel of a muzzle loader was insufficient for reliably killing game animals such as elephant, rhino, and buffalo. At this time, the only way to increase the firepower per person was to produce a firearm using two barrels, this meant that the hunter would have a very fast secondary follow up shot in the case that the first shot did not kill the animal, or in the case of a misfire [the rifle does not fire the projectile].
The low chamber pressure associated with black powder firearms translates into a low muzzle velocity and thus low kinetic energy for the caliber of projectile been fired, this low kinetic energy meant that calibers of less than 10 bore [19.69mm diameter] were incapable of achieving highly reliable penetration of an African elephants frontal skull [though an acceptable minimum with the right loads and the use of a double rifle]. Prior to the adoption of smokeless propellants, the only way a rifle could achieve more penetration [thus a more reliable kill shot] was to increase the bore diameter; propel more mass at an equal or slightly higher velocity will increase the kinetic energy as well as maintain the projectiles energy for longer during penetration. This need to increase the penetration resulted in very large bore rifles such as the two most common for elephant hunting: the 8 bore and the 4 bore, however elephant rifles were made up to 2 bore [33.67mm, 3,500grain pure lead round ball].
During the early to middle 1800's the caliber of rifles used for African large and dangerous game was getting larger and larger, this seemingly exaggerated trend forced James Purdey to conduct the most extensive research into the practicality of large bore rifles for use in hunting Africa's big five game. Purdey used technical information that he gathered along with feedback from African elephant hunters and the ivory trade to determine the most suitable caliber for hunting the largest of African elephants, the basic outline of his findings were as follows:
1) The 4 bore rifle was excessive: it produced recoil impulses so significant that any hunter using the rifle regularly would experience permanent damage to the shoulder joint and nervous system, and that unlike smaller calibers such as the 8 bore [and 10 bore], it could not use theoretically optimal loads without the guarantee of injury.
2) The 10 bore rifle was in some cases inadequate for elephant hunting, though when the caliber uses optimal heavy loads along with a double rifle it could offer a hunter a comfortable rifle if they are prepared for the risk associated with a slightly under powdered rifle. A 10 bore rifle is however a better choice for use against buffalo.
3) The 8 bore rifle was considered optimal and perfect for the task of hunting the largest of African elephants: the 8 bore rifle was capable of using optimal heavy loads, such loads offered more penetration than any reasonable 4 bore could. The 8 bore also did not have recoil impulses that caused permanent damage to strong shooter. The 8 bore rifle was considered the perfect caliber for hunting African elephants. An 8 bore rifle using optimal heavy loads can produce kinetic energy levels exceeding that of a modern .577 Nitro Express, but the advantage of an 8 bore is that it has a larger diameter projectile that can fragment more of the skull bone, making the 8 bore possibly the greatest elephant hunting caliber ever made.
4) Rifling offered projectile stability which resulted in dramatically increased accuracy at distance, however the rifling also contributed to the recoil as well as torque that would be experienced. Purdey refused to produce any 4 bore rifles due to the unsafe recoil impulses, however he did produce at least one smooth bore firearm chambered in the 4 bore caliber after his research. He also mentioned that though rifling does offer increased accuracy, all large and dangerous game were hunting at close range; where the accuracy difference between a smooth bore and a rifle was negligible a second to the factor of safety.
When smokeless propellants were introduced, along with the cartridge case and metal jacketed projectiles, double rifles were able to offer similar performance to the old large bore black powder calibers but with the reduced rifle weight and the increased reliability of unitary ammunition. The smokeless propellant ammunition can achieve such performance by offering a higher projectile velocity, where the higher velocity results in the increase of kinetic energy and penetration rather than the historical large projectile mass of an 8 bore or 4 bore.
There are still ongoing debates as to the optimal caliber/load for hunting large and dangerous game, some hunters argue that the large projectile diameter of the old "bore" caliber rifles are still more effective than their modern counterparts, such arguments can be summarized by the following:
Positives for large bore rifles using black powder: The larger projectile diameter will fragment more of an elephants skull bone, this has the effect of turning skull fragments into projectiles thus increase the effective projectile mass [firearms projectile + skull fragment projectiles]. The slower velocity of a black powder projectile will ensure that the projectile will not experience over penetration; the projectile will transfer its energy into the brain and other organs located in the middle of the target mass. The penetration of an 8 bore rifle is unquestionably suitable for hunting elephant, any argument against the capabilities of an 8 bore is void. For the caliber, black powder firearms offer lower recoil and thus are very comfortable to shoot.
Negatives for large bore rifles using black powder: The only notable negatives of a large bore black powder rifle is that it is logistically more difficult to hunt with, ammunition might not be available where you hunt and you might not be able to transport your ammunition with you. Though if you use a muzzle loader than all you need is for the hunting guide to arrange black powder and percussion caps.
Positives for smaller bore rifles using smokeless powder: These smaller calibers such as the .577NE offer similar performance to an 8 bore black powder rifle, however the rifles are lighter and the ammunition is often widely adopted by hunting guides.
Negatives for smaller bore rifles using smokeless powder: Calibers such as the .577NE do have similar performance to an 8 bore, however the higher velocity combined with the smaller projectile diameter could result in over penetration; over penetration is an inefficiency as less energy is transferred into the critical mass, this means that it is possible for a black powder large bore rifle to provide more efficiency for the energy available; if the projectile exits the body or penetrates beyond the brain, than the hunter might be better off going with a larger caliber. Modern smokeless powder is very energetic and thus a 8 bore rifling using smokeless powder might be unsafe and have similar health risks to a 4 bore black powder rifle.