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Very quick query which will probably do what every quick query does. Ha.
Is a spirometer the only way to accurately measure lung capacity?

That was a yes.
I'm trying to figure out a way to have something filled with water, blow air into it, and see by the amount of water displaced how much air was blown in, without having the air under pressure at the end.
All these people talk about liters of lung capacity and I have no idea how they arrive at that. Like so-and-so has four liters, and Jake used to have X and ended up with Y. How was that measured?

Not the most sophisticated scientific way you can figure it out using a home-made breathing bag:
Take a plastic bag, tape it close with a piece of 1/2" garden hose as only opening with roughly 4 or 5 litres capacity. You can insert your mouthpiece into the tube and trying to fill up the bag with one breath. Then make the bag smaller until you can fill it up completely and you can calculate the actual bag size which shows your usable lung capacity. As a long time tuba player you should be able to use 80-90% of your lung for breathing.
And don't worry about bigger or smaller lungs. Sam Pilafian was reported to have a very small lung capacity due to some illness. He just took a breath more often (said Pat Sheridan!)

I already did the bag thing. Looks like one liter to me. It's not much, and it's not enough for anything sustained in the bottom octave.