I guess that raises another question: how do they calibrate the barometer at all? I assume by taking one up a mountain. (And how do they know the height of the mountain? Using a sextant and simple trigonometry).
They could use a mountain. They could equally use a balloon (just not to 20k feet). British scientists by that time were knowledgable enough to extrapolate.
You can read about the height of Everest and other Himalayas. There are some interesting stories about the lengths people (mostly British and Europeans) went to precisely determine their heights from ground stations. Once, they thought Everest was exactly 29,000 feet but thought this figure lacked gravitas so added two feet to make it sound precise. So you can imagine the British ballooners might have played with the truth a bit too.
