I was thinking that since atmospheric pressure is 760mmHg what would happen if I shrink a mercury barometer until it's shorter that 760mm in height. What would happen? Would the barometer retain it's ratio of mercury height? Will the mercury fully fill the barometer? Is 760mmHg a constant and not affected by the size of the barometer (or diameter)? Thanks in advance.
A mercury barometer is designed to measure the difference in pressure between the surface of the mercury outside the tube and the surface of the mercury inside the tube.
The space inside the tube is filled with mercury vapour and hopefully nothing else.
The column of mercury is kept in position because the pressure exerted on the surface of mercury outside the tube is equal to the pressure inside the mercury column at the same horizontal level as the mercury surface outside the tube.
If the tube is less than $760 \, \rm mm$ then there will be insufficient height of mercury to equate the pressures even if the mercury column occupies the whole of the tube.
In such a case the wall of the glass tube exerts downward forces on the mercury inside the tube such that the pressure exerted on the surface of mercury outside the tube is equal to the pressure (due to the column of mercury and the tube) inside the mercury column at the same horizontal level as the mercury surface outside the tube.