So you thought that your high school physics (dimly remembered) was finally going to come in useful? Archimedes principle: "The buoyant force on a submerged object is equal to the weight of the fluid displaced". And it's converse, that if you know the weight of the object ( in this case a boat), you then know the weight of the fluid displaced ( in this case water) you then know the volume of your boat below the waterline. You would think that tonnage might refer to a simple calculation along those lines...well, think again. The "tonnage" measurement that Transport Canada needs to register a vessel is given by the following formula:
The net tonnage (NT) of a ship = K2Vc 4d2 + K3 (N1 + N2).
Don't even ask me what the variables stand for, but they are the subject of an international treaty (International Convention on Tonnage Measurement of Ships, 1969) to which Canada and the US are both signatories. What it means (according to Wikipedia) is: "...a calculation of the volume of all cargo spaces of the ship. It indicates a vessel’s earning space and is a function of the moulded volume of all cargo spaces of the ship."
Calculating the volume of the spaces in an irregularly shaped object like a boat is not easy, and there are therefore "tonnage measurers" available to work through the calculations. We had such a one visit us a few days ago, and a very pleasant fellow indeed, although I did notice that he had very little hair, which I attribute to the maths involved in this arcane calculation. Note also that this is very specifically Canadian math, because this boat came with a tonnage measurement done in the USA and duly engraved on a deck beam... of course this was arrived at using US math - totally unnaceptable of course to Transport Canada!
Addendum: More tonnage trivia... A ton ( as we know it) is 2,000 lbs. A "long ton" is 2,240 lbs and although it is a weight measure, it is historically linked to the volume of cargo that could be carried ( and taxed) in a ship. Casks of wine were called "tuns" and held approximately 252 gallons of wine which also weighed 2,240 lbs. When sail was replaced by steam part of the cargo space was now taken up by an engine, hence the development of complex tonnage measures to take this into account.
