In general, this term refers to the science of artillery and gunnery, which can also include geometry, trigonometry, conic sections, the laws of motion and so on. More particularly, the term refers to guns or cannons, mortars, howitzers and other similar weapons that fired a larger projectile than the muskets and rifles carried by a soldier.
A cannon (also simply called a "gun") during the War of 1812 was a metal tube (iron or bronze) usually placed on a wooden field or garrison carriage, which fired a solid iron ball as its primary ammunition. These balls, called solid or round shot, were fired on a fairly flat trajectory and did not explode, being made of solid iron. The fact that these solid balls were fairly constant in weight relative to their caliber allowed the different sizes of cannon to be designated by the weight of the ball they fired. Thus cannons were referred to as six-pounders, twelve-pounders and so on. The powder charge for a cannon firing a round ball (or shot) typically weighed one-third as much as the shot. For example, a six-pounder cannon used a two-pound powder charge. Cannons could also fire a variety of other (solid) projectiles under different circumstances and to achieve different effects. Two examples of these projectiles are grape shot and cannister shot.
A second classification of artillery was the mortar. Mortars were shorter-barreled weapons, usually fixed in a wooden "bed" at a 45-degree angle. The inside of a mortar was double-chambered. In other words, there was a large chamber for the projectile and a smaller one at the rear of the tube for the gunpowder charge. Rather than firing a solid ball like the cannon. mortars fired exploding projectiles called "bombs." A typical bomb resembled a solid cannon ball, but was hollow and filled with gunpowder. Just prior to firing, a wooden fuse was placed in a hole in the bomb after being cut to the proper length by one of the gunners. The flame created by firing the mortar would light the fuse, and when it burnt into the bomb, the powder inside would explode, sending large fragments of the bomb out in various directions. As the bomb was fired high in the air and flew in an arc (due to the angle of the barrel), the mortar was effective at firing over obstacles, such as fort walls, or trenches. Its explosive capability also made it a popular weapon for firing at personnel, or at powder magazines and other such targets. Because the mortar could not have its elevation changed to any great degree, the gunpowder charge was varied to accommodate the range desired.
Last of the three major types of artillery in use during the War of 1812 was the howitzer. Physically, the howitzer resembled the mortar in length and general design, with the major difference being that the trunnions (the outcroppings on the barrel which fixed the weapon to its carriage) were located at the midpoint of the barrel, rather than at the rear like the mortar. Like the mortar, the howitzer was a double-chambered weapon whose powder charge varied with the target, but like the cannon, the howitzer was placed on a wooden field carriage for use. In many ways, this weapon was something of a cross between a cannon and a mortar. It usually fired an exploding bomb on an arc like the mortar, but could also fire a solid shot or cannister shot on a flat trajectory like a cannon, albeit with a greatly reduced range.
Because the weight of the bombs for both howitzers and mortars could vary, these weapons were typically classified by the diameter of their barrels, much like modern U.S. artillery. Thus while a cannon might be classified as a twelve-pounder, the same army might be armed with a 5 1/2-inch howitzer and/or an 8-inch mortar.