Who devised for the first time,a method for measuring atmospheric pressure?

$A$ manometer reads the pressure of a gas in an enclosure as shown in the figure. The absolute and gauge pressure of the gas in $cm$ of mercury are (Take atmospheric pressure $= 76\,cm$ of mercury)

$A$ $U$-shaped tube is partially filled with an incompressible liquid of density $1.2 \ g \ cm^{-3}$. Oil,which does not mix with the liquid,is poured into the left side of the $U$-tube until the liquid rises by $15 \ cm$ on the right side. If the density of the oil is $0.9 \ g \ cm^{-3}$,the oil level will stand higher than the liquid level on the right side of the $U$-tube by: (in $cm$)

$(a)$ Pressure decreases as one ascends the atmosphere. If the density of air is $\rho$,what is the change in pressure $dp$ over differential height $dh$?
$(b)$ Considering the pressure $P$ to be proportional to the density,find the pressure $P$ at a height $h$ if the pressure on the surface of the earth is $P_{0}$.
$(c)$ If $P_{0} = 1.03 \times 10^5 \text{ N/m}^2$,$\rho_0 = 1.29 \text{ kg/m}^3$,and $g = 9.8 \text{ m/s}^2$,at what height will the pressure drop to $\frac{1}{10}$ of the value at the surface of the earth?
$(d)$ This model of the atmosphere works for relatively small distances. Identify the underlying assumption that limits the model.

If the pressure at half the depth of a lake is equal to $2/3$ of the pressure at the bottom of the lake,then what is the depth of the lake in $m$? (Assume atmospheric pressure $P_0 = 10^5 \ Pa$,density of water $\rho = 10^3 \ kg/m^3$,and $g = 10 \ m/s^2$)

$A$ barometer kept in an elevator reads $76 \, cm$ when it is at rest. If the elevator goes up with some acceleration, the reading will be .......... $cm$.