A good long time ago, I started writing a series of posts about my thoughts on Chainmail. At the time, I managed to get about a third of the way through the third edition rules. If you want to check out the previous posts, you can find links to them in the left sidebar. Starting with this post, I'm going to pick up where I left off and hopefully get through the rest of it.
Cannon in Chainmail strike me the same as arquebusiers. Historically, they have a place on the latest medieval battlefields, but they seem odd to someone coming at the rules backwards from years of reading Gygax's warnings about including firearms in D&D. Reading through the rules about arquebusiers and cannon in Chainmail, it is easy to see why some of those later warnings came about, though.
First, some basic rules. Cannon are treated the same as catapults in terms of rate of fire and fire arc. Field guns can only fire directly, but bombards have indirect fire as a catapult as well. Each type of gun uses a dowel rod of varying diameter - 5/8" for a light field gun, 3/4" for a heavy field gun, and 1" for a bombard. The dowel is marked in alternating white and black segments. There is also a variation measure marked off in 1½" segments. A die is rolled and the dowel is moved according to the variation measure. The firer names whether they are firing short or long. Any model (friend or foe!) touched by the white is hit and eliminated if firing short. If firing long, any model touched by a black segment is eliminated. Terrain will stop the cannonball.
Cannons are deadly in Chainmail! There are no adjustments for armor, troop type, or any other factors. This is probably the reason Gygax warns against including them in D&D. Despite their usefulness in sieges, which I'll get into in due time, they are simply too vicious for most D&D battlefields. This is especially true if cannon can eliminate some of the bigger threats or more powerful characters with a single hit. Smaug is not nearly the threat to Laketown we expect if a rank of cannon take shots as he passes!
The mitigating factors for the deadliness of cannon are mostly similar to catapults. The engines require a full crew to function quickly. They tend to have a fairly static position once deployed. Finally, terrain can interfere with their effectiveness. Best bet if encountering an army with cannon in open terrain with well-trained and defended crew is to avoid the field and try a different strategy.