Corrections to mercury barometers

Although mercury barometers are not used to measure the pressure on Canadian weather reporting vessels, a brief account of this instrument will be given here for the sake of completeness. In its simplest form a mercury barometer is made by completely filling with mercury a glass tube about one metre long and closed at one end. The open end of the tube is then immersed in a small cistern also containing mercury, and the tube is held upright.

The mercury in the tube falls, leaving a vacuum at the top of the tube, until the weight of the mercury column just balances the atmospheric pressure exerted on the free surface of the mercury in the cistern. The length of the mercury column rises or falls as the atmospheric pressure increases or decreases. The pressure is then directly proportional to the length of the mercury column (in the past pressure was measured in units of length, e.g. 750.1 mm of mercury, or 29.53 in. of mercury). The measuring scales of most mercury barometers are graduated in millibars (or hPa) which are true units of pressure.

7.2.1.1 Corrections to mercury barometers

For a given sea level pressure, the length of the mercury column is not constant, but varies to some extent according to the temperature of the mercury, the height of the instrument above sea level, and the latitude. In order that the barometer readings all over the world may be compared, it is necessary to adjust the readings so that they will be related to standard conditions of temperature, latitude and altitude. The following corrections must therefore be applied.

7.2.1.1.1 Temperature correction

Mercury expands as its temperature increases, and contracts as its temperature decreases, so that the same atmospheric pressure is balanced by a longer column when the mercury is warm, and a shorter column when the mercury is cold. A correction is applied to obtain the reading which the barometer would show at standard temperatures of 12 °C or 0 °C

depending on whether the barometer was made before or after 1954. A universal formula for the temperature correction cannot be given as the amount of the correction depends on the design of the instrument.

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7.2.1.1.2 Latitude correction

The force of gravity is least at the equator because the earth’s surface in this region is farthest from the earth’s center of gravity, and also because the vertical component of the centrifugal force due to the earth’s rotation is greatest here. The force of gravity is greatest at the poles as they are closest to the earth’s center of gravity and the vertical centrifugal force is zero. In low latitudes the mercury in the barometer will actually weigh less than in higher latitudes, and will require a greater length of the mercury column to balance a given pressure. This effect is not desirable, so all readings are corrected to what they would be within the standard latitude of 45° (North or South). The correction is subtracted in latitudes less than 45°, and added in latitudes greater than 45°. To a high degree of accuracy, the latitude correction is given by the formula:

𝐶 = −0.00259𝑝 cos 20 where:

𝐶 = correction in hPa

𝑝 = observed pressure in hPa 0 = latitude

The correction does not change greatly with pressure, so an average pressure of 1000 hPa can be assumed. An approximate formula for the latitude correction is then:

𝐶 = −5 /2 cos 20 7.2.1.1.3 Sea level correction

The pressure at any level is the weight of the vertical column of air of unit cross section above the given level. Hence the pressure will be greater at sea level than say at the top of a nearby lighthouse, where a certain weight of the air is below the observer and cannot contribute to the pressure recorded by his instrument. Pressure cannot be compared therefore, unless a correction is applied to obtain the pressure which the instrument would indicate if it were located at a standard level in the atmosphere. This standard level is sea level, and the correction is called the sea level correction. Its value depends of course on the altitude of the barometer above sea level, and also the temperature of the outside air. Since the pressure is greater at sea level than at any higher level, this correction is always added.

Table 7—1 lists the values of sea level correction for various values of height above sea level, and air temperature. For example the correction to be added when the height of the barometer is 12.2 m (40 ft) above the sea surface and the outside temperature is 20 °C, is 1.4 hPa.

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Table 7—1: Correction of pressure in millibars to mean sea level for outside air temperatures from -20 °C to 30 °C

Height of

In addition to the temperature, latitude, and sea level corrections, it is usually necessary to apply another small index correction which is brought about by differing values of the capillarity of mercury and other effects. The index correction may vary slowly with time. It can be determined by comparing the ship’s barometer with a standard instrument.

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As an example of how the corrections are applied in a typical case, suppose the mercury barometer reads 1024.2 hPa in latitude 23° N, at a height of 12.5 m (41 ft) above sea level.

The outside air temperature is 26 °C, and the index correction is -0.2 hPa.

𝑈𝑛𝑐𝑜𝑟𝑟𝑒𝑐𝑡𝑒𝑑 𝑟𝑒𝑎𝑑𝑖𝑛𝑔 = 1024.2 hPa 𝐼𝑛𝑑𝑒𝑥 𝑐𝑜𝑟𝑟𝑒𝑐𝑡𝑖𝑜𝑛 = −0.2 hPa

= 1024.0 hPa

𝑇𝑒𝑚𝑝𝑒𝑟𝑎𝑡𝑢𝑟𝑒 𝑐𝑜𝑟𝑟𝑒𝑐𝑡𝑖𝑜𝑛 = −2.3 hPa (obtained from tables prepared for instrument)

= 1021.7 hPa 𝐿𝑎𝑡𝑖𝑡𝑢𝑑𝑒 𝑐𝑜𝑟𝑟𝑒𝑐𝑡𝑖𝑜𝑛 = −1.8 hPa

= 1019.9 hPa

𝑆𝑒𝑎 𝑙𝑒𝑣𝑒𝑙 𝑐𝑜𝑟𝑟𝑒𝑐𝑡𝑖𝑜𝑛 = +1.4 hPa (see Table 7— 1) 𝐶𝑜𝑟𝑟𝑒𝑐𝑡𝑒𝑑 𝑏𝑎𝑟𝑜𝑚𝑒𝑡𝑒𝑟 𝑟𝑒𝑎𝑑𝑖𝑛𝑔 = 1021.3 hPa

If the barometer is equipped with a Gold Scale, the determination of the total correction is quite simple. The Gold Scale uses a kind of slide-rule which enables the corrections to be applied mechanically and dispenses with the use of tables.

The aneroid barometer 7.2.2

The principle by which the aneroid barometer functions is the balancing of atmospheric pressure by the elasticity of metal. The fundamental part of the instrument consists of a small circular capsule or bellows which has been partially exhausted of air and hermetically sealed. As the atmospheric pressure rises, the ends of the bellows are squeezed inwards under the increased pressure. Conversely, as the pressure falls, the ends of the bellows expand due to the decreased pressure. By means of a system of levers and springs the movement of these ends causes a pointer to rotate over a graduated dial. Hence the pressure can be read directly

Aneroid barometers have the advantage of being relatively easy to read, and require no corrections for change in temperature or latitude. The instruments are compensated for temperature changes by leaving a calculated amount of air in the metal box or by means of a bimetallic lever. The principal of the instrument does not involve the force of gravity, so latitude corrections are not necessary. In general however the aneroid does not retain its accuracy over as long a period as the mercury barometer. It is therefore necessary to compare its readings with a standard barometer at fairly frequent intervals (at least once every three months is recommended), to ensure that changes in the elasticity of the metal have not altered its readings.

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