Mountain Height and Mean Sea Level.

How do we measure the height of a mountain? Is the sea level same for all oceans?
There are several methods of measuring the height of a mountain. In a physics-based method, the height of the mountain is related to the barometric pressure which reduces with increasing height by a well established formula. Approximately a height of about 115metres reduces the atmospheric pressure by 10 mm of mercury.
Thus a measurement of the atmospheric pressure at the top of the mountain would provide the height. However this method has two main deficiencies. First, because the barometer reading also depends on the atmospheric temperature, a complete temperature profile along the height of the mountain needs to be known.
This is not only difficult but varies with time; so the height measurement by this method can be inaccurate. Secondly, one needs to climb the mountain in order to measure its height. The following methods overcome these problems easily.
In one of the methods, the length of the shadow of the mountain is compared with the length of the shadow of a pole of known height. The height of the mountain is calculated as the product of the height of the pole and the length of the shadow of the mountain divided by the length of the shadow of the pole. This is a simple but elegant method.
In yet another method, the angular elevations of the tip of the mountain are noted from two points on the ground along a line passing through the base of the mountain. Such a line is easily identified by joining the shadow of the tip of the mountain at two different time of the day.
Use of the trigonometric tangent ratio of the two angles of elevation and the accurately measured distance, between the two points of observation yields the required height of the mountain. In this method the two chosen points are required to have same mean sea level (MSL). Because d is in the range of about 500metres, the MSL does not differ significantly.
Therefore, this method gives fairly accurate value of the height of the mountain.
Coming to the second question, the MSL of all the oceans of the world is not the same. The mean sea level at the south-east end of the Panama Canal, in the Pacific Ocean, is seen to be higher than at the north-west side in the Atlantic Ocean.
Such variations arise from the oceanic currents, variations in atmospheric pressure, temperature and local salinity. In the same ocean itself, the earth rotation alters the MSL at different latitudes. Even temporal variation in MSL is observed at the same location mainly owing to tidal conditions.