By early 18th century i assume you mean the early 1700s. Can you give us the paragraph in question as that will help us to figure out the term the author means to use.
Pulling out my copy of "The book of old ships" by Henry B. Culver i get the following information
Falconet:
feet long, 2 inch bore, weight of shot is unlisted; but the next size up is the "minion" which was also rail mounted on vessels of the 15/1600s which fired a 3 to 4 pound ball from a 2.75 inch bore.
Now look at the weight of the gun itself. A railing piece is designed to be small and light and easily lifted onto its railing mount by 2 men without the use of rope and tackle.
Consider the "saker" which was a 9 foot 3.5 inch bored cannon firing a 6-8 pound cannon ball, yet in the 1500s they used a riling mounted gun called a saker.
And if your book is set in the napoleonic wars, look at the british armed launches carried by british men of war. they would have a few swivel guns firing up to 4 pound balls. And they would have a small carronade that was on a type of rotating carraige to support troops onshore.
Please send more info on the boook, sounds interesting.