This section is from the book "Cassell's Cyclopaedia Of Mechanics", by Paul N. Hasluck. Also available from Amazon: Cassell's Cyclopaedia Of Mechanics.
The mode of ascertaining the height above sea level of a hill depends on circumstances. The term "sea level" indicates the mean half-tide level of the sea, and if the distance is short and the height limited, the height of a hill may be most accurately taken by using an ordinary dumpy level and staff. If the distance and height are more extended, a surveyor's compensated aneroid barometer, which is actuated by the pressure of the atmosphere, may be used. A good instrument is divided to show heights varying by 20 ft., but may be read by estimation to 5-ft. intervals. It is adjusted to zero at the lower level and then carried to the top of the hill and read off, but if it is important to ensure accuracy, and the distance to be covered or the time occupied be great, it is advisable to have a second instrument left with an observer at the first station, and the indications recorded every half-hour, so that a correction of the observed heights may he made for the natural fluctuations of atmospheric pressure, the time of each observation being duly entered. When the height of a mountain is to be determined, a mercurial mountain barometer made on Fortin's plan may be used.
This construction permits the mercury cistern to be closed entirely secure from leakage of mercury in whatever position the barometer may be placed. The rule for height in using a mercurial barometer is as follows. Read the barometer to the nearest hundredth of an inch: subtract the upper reading from the lower, leaving out the decimal point; and then multiply the difference by 9, which gives ths elevation in feet. Thus: Lower station 29.25in., upper station 28.02in.; difference, leaving out the decimal point, - 123 ; this multiplied by 9 = 1,107 ft. elevation. There are small corrections to be made for capillarity, temperature, gravity, etc. The height of a mountain has perhaps been more often determined by observing the boiling point of water than by any other means. It is found that with the barometer at 30in.,which maybe taken as mean pressure at sea level, pure water boils at 212 F., and at a lower temperature as the atmospheric pressure decreases. The self-evident reason of this is that the steam can escape more easily from the water when there is less pressure on the surface.
There is a simple rule for height of mountain from boiling point which may be seen more clearly from the following: 212° boiling point = datum level; 21P = 511 ft. elevation; 210° = 511 + 513 ft. elevation; and 209° = 511 + 513 + 515 ft. elevation, and so on, increasing the added figures by two each time.
 
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