Hello!
A barometer is used for measuring pressure, in our case the atmospheric pressure. This is achieved by balancing atmospheric pressure with the pressure of a liquid column.
The pressure of a liquid column depends only on its height, `P = rho g H,` where `rho` is the density of a liquid, `H` is the height of a column and `g` is the gravity acceleration. Mercury is often used for this purpose because of its high density (about `13.7 (g)/(cm^3)`) which results in a relatively low height.
The `13.4` times greater height of an unknown liquid means that its density is `13.4` times less than that of mercury. It is about `13.7/13.4 approx 1.022 g/(cm^3).` This isn't the density of pure water but close to it; sea water has approximately such a density.
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