\t ) ( > Tables 45 and 46 



REDUCTION OF THE MERCURY COLUMN TO STANDARD TEMPERATURE 



The indicated height of the mercurial column in a barometer or manometer varies not 

 only with changes of atmospheric pressure, but also with variations of the temperature 

 of the mercury and of the scale. It is evident therefore that if the height of the barometric 

 column is to be a true relative measure of atmospheric pressure, the observed readings 

 must be reduced to the values they would have if the mercury and brass scale were 

 maintained at a constant standard temperature. This reduction is known as the reduction 

 for temperature, and combines both the correction for the expansion of the mercury and 

 that for the expansion of the scale, on the assumption that the attached thermometer gives 

 the temperature both of the mercury and of the scale. 



The freezing point of water is universally adopted as the standard temperature of the 

 mercury, to which all readings are to be reduced. The temperature to which the scale is 

 reduced is the normal or standard temperature of the adopted standard of length. For 

 English scales, which depend upon the English yard, this is 62° Fahrenheit. For metric 

 scales, which depend upon the meter, it is 0° centigrade. As thus reduced, observations 

 made with English and metric barometers become perfectly comparable when converted 

 by the ordinary tables or linear conversion, inches to millimeters and millimeters to inches 

 (Tables 13 and 14), for these conversions refer to the meter at 0° centigrade and the 

 English yard at 62° Fahrenheit. 



Professor Marvin * has pointed out the necessity of caution in conversion of metric and 

 English barometer readings. 



Example : 



Attached thermometer, 25.4° C. 

 Barometer reading, 762.15 mm. 



If the temperature is converted to Fahrenheit, 77.7°, and the reading to 30.006 in., the 

 temperature correction according to Table 45 would be —0.133 inch and the reduced 

 reading 29.873. This would be erroneous. The correct conversion is found by taking the 

 correction corresponding to 25.4° C. and 762 mm., i.e., — 3.15 mm., which gives a corrected 

 reading of 759 mm., and converted into inches gives 29.882 which is the correct result. 



Professor Marvin further remarks that circumstances sometimes arise in which a 

 centigrade thermometer may be used to determine the temperature of an English barom- 

 eter, or a Fahrenheit attached thermometer may be used with a metric scale. In all such 

 cases the temperature must be brought into the same system of units as the observed-scale 

 reading before corrections can be applied, and the observed reading must then be 

 corrected for temperature before any conversion can be made. 



With aneroid barometers corrections for temperature and instrumental error must 

 be determined for each instrument. 



The general formula for reducing Fortin-type mercurial barometers with brass scales 

 to the standard temperature is 



C -~ B 1 +„(,_,..) 0) 



where 



C = correction for temperature, 



B = observed height of the barometric column, 



t = temperature of the attached thermometer, 

 hg = standard temperature of the mercury, 

 m = coefficient of expansion of mercury, 



J = coefficient of linear expansion of brass, 

 t, = standard temperature of the scale. 



See below for application to fixed-cistern barometers. 



The accepted determination of the coefficient of expansion of mercury is that given by 

 Broch's reduction of Regnault's experiments 



m = 10-' (181792 + 0.175* -f- 0.035116/') °C.- 1 (2) 



As a sufficiently accurate approximation, the intermediate value tn = 0.0001818 has been 

 adopted uniformly for all temperatures in conformity with the usage of the International 

 Meteorological Tables. 



Various specimens of brass scales made of alloys of different composition show dif- 

 ferences in their coefficients of expansion amounting to 8 and sometimes 10 percent of 

 the total amount. For the sake of uniformity with the International Meteorological 

 Tables, the value / = 0.0000184 has been used in the present volume. 



1 Marvin, C. F., Month. Weath. Rev., vol. 26, p. 302, 1898. 



(Continued) 



SMITHSONIAN METEOROLOGICAL TABLES 



